idx int64 1 56k | question stringlengths 15 155 | answer stringlengths 2 29.2k ⌀ | question_cut stringlengths 15 100 | answer_cut stringlengths 2 200 ⌀ | conversation stringlengths 47 29.3k | conversation_cut stringlengths 47 301 |
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41,801 | Non-trivial bound for $E[\exp(Z^2)]$ when $Z \sim {\rm Bin}(n, n^{-\beta})$ with $\beta \in (0,1)$ | (I will delete my other non-answer, the edit of which had this nugget in it)
No. Asymptotically, the 'trivial' upper bound is the least upper bound. To see this, Let $P_n = P(Z = n)$. Trivially, $E[\exp{(Z^2)}] \ge P_n \exp{(n^2)} = L$, where $L$ is the lower bound of interest. Since $Z$ is binomial, we have $P_n = {n\... | Non-trivial bound for $E[\exp(Z^2)]$ when $Z \sim {\rm Bin}(n, n^{-\beta})$ with $\beta \in (0,1)$ | (I will delete my other non-answer, the edit of which had this nugget in it)
No. Asymptotically, the 'trivial' upper bound is the least upper bound. To see this, Let $P_n = P(Z = n)$. Trivially, $E[\e | Non-trivial bound for $E[\exp(Z^2)]$ when $Z \sim {\rm Bin}(n, n^{-\beta})$ with $\beta \in (0,1)$
(I will delete my other non-answer, the edit of which had this nugget in it)
No. Asymptotically, the 'trivial' upper bound is the least upper bound. To see this, Let $P_n = P(Z = n)$. Trivially, $E[\exp{(Z^2)}] \ge P_n \e... | Non-trivial bound for $E[\exp(Z^2)]$ when $Z \sim {\rm Bin}(n, n^{-\beta})$ with $\beta \in (0,1)$
(I will delete my other non-answer, the edit of which had this nugget in it)
No. Asymptotically, the 'trivial' upper bound is the least upper bound. To see this, Let $P_n = P(Z = n)$. Trivially, $E[\e |
41,802 | Non-trivial bound for $E[\exp(Z^2)]$ when $Z \sim {\rm Bin}(n, n^{-\beta})$ with $\beta \in (0,1)$ | Numerical experiments (for 2 <= n <= 4000 and all values of beta) indicate the estimate n^2 - (n Ln(n))*beta exceeds the logarithm of the expectation by an amount on the order of beta*Exp(-n). The error appears to increase monotonically in beta for each n. This should provide some useful clues about how to proceed (f... | Non-trivial bound for $E[\exp(Z^2)]$ when $Z \sim {\rm Bin}(n, n^{-\beta})$ with $\beta \in (0,1)$ | Numerical experiments (for 2 <= n <= 4000 and all values of beta) indicate the estimate n^2 - (n Ln(n))*beta exceeds the logarithm of the expectation by an amount on the order of beta*Exp(-n). The er | Non-trivial bound for $E[\exp(Z^2)]$ when $Z \sim {\rm Bin}(n, n^{-\beta})$ with $\beta \in (0,1)$
Numerical experiments (for 2 <= n <= 4000 and all values of beta) indicate the estimate n^2 - (n Ln(n))*beta exceeds the logarithm of the expectation by an amount on the order of beta*Exp(-n). The error appears to increa... | Non-trivial bound for $E[\exp(Z^2)]$ when $Z \sim {\rm Bin}(n, n^{-\beta})$ with $\beta \in (0,1)$
Numerical experiments (for 2 <= n <= 4000 and all values of beta) indicate the estimate n^2 - (n Ln(n))*beta exceeds the logarithm of the expectation by an amount on the order of beta*Exp(-n). The er |
41,803 | Non-trivial bound for $E[\exp(Z^2)]$ when $Z \sim {\rm Bin}(n, n^{-\beta})$ with $\beta \in (0,1)$ | This answer is inspired by shabbychef's answer using the median. By definition:
$E[exp(Z^2)] = \sum_{z=1}^{z=n} exp(z^2) P(z;n,n^{-\beta})$
where,
$P(z;n,n^{-\beta})$ is the binomial probability.
Denote the mode of this binomial distribution by: $m(n,n^{-\beta})$. Thus, by definition we have:
$P(z;n,n^{-\beta}) \le P(... | Non-trivial bound for $E[\exp(Z^2)]$ when $Z \sim {\rm Bin}(n, n^{-\beta})$ with $\beta \in (0,1)$ | This answer is inspired by shabbychef's answer using the median. By definition:
$E[exp(Z^2)] = \sum_{z=1}^{z=n} exp(z^2) P(z;n,n^{-\beta})$
where,
$P(z;n,n^{-\beta})$ is the binomial probability.
Den | Non-trivial bound for $E[\exp(Z^2)]$ when $Z \sim {\rm Bin}(n, n^{-\beta})$ with $\beta \in (0,1)$
This answer is inspired by shabbychef's answer using the median. By definition:
$E[exp(Z^2)] = \sum_{z=1}^{z=n} exp(z^2) P(z;n,n^{-\beta})$
where,
$P(z;n,n^{-\beta})$ is the binomial probability.
Denote the mode of this ... | Non-trivial bound for $E[\exp(Z^2)]$ when $Z \sim {\rm Bin}(n, n^{-\beta})$ with $\beta \in (0,1)$
This answer is inspired by shabbychef's answer using the median. By definition:
$E[exp(Z^2)] = \sum_{z=1}^{z=n} exp(z^2) P(z;n,n^{-\beta})$
where,
$P(z;n,n^{-\beta})$ is the binomial probability.
Den |
41,804 | How can I apply a Pareto tail to a truncated distribution? | The following paper describes a couple of approaches for imputing right censored data in the same domain (i.e. topcoded wage data). They use a truncated normal distribution and describe a single imputation model assuming homoscedasticity, and a multiple imputation model assuming heterscedasticity. Also a second paper... | How can I apply a Pareto tail to a truncated distribution? | The following paper describes a couple of approaches for imputing right censored data in the same domain (i.e. topcoded wage data). They use a truncated normal distribution and describe a single impu | How can I apply a Pareto tail to a truncated distribution?
The following paper describes a couple of approaches for imputing right censored data in the same domain (i.e. topcoded wage data). They use a truncated normal distribution and describe a single imputation model assuming homoscedasticity, and a multiple imputa... | How can I apply a Pareto tail to a truncated distribution?
The following paper describes a couple of approaches for imputing right censored data in the same domain (i.e. topcoded wage data). They use a truncated normal distribution and describe a single impu |
41,805 | Nonhomogeneous Poisson and Heavy tail inter arrival time distribution | Well, if you have a point process that you try modeling as a Poisson process, and find it has heavy tails, there are several possibilities. What are the key assumptions for a Poisson Process:
-There is a constant rate function
-Events are memoryless, that is P(E in (t,t+d)) is independent of t and when other events ar... | Nonhomogeneous Poisson and Heavy tail inter arrival time distribution | Well, if you have a point process that you try modeling as a Poisson process, and find it has heavy tails, there are several possibilities. What are the key assumptions for a Poisson Process:
-There | Nonhomogeneous Poisson and Heavy tail inter arrival time distribution
Well, if you have a point process that you try modeling as a Poisson process, and find it has heavy tails, there are several possibilities. What are the key assumptions for a Poisson Process:
-There is a constant rate function
-Events are memoryless... | Nonhomogeneous Poisson and Heavy tail inter arrival time distribution
Well, if you have a point process that you try modeling as a Poisson process, and find it has heavy tails, there are several possibilities. What are the key assumptions for a Poisson Process:
-There |
41,806 | Nonhomogeneous Poisson and Heavy tail inter arrival time distribution | In general there is none. A Poisson process has inter-arrival times that are exponentially distributed, which does not have heavy tails. | Nonhomogeneous Poisson and Heavy tail inter arrival time distribution | In general there is none. A Poisson process has inter-arrival times that are exponentially distributed, which does not have heavy tails. | Nonhomogeneous Poisson and Heavy tail inter arrival time distribution
In general there is none. A Poisson process has inter-arrival times that are exponentially distributed, which does not have heavy tails. | Nonhomogeneous Poisson and Heavy tail inter arrival time distribution
In general there is none. A Poisson process has inter-arrival times that are exponentially distributed, which does not have heavy tails. |
41,807 | Nonhomogeneous Poisson and Heavy tail inter arrival time distribution | The assumption that
Heavy tail distribution for its inter arrival times
along with the assumption that each inter-arrival time is independent, you have a renewal process. There are different ways that a renewal process can have a inhomogeneous marginal rate. Most frequently this is done by stretch time (time-rescali... | Nonhomogeneous Poisson and Heavy tail inter arrival time distribution | The assumption that
Heavy tail distribution for its inter arrival times
along with the assumption that each inter-arrival time is independent, you have a renewal process. There are different ways t | Nonhomogeneous Poisson and Heavy tail inter arrival time distribution
The assumption that
Heavy tail distribution for its inter arrival times
along with the assumption that each inter-arrival time is independent, you have a renewal process. There are different ways that a renewal process can have a inhomogeneous mar... | Nonhomogeneous Poisson and Heavy tail inter arrival time distribution
The assumption that
Heavy tail distribution for its inter arrival times
along with the assumption that each inter-arrival time is independent, you have a renewal process. There are different ways t |
41,808 | statistical comparison of two markov chain transition matrices | The answer by user @krkeane is interesting.
Following is a different kind of answer, which considers the "effective behavior" of the Markov chain transition matrices.
For a given $n$-by-$n$ Markov chain transition matrix, the most important things are:
Does the Stochastic matrix converge? In other words, are the condi... | statistical comparison of two markov chain transition matrices | The answer by user @krkeane is interesting.
Following is a different kind of answer, which considers the "effective behavior" of the Markov chain transition matrices.
For a given $n$-by-$n$ Markov cha | statistical comparison of two markov chain transition matrices
The answer by user @krkeane is interesting.
Following is a different kind of answer, which considers the "effective behavior" of the Markov chain transition matrices.
For a given $n$-by-$n$ Markov chain transition matrix, the most important things are:
Doe... | statistical comparison of two markov chain transition matrices
The answer by user @krkeane is interesting.
Following is a different kind of answer, which considers the "effective behavior" of the Markov chain transition matrices.
For a given $n$-by-$n$ Markov cha |
41,809 | statistical comparison of two markov chain transition matrices | The empirical state transition matrices may be thought of as a collection of (row) histograms of a counting process given an initial state. You could compare the histograms using Kullback-Leibler divergence for the Dirichlet distribution. The row divergences could be combined using estimated state probabilities. This a... | statistical comparison of two markov chain transition matrices | The empirical state transition matrices may be thought of as a collection of (row) histograms of a counting process given an initial state. You could compare the histograms using Kullback-Leibler dive | statistical comparison of two markov chain transition matrices
The empirical state transition matrices may be thought of as a collection of (row) histograms of a counting process given an initial state. You could compare the histograms using Kullback-Leibler divergence for the Dirichlet distribution. The row divergence... | statistical comparison of two markov chain transition matrices
The empirical state transition matrices may be thought of as a collection of (row) histograms of a counting process given an initial state. You could compare the histograms using Kullback-Leibler dive |
41,810 | Is the converse of de Finetti's theorem true? | Finetti's theorem states that you can write an exchangeable multivariate Bernoulli distribution $X_1, X_2, \dots, X_n$ (that can be extended infinitely) as a mixture of multiple identical and independent distributions.
$$P(x_i, x_2, \dots, x_n) = \overbrace{\int_0^1 \underbrace{\sum_{i = 1}^n \theta^{x_i} (1-\theta)^{1... | Is the converse of de Finetti's theorem true? | Finetti's theorem states that you can write an exchangeable multivariate Bernoulli distribution $X_1, X_2, \dots, X_n$ (that can be extended infinitely) as a mixture of multiple identical and independ | Is the converse of de Finetti's theorem true?
Finetti's theorem states that you can write an exchangeable multivariate Bernoulli distribution $X_1, X_2, \dots, X_n$ (that can be extended infinitely) as a mixture of multiple identical and independent distributions.
$$P(x_i, x_2, \dots, x_n) = \overbrace{\int_0^1 \underb... | Is the converse of de Finetti's theorem true?
Finetti's theorem states that you can write an exchangeable multivariate Bernoulli distribution $X_1, X_2, \dots, X_n$ (that can be extended infinitely) as a mixture of multiple identical and independ |
41,811 | Intuition for $RSS_2 - RSS_1$ having chi-square distribution in F-test for linear models | Below we assume we have a model $y=Xb+e$ where the components of vector $e$ are distributed iid $N(0, \sigma^2)$ and that $H$ is the projection matrix onto the range of $X$. Use a subscript of $r$ to denote corresponding quantities of the restricted model and use $\hat{e} = (I-H)y$ to mean the estimated value of the un... | Intuition for $RSS_2 - RSS_1$ having chi-square distribution in F-test for linear models | Below we assume we have a model $y=Xb+e$ where the components of vector $e$ are distributed iid $N(0, \sigma^2)$ and that $H$ is the projection matrix onto the range of $X$. Use a subscript of $r$ to | Intuition for $RSS_2 - RSS_1$ having chi-square distribution in F-test for linear models
Below we assume we have a model $y=Xb+e$ where the components of vector $e$ are distributed iid $N(0, \sigma^2)$ and that $H$ is the projection matrix onto the range of $X$. Use a subscript of $r$ to denote corresponding quantities... | Intuition for $RSS_2 - RSS_1$ having chi-square distribution in F-test for linear models
Below we assume we have a model $y=Xb+e$ where the components of vector $e$ are distributed iid $N(0, \sigma^2)$ and that $H$ is the projection matrix onto the range of $X$. Use a subscript of $r$ to |
41,812 | Intuition for $RSS_2 - RSS_1$ having chi-square distribution in F-test for linear models | Since, there is a sense of ambiguity as to how the 'difference' of residuals of the restricted and unrestricted models leads to the $F$-statistic, it is deemed to be apt enough to briefly sketch the development in a general setting which would provide a better insight.
Theorem $[\rm I]:$ If $\mathbf x\sim \mathsf{MVN}... | Intuition for $RSS_2 - RSS_1$ having chi-square distribution in F-test for linear models | Since, there is a sense of ambiguity as to how the 'difference' of residuals of the restricted and unrestricted models leads to the $F$-statistic, it is deemed to be apt enough to briefly sketch the d | Intuition for $RSS_2 - RSS_1$ having chi-square distribution in F-test for linear models
Since, there is a sense of ambiguity as to how the 'difference' of residuals of the restricted and unrestricted models leads to the $F$-statistic, it is deemed to be apt enough to briefly sketch the development in a general setting... | Intuition for $RSS_2 - RSS_1$ having chi-square distribution in F-test for linear models
Since, there is a sense of ambiguity as to how the 'difference' of residuals of the restricted and unrestricted models leads to the $F$-statistic, it is deemed to be apt enough to briefly sketch the d |
41,813 | Expectation of truncated distribution | There are many ways to analyze this. The methods shown in this answer are chosen for their usefulness and helpfulness in understanding expectations and conditional expectations. That is, it is hoped the journey to the result will be more interesting than the result itself.
Because "$\mid Y$" occurs everywhere, let's... | Expectation of truncated distribution | There are many ways to analyze this. The methods shown in this answer are chosen for their usefulness and helpfulness in understanding expectations and conditional expectations. That is, it is hoped | Expectation of truncated distribution
There are many ways to analyze this. The methods shown in this answer are chosen for their usefulness and helpfulness in understanding expectations and conditional expectations. That is, it is hoped the journey to the result will be more interesting than the result itself.
Becau... | Expectation of truncated distribution
There are many ways to analyze this. The methods shown in this answer are chosen for their usefulness and helpfulness in understanding expectations and conditional expectations. That is, it is hoped |
41,814 | Expectation of truncated distribution | Using the law of total probability and $E_{p(x|x<a, y)} \leq a \leq E_{p(x|x\geq a, y)}$, we have
\begin{align*}
E_{p(x|y)}x
&= p(x\geq a) E_{p(x|x\geq a, y)}x + p(x<a) E_{p(x|x<a, y)}x
\\&\leq p(x\geq a) E_{p(x|x\geq a, y)}x + p(x<a) E_{p(x|x\geq a, y)}x
\\&= (p(x\geq a)+p(x<a)) E_{p(x|x\geq a, y)}x
\\&= E_{p(x|x\geq ... | Expectation of truncated distribution | Using the law of total probability and $E_{p(x|x<a, y)} \leq a \leq E_{p(x|x\geq a, y)}$, we have
\begin{align*}
E_{p(x|y)}x
&= p(x\geq a) E_{p(x|x\geq a, y)}x + p(x<a) E_{p(x|x<a, y)}x
\\&\leq p(x\ge | Expectation of truncated distribution
Using the law of total probability and $E_{p(x|x<a, y)} \leq a \leq E_{p(x|x\geq a, y)}$, we have
\begin{align*}
E_{p(x|y)}x
&= p(x\geq a) E_{p(x|x\geq a, y)}x + p(x<a) E_{p(x|x<a, y)}x
\\&\leq p(x\geq a) E_{p(x|x\geq a, y)}x + p(x<a) E_{p(x|x\geq a, y)}x
\\&= (p(x\geq a)+p(x<a)) E... | Expectation of truncated distribution
Using the law of total probability and $E_{p(x|x<a, y)} \leq a \leq E_{p(x|x\geq a, y)}$, we have
\begin{align*}
E_{p(x|y)}x
&= p(x\geq a) E_{p(x|x\geq a, y)}x + p(x<a) E_{p(x|x<a, y)}x
\\&\leq p(x\ge |
41,815 | Sufficient condition for when a shifted likelihood function shifts the posterior expected value in the same direction | Here's a very restrictive sufficient condition: both the prior and likelihood are normal.
If the likelihood is normal with known variance $\sigma^2$, and the prior is normal, then the posterior is normal. Say the likelihood is normal centred on $z$ with variance $\sigma^2$, and the prior has mean $\mu_0$ and variance $... | Sufficient condition for when a shifted likelihood function shifts the posterior expected value in t | Here's a very restrictive sufficient condition: both the prior and likelihood are normal.
If the likelihood is normal with known variance $\sigma^2$, and the prior is normal, then the posterior is nor | Sufficient condition for when a shifted likelihood function shifts the posterior expected value in the same direction
Here's a very restrictive sufficient condition: both the prior and likelihood are normal.
If the likelihood is normal with known variance $\sigma^2$, and the prior is normal, then the posterior is norma... | Sufficient condition for when a shifted likelihood function shifts the posterior expected value in t
Here's a very restrictive sufficient condition: both the prior and likelihood are normal.
If the likelihood is normal with known variance $\sigma^2$, and the prior is normal, then the posterior is nor |
41,816 | Sufficient condition for when a shifted likelihood function shifts the posterior expected value in the same direction | It works for all priors in the case that $ \mathcal L $ is normal. The key property is that $ \mathcal L'(\theta) = -\theta \mathcal L(\theta) $.
To see this, start with expressing the expectation under the two hypotheses as
$$ \mathbb E[\theta \mid D] = \frac{\mathbb E[\theta \mathcal L_D(\theta)]}{\mathbb E[\mathcal ... | Sufficient condition for when a shifted likelihood function shifts the posterior expected value in t | It works for all priors in the case that $ \mathcal L $ is normal. The key property is that $ \mathcal L'(\theta) = -\theta \mathcal L(\theta) $.
To see this, start with expressing the expectation und | Sufficient condition for when a shifted likelihood function shifts the posterior expected value in the same direction
It works for all priors in the case that $ \mathcal L $ is normal. The key property is that $ \mathcal L'(\theta) = -\theta \mathcal L(\theta) $.
To see this, start with expressing the expectation under... | Sufficient condition for when a shifted likelihood function shifts the posterior expected value in t
It works for all priors in the case that $ \mathcal L $ is normal. The key property is that $ \mathcal L'(\theta) = -\theta \mathcal L(\theta) $.
To see this, start with expressing the expectation und |
41,817 | Sufficient condition for when a shifted likelihood function shifts the posterior expected value in the same direction | Thanks to everyone who contributed. Here are some results I've been able to find in the literature.
The strongest result is that the property holds for any prior when the likelihood function arises from a strongly unimodally distributed observation.
Andrews et al. 1972 (Biometrika, Vol. 59, No. 3 (Dec., 1972), pp. 693-... | Sufficient condition for when a shifted likelihood function shifts the posterior expected value in t | Thanks to everyone who contributed. Here are some results I've been able to find in the literature.
The strongest result is that the property holds for any prior when the likelihood function arises fr | Sufficient condition for when a shifted likelihood function shifts the posterior expected value in the same direction
Thanks to everyone who contributed. Here are some results I've been able to find in the literature.
The strongest result is that the property holds for any prior when the likelihood function arises from... | Sufficient condition for when a shifted likelihood function shifts the posterior expected value in t
Thanks to everyone who contributed. Here are some results I've been able to find in the literature.
The strongest result is that the property holds for any prior when the likelihood function arises fr |
41,818 | Inferring Causal Direction | Causal direction, or causal discovery from data is a large research topic. Causal Discovery Algorithms notebook of Cosma Shalizi given a nice list of approaches. However, one has to distinguish, structure discovery i.e., causal graphs as a separate task than only discovering directions.
A nice overview of, Answering c... | Inferring Causal Direction | Causal direction, or causal discovery from data is a large research topic. Causal Discovery Algorithms notebook of Cosma Shalizi given a nice list of approaches. However, one has to distinguish, stru | Inferring Causal Direction
Causal direction, or causal discovery from data is a large research topic. Causal Discovery Algorithms notebook of Cosma Shalizi given a nice list of approaches. However, one has to distinguish, structure discovery i.e., causal graphs as a separate task than only discovering directions.
A ni... | Inferring Causal Direction
Causal direction, or causal discovery from data is a large research topic. Causal Discovery Algorithms notebook of Cosma Shalizi given a nice list of approaches. However, one has to distinguish, stru |
41,819 | Inferring Causal Direction | It's tricky to answer this question because you'd have to be much clearer on what you mean by I am already convinced that there is a causal relationship between the two, but let's assume God came down to earth and told you that there is a causal relationship between A and B. In this case, because it's time-series data,... | Inferring Causal Direction | It's tricky to answer this question because you'd have to be much clearer on what you mean by I am already convinced that there is a causal relationship between the two, but let's assume God came down | Inferring Causal Direction
It's tricky to answer this question because you'd have to be much clearer on what you mean by I am already convinced that there is a causal relationship between the two, but let's assume God came down to earth and told you that there is a causal relationship between A and B. In this case, bec... | Inferring Causal Direction
It's tricky to answer this question because you'd have to be much clearer on what you mean by I am already convinced that there is a causal relationship between the two, but let's assume God came down |
41,820 | Inferring Causal Direction | Up front, please node that you always have to consider the possibility of latent confounders. Those lead to two random variables being stochastically dependent without causal dependency. They are not measured (that's why they are called latent or sometimes hidden), but are almost always present and usually screw up you... | Inferring Causal Direction | Up front, please node that you always have to consider the possibility of latent confounders. Those lead to two random variables being stochastically dependent without causal dependency. They are not | Inferring Causal Direction
Up front, please node that you always have to consider the possibility of latent confounders. Those lead to two random variables being stochastically dependent without causal dependency. They are not measured (that's why they are called latent or sometimes hidden), but are almost always prese... | Inferring Causal Direction
Up front, please node that you always have to consider the possibility of latent confounders. Those lead to two random variables being stochastically dependent without causal dependency. They are not |
41,821 | Why do we need identification in causal inference? | In causal inference you can think about identifiability as the condition that permit to measure causal quantity from observed data. Among parametric models is the condition that permit to estimate causal parameters from regressional. Formally
$E[Y|do(X)] = E[Y|X] $
Can be consider as identifiability condition.
Identifi... | Why do we need identification in causal inference? | In causal inference you can think about identifiability as the condition that permit to measure causal quantity from observed data. Among parametric models is the condition that permit to estimate cau | Why do we need identification in causal inference?
In causal inference you can think about identifiability as the condition that permit to measure causal quantity from observed data. Among parametric models is the condition that permit to estimate causal parameters from regressional. Formally
$E[Y|do(X)] = E[Y|X] $
Can... | Why do we need identification in causal inference?
In causal inference you can think about identifiability as the condition that permit to measure causal quantity from observed data. Among parametric models is the condition that permit to estimate cau |
41,822 | Why do we need identification in causal inference? | Let's say you have a Treatment variable, an Outcome variable and numerous other variables. One could do a regression of one on the other, adjusting by everything else, but we're smarter than this, right? How do we know this measures the direct relationship between treatment and outcome? Maybe we're not adjusting for an... | Why do we need identification in causal inference? | Let's say you have a Treatment variable, an Outcome variable and numerous other variables. One could do a regression of one on the other, adjusting by everything else, but we're smarter than this, rig | Why do we need identification in causal inference?
Let's say you have a Treatment variable, an Outcome variable and numerous other variables. One could do a regression of one on the other, adjusting by everything else, but we're smarter than this, right? How do we know this measures the direct relationship between trea... | Why do we need identification in causal inference?
Let's say you have a Treatment variable, an Outcome variable and numerous other variables. One could do a regression of one on the other, adjusting by everything else, but we're smarter than this, rig |
41,823 | Why do we need identification in causal inference? | This is my understanding. Correct me if I am wrong.
Suppose I am conducting a randomized clinical trial to investigate the difference in means between two treatments, A and B. If I randomize everyone to treatment B with probability 1 then the population mean for treatment A and the difference in means are both uniden... | Why do we need identification in causal inference? | This is my understanding. Correct me if I am wrong.
Suppose I am conducting a randomized clinical trial to investigate the difference in means between two treatments, A and B. If I randomize everyon | Why do we need identification in causal inference?
This is my understanding. Correct me if I am wrong.
Suppose I am conducting a randomized clinical trial to investigate the difference in means between two treatments, A and B. If I randomize everyone to treatment B with probability 1 then the population mean for trea... | Why do we need identification in causal inference?
This is my understanding. Correct me if I am wrong.
Suppose I am conducting a randomized clinical trial to investigate the difference in means between two treatments, A and B. If I randomize everyon |
41,824 | What is the role of 'shuffle' in train_test_split()? | With time-series data, where you can expect auto-correlation in the data you should not split the data randomly to train and test set, but you should rather split it on time so you train on past values to predict future. Scikit-learn has the TimeSeriesSplit functionality for this.
The shuffle parameter is needed to pre... | What is the role of 'shuffle' in train_test_split()? | With time-series data, where you can expect auto-correlation in the data you should not split the data randomly to train and test set, but you should rather split it on time so you train on past value | What is the role of 'shuffle' in train_test_split()?
With time-series data, where you can expect auto-correlation in the data you should not split the data randomly to train and test set, but you should rather split it on time so you train on past values to predict future. Scikit-learn has the TimeSeriesSplit functiona... | What is the role of 'shuffle' in train_test_split()?
With time-series data, where you can expect auto-correlation in the data you should not split the data randomly to train and test set, but you should rather split it on time so you train on past value |
41,825 | What is the role of 'shuffle' in train_test_split()? | Omitting shuffle on a time-sorted DataFrame would lead to a time-based bias where similar periods are in the same dataset. By toggling shuffle=True you make sure that that the data is mixed prior to creation of test/train datasets. | What is the role of 'shuffle' in train_test_split()? | Omitting shuffle on a time-sorted DataFrame would lead to a time-based bias where similar periods are in the same dataset. By toggling shuffle=True you make sure that that the data is mixed prior to c | What is the role of 'shuffle' in train_test_split()?
Omitting shuffle on a time-sorted DataFrame would lead to a time-based bias where similar periods are in the same dataset. By toggling shuffle=True you make sure that that the data is mixed prior to creation of test/train datasets. | What is the role of 'shuffle' in train_test_split()?
Omitting shuffle on a time-sorted DataFrame would lead to a time-based bias where similar periods are in the same dataset. By toggling shuffle=True you make sure that that the data is mixed prior to c |
41,826 | Intutition of why Bootstrap aggregating reduces overfitting? | This is a phenomenon so called weak learners (see) in an ensemble decision yields a good performance. The reason of this explained by Dietterich here:
Uncorrelated errors made by the
individual classifiers can be
removed by voting.
Further explanation or theoretical justification of the statement could be an open res... | Intutition of why Bootstrap aggregating reduces overfitting? | This is a phenomenon so called weak learners (see) in an ensemble decision yields a good performance. The reason of this explained by Dietterich here:
Uncorrelated errors made by the
individual class | Intutition of why Bootstrap aggregating reduces overfitting?
This is a phenomenon so called weak learners (see) in an ensemble decision yields a good performance. The reason of this explained by Dietterich here:
Uncorrelated errors made by the
individual classifiers can be
removed by voting.
Further explanation or th... | Intutition of why Bootstrap aggregating reduces overfitting?
This is a phenomenon so called weak learners (see) in an ensemble decision yields a good performance. The reason of this explained by Dietterich here:
Uncorrelated errors made by the
individual class |
41,827 | Intutition of why Bootstrap aggregating reduces overfitting? | In order to illustrate why averaging reduce the standard deviation and make prediction more accurate i'll give an example.
Let's suppose that we have two models. The predictions are random variables $X_1 \sim N(\mu, \sigma), X_2 \sim N(\mu, \sigma)$
i.e. the prediction has a mean value plus an error term.
Considering t... | Intutition of why Bootstrap aggregating reduces overfitting? | In order to illustrate why averaging reduce the standard deviation and make prediction more accurate i'll give an example.
Let's suppose that we have two models. The predictions are random variables $ | Intutition of why Bootstrap aggregating reduces overfitting?
In order to illustrate why averaging reduce the standard deviation and make prediction more accurate i'll give an example.
Let's suppose that we have two models. The predictions are random variables $X_1 \sim N(\mu, \sigma), X_2 \sim N(\mu, \sigma)$
i.e. the ... | Intutition of why Bootstrap aggregating reduces overfitting?
In order to illustrate why averaging reduce the standard deviation and make prediction more accurate i'll give an example.
Let's suppose that we have two models. The predictions are random variables $ |
41,828 | How much of neural network overconfidence in predictions can be attributed to modelers optimizing threshold-based metrics? | "If neural networks are optimizing a proper scoring rule like cross-entropy loss, how can this be?"
This is likely to be traditional over-fitting of the training data. A deep neural network can implement any mapping that a radial basis function neural network can implement (they are both universal aproximators). Cons... | How much of neural network overconfidence in predictions can be attributed to modelers optimizing th | "If neural networks are optimizing a proper scoring rule like cross-entropy loss, how can this be?"
This is likely to be traditional over-fitting of the training data. A deep neural network can imple | How much of neural network overconfidence in predictions can be attributed to modelers optimizing threshold-based metrics?
"If neural networks are optimizing a proper scoring rule like cross-entropy loss, how can this be?"
This is likely to be traditional over-fitting of the training data. A deep neural network can im... | How much of neural network overconfidence in predictions can be attributed to modelers optimizing th
"If neural networks are optimizing a proper scoring rule like cross-entropy loss, how can this be?"
This is likely to be traditional over-fitting of the training data. A deep neural network can imple |
41,829 | How much of neural network overconfidence in predictions can be attributed to modelers optimizing threshold-based metrics? | There are some interesting properties about cross entropy loss (well, even logistic loss).
Not only we want to classify the instance correctly, we want strong options
Please check following example, note, weakly and correctly classifying one data point is almost as bad ad wrongly classifying the point.
import numpy a... | How much of neural network overconfidence in predictions can be attributed to modelers optimizing th | There are some interesting properties about cross entropy loss (well, even logistic loss).
Not only we want to classify the instance correctly, we want strong options
Please check following example, n | How much of neural network overconfidence in predictions can be attributed to modelers optimizing threshold-based metrics?
There are some interesting properties about cross entropy loss (well, even logistic loss).
Not only we want to classify the instance correctly, we want strong options
Please check following example... | How much of neural network overconfidence in predictions can be attributed to modelers optimizing th
There are some interesting properties about cross entropy loss (well, even logistic loss).
Not only we want to classify the instance correctly, we want strong options
Please check following example, n |
41,830 | variance estimation using order statistics | If you know the sample size (as opposed to just knowing that the sample size is between 50 and 200), then maximum likelihood might work in this case. Using Mathematica:
(* Joint distribution of largest 4 order statistics from a sample size of 100 *)
dist = OrderDistribution[{NormalDistribution[0, \[Sigma]], 100}, {97,... | variance estimation using order statistics | If you know the sample size (as opposed to just knowing that the sample size is between 50 and 200), then maximum likelihood might work in this case. Using Mathematica:
(* Joint distribution of large | variance estimation using order statistics
If you know the sample size (as opposed to just knowing that the sample size is between 50 and 200), then maximum likelihood might work in this case. Using Mathematica:
(* Joint distribution of largest 4 order statistics from a sample size of 100 *)
dist = OrderDistribution[{... | variance estimation using order statistics
If you know the sample size (as opposed to just knowing that the sample size is between 50 and 200), then maximum likelihood might work in this case. Using Mathematica:
(* Joint distribution of large |
41,831 | variance estimation using order statistics | Comment: This the germ of an idea, not yet a solution. [I am assuming the mean $\mu$ is also unknown.]
Suppose $n = 100$ observations from a standard normal distribution.
You might find the distance $D$ between order statistics 97 and 100.
Then $1/D$ should estimate $1.$ Several runs give various answers. In R,
set.see... | variance estimation using order statistics | Comment: This the germ of an idea, not yet a solution. [I am assuming the mean $\mu$ is also unknown.]
Suppose $n = 100$ observations from a standard normal distribution.
You might find the distance $ | variance estimation using order statistics
Comment: This the germ of an idea, not yet a solution. [I am assuming the mean $\mu$ is also unknown.]
Suppose $n = 100$ observations from a standard normal distribution.
You might find the distance $D$ between order statistics 97 and 100.
Then $1/D$ should estimate $1.$ Sever... | variance estimation using order statistics
Comment: This the germ of an idea, not yet a solution. [I am assuming the mean $\mu$ is also unknown.]
Suppose $n = 100$ observations from a standard normal distribution.
You might find the distance $ |
41,832 | Basis dimension (k) too low for the smooth term in a GAMM | It's not a huge problem in your case.
The best I can find on it is p.330-331 of this guide by Simon Wood.
Because the edf is way below the basis dimension I don't see it as a problem (quote from Wood on page 331: "The...test still gives a low p-value, but since the edf is...below the basis dimension, and increasing the... | Basis dimension (k) too low for the smooth term in a GAMM | It's not a huge problem in your case.
The best I can find on it is p.330-331 of this guide by Simon Wood.
Because the edf is way below the basis dimension I don't see it as a problem (quote from Wood | Basis dimension (k) too low for the smooth term in a GAMM
It's not a huge problem in your case.
The best I can find on it is p.330-331 of this guide by Simon Wood.
Because the edf is way below the basis dimension I don't see it as a problem (quote from Wood on page 331: "The...test still gives a low p-value, but since ... | Basis dimension (k) too low for the smooth term in a GAMM
It's not a huge problem in your case.
The best I can find on it is p.330-331 of this guide by Simon Wood.
Because the edf is way below the basis dimension I don't see it as a problem (quote from Wood |
41,833 | What is the distribution of time's to ruin in the gambler's ruin problem (random walk)? | Time-to-ruin in the discrete-time random walk: From your question, I take it that you are referring to a discrete-time version of the gambler's ruin problem. Without loss of generality we can consider the wealth of the gambler denominated in units equivalent to the betting amount. We will assume that the wealth of th... | What is the distribution of time's to ruin in the gambler's ruin problem (random walk)? | Time-to-ruin in the discrete-time random walk: From your question, I take it that you are referring to a discrete-time version of the gambler's ruin problem. Without loss of generality we can conside | What is the distribution of time's to ruin in the gambler's ruin problem (random walk)?
Time-to-ruin in the discrete-time random walk: From your question, I take it that you are referring to a discrete-time version of the gambler's ruin problem. Without loss of generality we can consider the wealth of the gambler deno... | What is the distribution of time's to ruin in the gambler's ruin problem (random walk)?
Time-to-ruin in the discrete-time random walk: From your question, I take it that you are referring to a discrete-time version of the gambler's ruin problem. Without loss of generality we can conside |
41,834 | What is the distribution of time's to ruin in the gambler's ruin problem (random walk)? | Say your starting wealth is $W(0) = 6$ and we take 20 steps of the random walk, where a gambler has fifty-fifty probability to loose or win 1, then probability distribution for wealth looks like a (scaled and shifted) binomial distribution.
Obviously the cases with $W(20) \leq 0$ have gone bankrupt. But the amount of ... | What is the distribution of time's to ruin in the gambler's ruin problem (random walk)? | Say your starting wealth is $W(0) = 6$ and we take 20 steps of the random walk, where a gambler has fifty-fifty probability to loose or win 1, then probability distribution for wealth looks like a (sc | What is the distribution of time's to ruin in the gambler's ruin problem (random walk)?
Say your starting wealth is $W(0) = 6$ and we take 20 steps of the random walk, where a gambler has fifty-fifty probability to loose or win 1, then probability distribution for wealth looks like a (scaled and shifted) binomial distr... | What is the distribution of time's to ruin in the gambler's ruin problem (random walk)?
Say your starting wealth is $W(0) = 6$ and we take 20 steps of the random walk, where a gambler has fifty-fifty probability to loose or win 1, then probability distribution for wealth looks like a (sc |
41,835 | What is the name of this metric? | No, there is not, at least according to what I could find in Google and Wikipedia.
I would argue that, while that can be an interesting metric to characterize errors, it does not convey any new information that the habitual metrics didn't already. | What is the name of this metric? | No, there is not, at least according to what I could find in Google and Wikipedia.
I would argue that, while that can be an interesting metric to characterize errors, it does not convey any new inform | What is the name of this metric?
No, there is not, at least according to what I could find in Google and Wikipedia.
I would argue that, while that can be an interesting metric to characterize errors, it does not convey any new information that the habitual metrics didn't already. | What is the name of this metric?
No, there is not, at least according to what I could find in Google and Wikipedia.
I would argue that, while that can be an interesting metric to characterize errors, it does not convey any new inform |
41,836 | What is the name of this metric? | I once (can't remember when or where) saw a journal article in which authors called it "harmfulness". In that article FP was "worse kind of error" than FN (it had something to do with amputations). So FP/(FP+FN) was measuring how harmfull a diagnostic method is when it actually "makes" a mistake. | What is the name of this metric? | I once (can't remember when or where) saw a journal article in which authors called it "harmfulness". In that article FP was "worse kind of error" than FN (it had something to do with amputations). So | What is the name of this metric?
I once (can't remember when or where) saw a journal article in which authors called it "harmfulness". In that article FP was "worse kind of error" than FN (it had something to do with amputations). So FP/(FP+FN) was measuring how harmfull a diagnostic method is when it actually "makes" ... | What is the name of this metric?
I once (can't remember when or where) saw a journal article in which authors called it "harmfulness". In that article FP was "worse kind of error" than FN (it had something to do with amputations). So |
41,837 | Causal Bayesian network, causal diagram, structural causal model and marginal structural model: what do they exactly mean? | I will give my answer based on Pearl's other book (Causality)
First, some terminology: there are 3 types of queries: observational, interventional, and counterfactual.
For observational queries, you only need a joint distribution
For interventional queries, you also need a directed graph (e.g. a Bayesian Network(BN), ... | Causal Bayesian network, causal diagram, structural causal model and marginal structural model: what | I will give my answer based on Pearl's other book (Causality)
First, some terminology: there are 3 types of queries: observational, interventional, and counterfactual.
For observational queries, you | Causal Bayesian network, causal diagram, structural causal model and marginal structural model: what do they exactly mean?
I will give my answer based on Pearl's other book (Causality)
First, some terminology: there are 3 types of queries: observational, interventional, and counterfactual.
For observational queries, y... | Causal Bayesian network, causal diagram, structural causal model and marginal structural model: what
I will give my answer based on Pearl's other book (Causality)
First, some terminology: there are 3 types of queries: observational, interventional, and counterfactual.
For observational queries, you |
41,838 | Regression With Uncertainty/Range In Target Variable | This can be modeled as interval censored data. Most references you will find on interval censoring are in the survival time context, but the same techniques apply to any measurement that is censored. The survival package in R has the required methods for this. I suggest the accelerated failure model.
E.g.
N <- 100
s... | Regression With Uncertainty/Range In Target Variable | This can be modeled as interval censored data. Most references you will find on interval censoring are in the survival time context, but the same techniques apply to any measurement that is censored. | Regression With Uncertainty/Range In Target Variable
This can be modeled as interval censored data. Most references you will find on interval censoring are in the survival time context, but the same techniques apply to any measurement that is censored. The survival package in R has the required methods for this. I s... | Regression With Uncertainty/Range In Target Variable
This can be modeled as interval censored data. Most references you will find on interval censoring are in the survival time context, but the same techniques apply to any measurement that is censored. |
41,839 | When a classifier predicting probability should be calibrated? | There are several possible scenarios when one would think about calibrating probabilities:
The model is misspecified or not optimally trained. That will be the case when non-linear relationships are modeled with a linear learner; or model is too rigid due to excessive regularization (model underfits); or to the contra... | When a classifier predicting probability should be calibrated? | There are several possible scenarios when one would think about calibrating probabilities:
The model is misspecified or not optimally trained. That will be the case when non-linear relationships are | When a classifier predicting probability should be calibrated?
There are several possible scenarios when one would think about calibrating probabilities:
The model is misspecified or not optimally trained. That will be the case when non-linear relationships are modeled with a linear learner; or model is too rigid due ... | When a classifier predicting probability should be calibrated?
There are several possible scenarios when one would think about calibrating probabilities:
The model is misspecified or not optimally trained. That will be the case when non-linear relationships are |
41,840 | Can I scale and then interpret shap values as percent contribution to the prediction? | Almost yes. There are a few caveats regarding directly interpreting the scaled SHAP values, as the percentage contributions of our final classification prediction for a single observation.
Raw SHAP values for classification tasks are often shown as additive contribution in the log-odds domain. That means that it is no... | Can I scale and then interpret shap values as percent contribution to the prediction? | Almost yes. There are a few caveats regarding directly interpreting the scaled SHAP values, as the percentage contributions of our final classification prediction for a single observation.
Raw SHAP v | Can I scale and then interpret shap values as percent contribution to the prediction?
Almost yes. There are a few caveats regarding directly interpreting the scaled SHAP values, as the percentage contributions of our final classification prediction for a single observation.
Raw SHAP values for classification tasks are... | Can I scale and then interpret shap values as percent contribution to the prediction?
Almost yes. There are a few caveats regarding directly interpreting the scaled SHAP values, as the percentage contributions of our final classification prediction for a single observation.
Raw SHAP v |
41,841 | Sampling uniformly from the set of partitions of a set? | The "appropriate exponential distribution" for the number of bins $K$ is not exponential by any means. It actually is the discrete distribution of parameter $n$ given by
$$\Pr(K=k)\ \propto\ \frac{k^n}{k!}\tag{1.4}$$
for $k=1, 2, \ldots.$
In the original paper, A. J. Stam argued as follows. When a partition $\pi$ co... | Sampling uniformly from the set of partitions of a set? | The "appropriate exponential distribution" for the number of bins $K$ is not exponential by any means. It actually is the discrete distribution of parameter $n$ given by
$$\Pr(K=k)\ \propto\ \frac{k^ | Sampling uniformly from the set of partitions of a set?
The "appropriate exponential distribution" for the number of bins $K$ is not exponential by any means. It actually is the discrete distribution of parameter $n$ given by
$$\Pr(K=k)\ \propto\ \frac{k^n}{k!}\tag{1.4}$$
for $k=1, 2, \ldots.$
In the original paper, ... | Sampling uniformly from the set of partitions of a set?
The "appropriate exponential distribution" for the number of bins $K$ is not exponential by any means. It actually is the discrete distribution of parameter $n$ given by
$$\Pr(K=k)\ \propto\ \frac{k^ |
41,842 | What's the DGP in causal inference? | The Data Generating Process interpretation is matter of debate. For examples read here: What is a 'true' model? and What does a data-generating process (DGP) actually mean?
If we want make causal inference properly we have to intend the DGP as in Pearl literature, then his properties are encoded in a Pearl Structural C... | What's the DGP in causal inference? | The Data Generating Process interpretation is matter of debate. For examples read here: What is a 'true' model? and What does a data-generating process (DGP) actually mean?
If we want make causal infe | What's the DGP in causal inference?
The Data Generating Process interpretation is matter of debate. For examples read here: What is a 'true' model? and What does a data-generating process (DGP) actually mean?
If we want make causal inference properly we have to intend the DGP as in Pearl literature, then his properties... | What's the DGP in causal inference?
The Data Generating Process interpretation is matter of debate. For examples read here: What is a 'true' model? and What does a data-generating process (DGP) actually mean?
If we want make causal infe |
41,843 | Does it make sense to regularize the loss function for binary/multi-class classification? | Depending on what you are trying to do with your CNN, regularization may indeed make sense. Pruning your network by regularization to make it sparse has two main advantages:
It simplifies the network, making training and computation faster and easier;
It prevents overfitting, and allows to make sure your network will ... | Does it make sense to regularize the loss function for binary/multi-class classification? | Depending on what you are trying to do with your CNN, regularization may indeed make sense. Pruning your network by regularization to make it sparse has two main advantages:
It simplifies the network | Does it make sense to regularize the loss function for binary/multi-class classification?
Depending on what you are trying to do with your CNN, regularization may indeed make sense. Pruning your network by regularization to make it sparse has two main advantages:
It simplifies the network, making training and computat... | Does it make sense to regularize the loss function for binary/multi-class classification?
Depending on what you are trying to do with your CNN, regularization may indeed make sense. Pruning your network by regularization to make it sparse has two main advantages:
It simplifies the network |
41,844 | What is the name of this quantity? | This is a measure of squared dispersion between two sets of values but not between paired values. I doubt it has a name.
Indeed you do not need to have the same number of $x$ and $y$ values, and using the $\frac1n$ calculation of variance, you can say:
$$\frac{1}{mn}\sum_{i=1}^m\sum_{j=1}^n(x_i-y_j)^2\qquad \\\qquad\qq... | What is the name of this quantity? | This is a measure of squared dispersion between two sets of values but not between paired values. I doubt it has a name.
Indeed you do not need to have the same number of $x$ and $y$ values, and using | What is the name of this quantity?
This is a measure of squared dispersion between two sets of values but not between paired values. I doubt it has a name.
Indeed you do not need to have the same number of $x$ and $y$ values, and using the $\frac1n$ calculation of variance, you can say:
$$\frac{1}{mn}\sum_{i=1}^m\sum_{... | What is the name of this quantity?
This is a measure of squared dispersion between two sets of values but not between paired values. I doubt it has a name.
Indeed you do not need to have the same number of $x$ and $y$ values, and using |
41,845 | Gelman & Hill's 'no', 'complete' and 'partial' pooling in the context of longitudinal data | It's helpful to start with the equation of the multilevel model, which applies whether the data is cross-sectional (multilevel) or person-period (longitudinal):
At level 1 (within cluster): $y_{ij} = \beta_{0j} + e_{ij}, e_{ij}\sim N(0, \sigma_e^2)$
and at level 2 (between cluster): $\beta_{0j} = \gamma_{00} + u_{0j},... | Gelman & Hill's 'no', 'complete' and 'partial' pooling in the context of longitudinal data | It's helpful to start with the equation of the multilevel model, which applies whether the data is cross-sectional (multilevel) or person-period (longitudinal):
At level 1 (within cluster): $y_{ij} = | Gelman & Hill's 'no', 'complete' and 'partial' pooling in the context of longitudinal data
It's helpful to start with the equation of the multilevel model, which applies whether the data is cross-sectional (multilevel) or person-period (longitudinal):
At level 1 (within cluster): $y_{ij} = \beta_{0j} + e_{ij}, e_{ij}\... | Gelman & Hill's 'no', 'complete' and 'partial' pooling in the context of longitudinal data
It's helpful to start with the equation of the multilevel model, which applies whether the data is cross-sectional (multilevel) or person-period (longitudinal):
At level 1 (within cluster): $y_{ij} = |
41,846 | Why are my bootstrap confidence intervals for regression coefficients consistently wider than standard confidence intervals? | You always have to be careful about how closely your data fit the underlying assumptions of the model. In your linear regression, the severe heteroscedasticity and occasional large outliers, with most of the highest-magnitude outliers tending to be positive rather than negative, probably play the biggest part in the (r... | Why are my bootstrap confidence intervals for regression coefficients consistently wider than standa | You always have to be careful about how closely your data fit the underlying assumptions of the model. In your linear regression, the severe heteroscedasticity and occasional large outliers, with most | Why are my bootstrap confidence intervals for regression coefficients consistently wider than standard confidence intervals?
You always have to be careful about how closely your data fit the underlying assumptions of the model. In your linear regression, the severe heteroscedasticity and occasional large outliers, with... | Why are my bootstrap confidence intervals for regression coefficients consistently wider than standa
You always have to be careful about how closely your data fit the underlying assumptions of the model. In your linear regression, the severe heteroscedasticity and occasional large outliers, with most |
41,847 | Why are my bootstrap confidence intervals for regression coefficients consistently wider than standard confidence intervals? | This can happen when your data are not independent but instead have some dependence structure. For example, consider homes from across the country with some being in large expensive cities while some are in more affordable small towns. Homes in the same locale are likely to have similar prices and to have prices vary s... | Why are my bootstrap confidence intervals for regression coefficients consistently wider than standa | This can happen when your data are not independent but instead have some dependence structure. For example, consider homes from across the country with some being in large expensive cities while some | Why are my bootstrap confidence intervals for regression coefficients consistently wider than standard confidence intervals?
This can happen when your data are not independent but instead have some dependence structure. For example, consider homes from across the country with some being in large expensive cities while ... | Why are my bootstrap confidence intervals for regression coefficients consistently wider than standa
This can happen when your data are not independent but instead have some dependence structure. For example, consider homes from across the country with some being in large expensive cities while some |
41,848 | Why are my bootstrap confidence intervals for regression coefficients consistently wider than standard confidence intervals? | CI from OLS assume normal distribution of coefficient estimators. When using bootstrap you are characterizing the empirical distribution of coefficient estimators (which could be non-normal). Hence if there exist some deviations of OLS assumptions (conditional normality, homoscedasticity and independent observations), ... | Why are my bootstrap confidence intervals for regression coefficients consistently wider than standa | CI from OLS assume normal distribution of coefficient estimators. When using bootstrap you are characterizing the empirical distribution of coefficient estimators (which could be non-normal). Hence if | Why are my bootstrap confidence intervals for regression coefficients consistently wider than standard confidence intervals?
CI from OLS assume normal distribution of coefficient estimators. When using bootstrap you are characterizing the empirical distribution of coefficient estimators (which could be non-normal). Hen... | Why are my bootstrap confidence intervals for regression coefficients consistently wider than standa
CI from OLS assume normal distribution of coefficient estimators. When using bootstrap you are characterizing the empirical distribution of coefficient estimators (which could be non-normal). Hence if |
41,849 | How to handle different important variables, including overlapping information, in regression? | Should I adjust for town or not? It seems, et adding town kills the effect. How you handle such situations?
Yes, you will want to include town in your model because it is a confounder according to the DAG.
How does it differ if "town" is added as a another level into model + (1 |town)?
Not only is it a confounder... | How to handle different important variables, including overlapping information, in regression? | Should I adjust for town or not? It seems, et adding town kills the effect. How you handle such situations?
Yes, you will want to include town in your model because it is a confounder according to t | How to handle different important variables, including overlapping information, in regression?
Should I adjust for town or not? It seems, et adding town kills the effect. How you handle such situations?
Yes, you will want to include town in your model because it is a confounder according to the DAG.
How does it dif... | How to handle different important variables, including overlapping information, in regression?
Should I adjust for town or not? It seems, et adding town kills the effect. How you handle such situations?
Yes, you will want to include town in your model because it is a confounder according to t |
41,850 | How to interprete Discriminator and Generator loss in WGAN | A few points to make
You mentioned you're using WGAN, I strongly suggest using gradient penalty instead of clipping if you aren't already.
The generator loss is not very meaningful in WGAN. Also in general, there is nothing wrong with negative numbers at all.
Read the WGAN paper. The theory is dense, but there are imp... | How to interprete Discriminator and Generator loss in WGAN | A few points to make
You mentioned you're using WGAN, I strongly suggest using gradient penalty instead of clipping if you aren't already.
The generator loss is not very meaningful in WGAN. Also in g | How to interprete Discriminator and Generator loss in WGAN
A few points to make
You mentioned you're using WGAN, I strongly suggest using gradient penalty instead of clipping if you aren't already.
The generator loss is not very meaningful in WGAN. Also in general, there is nothing wrong with negative numbers at all.
... | How to interprete Discriminator and Generator loss in WGAN
A few points to make
You mentioned you're using WGAN, I strongly suggest using gradient penalty instead of clipping if you aren't already.
The generator loss is not very meaningful in WGAN. Also in g |
41,851 | What exactly does a proper scoring rule want to do? | Your thinking is correct. I recommend Gneiting & Raftery (2007, JASA) for an in-depth discussion of scoring rules.
A scoring rule $S$ is a mapping that takes a probabilistic prediction $\hat{p}$ and a corresponding observed outcome $y$ to a loss value $S(\hat{p},y)$. In our application, $\hat{p}$ is just a single numbe... | What exactly does a proper scoring rule want to do? | Your thinking is correct. I recommend Gneiting & Raftery (2007, JASA) for an in-depth discussion of scoring rules.
A scoring rule $S$ is a mapping that takes a probabilistic prediction $\hat{p}$ and a | What exactly does a proper scoring rule want to do?
Your thinking is correct. I recommend Gneiting & Raftery (2007, JASA) for an in-depth discussion of scoring rules.
A scoring rule $S$ is a mapping that takes a probabilistic prediction $\hat{p}$ and a corresponding observed outcome $y$ to a loss value $S(\hat{p},y)$. ... | What exactly does a proper scoring rule want to do?
Your thinking is correct. I recommend Gneiting & Raftery (2007, JASA) for an in-depth discussion of scoring rules.
A scoring rule $S$ is a mapping that takes a probabilistic prediction $\hat{p}$ and a |
41,852 | What exactly does a proper scoring rule want to do? | I kind of figured out the answer as I was writing the question, so a few days later, I'm going to write a self-answer.
The right answer is that the distribution of $Y$ when $x_1=0$ and $x_2=0$ is that $P(Y=1) = 0.73$. We get a discrete outcome of either a $0$ or a $1$, but the model should be able figure out that the d... | What exactly does a proper scoring rule want to do? | I kind of figured out the answer as I was writing the question, so a few days later, I'm going to write a self-answer.
The right answer is that the distribution of $Y$ when $x_1=0$ and $x_2=0$ is that | What exactly does a proper scoring rule want to do?
I kind of figured out the answer as I was writing the question, so a few days later, I'm going to write a self-answer.
The right answer is that the distribution of $Y$ when $x_1=0$ and $x_2=0$ is that $P(Y=1) = 0.73$. We get a discrete outcome of either a $0$ or a $1$... | What exactly does a proper scoring rule want to do?
I kind of figured out the answer as I was writing the question, so a few days later, I'm going to write a self-answer.
The right answer is that the distribution of $Y$ when $x_1=0$ and $x_2=0$ is that |
41,853 | What exactly does a proper scoring rule want to do? | Scoring rules assess the quality of a probabilistic forecast; i.e. a prediction with some uncertainty measure associated to it. This could be something simple like a mean and standard deviation, or it could be a full probability distribution (or something in between!). The idea behind a (proper) scoring rule is to enco... | What exactly does a proper scoring rule want to do? | Scoring rules assess the quality of a probabilistic forecast; i.e. a prediction with some uncertainty measure associated to it. This could be something simple like a mean and standard deviation, or it | What exactly does a proper scoring rule want to do?
Scoring rules assess the quality of a probabilistic forecast; i.e. a prediction with some uncertainty measure associated to it. This could be something simple like a mean and standard deviation, or it could be a full probability distribution (or something in between!)... | What exactly does a proper scoring rule want to do?
Scoring rules assess the quality of a probabilistic forecast; i.e. a prediction with some uncertainty measure associated to it. This could be something simple like a mean and standard deviation, or it |
41,854 | Mixed Effects Model: Writing out and interpreting coefficients on Level 1, 2, and 3 Models | Question: Have I written formulas that convey the correct mathematical representation for my three-level model? Is my written interpretation of the coefficients in the equations correct?
Unfortunately, no. The model you are fitting:
lmer(value ~ A + B + C + (1|ID/stimulus_num), data = data)
has the following featur... | Mixed Effects Model: Writing out and interpreting coefficients on Level 1, 2, and 3 Models | Question: Have I written formulas that convey the correct mathematical representation for my three-level model? Is my written interpretation of the coefficients in the equations correct?
Unfortunatel | Mixed Effects Model: Writing out and interpreting coefficients on Level 1, 2, and 3 Models
Question: Have I written formulas that convey the correct mathematical representation for my three-level model? Is my written interpretation of the coefficients in the equations correct?
Unfortunately, no. The model you are fitt... | Mixed Effects Model: Writing out and interpreting coefficients on Level 1, 2, and 3 Models
Question: Have I written formulas that convey the correct mathematical representation for my three-level model? Is my written interpretation of the coefficients in the equations correct?
Unfortunatel |
41,855 | Does this distribution have a name? $p(x) \propto |x|^a \exp\left(-\frac{1}{2} (x-b)^2 \right)$ | TL;DR We can develop a uniformly bounded rejection sampler, which will generate a variate from the desired density requiring an expected (worst case) $\approx 4.75$ independent uniform variates. Although the set-up is fairly straightforward/fast, it is non-trivial and this approach may be slow with varying parameters (... | Does this distribution have a name? $p(x) \propto |x|^a \exp\left(-\frac{1}{2} (x-b)^2 \right)$ | TL;DR We can develop a uniformly bounded rejection sampler, which will generate a variate from the desired density requiring an expected (worst case) $\approx 4.75$ independent uniform variates. Altho | Does this distribution have a name? $p(x) \propto |x|^a \exp\left(-\frac{1}{2} (x-b)^2 \right)$
TL;DR We can develop a uniformly bounded rejection sampler, which will generate a variate from the desired density requiring an expected (worst case) $\approx 4.75$ independent uniform variates. Although the set-up is fairly... | Does this distribution have a name? $p(x) \propto |x|^a \exp\left(-\frac{1}{2} (x-b)^2 \right)$
TL;DR We can develop a uniformly bounded rejection sampler, which will generate a variate from the desired density requiring an expected (worst case) $\approx 4.75$ independent uniform variates. Altho |
41,856 | Intuitive explanation of PSIS-LOO cross-validation | I'm a scientist, not a statistician, but given that it has been almost a year since this question was first asked and it still has not received any answers, I will do my best to provide some insight. Revisions/corrections to my answer are welcome as I have also spent considerable time and effort trying to figure out th... | Intuitive explanation of PSIS-LOO cross-validation | I'm a scientist, not a statistician, but given that it has been almost a year since this question was first asked and it still has not received any answers, I will do my best to provide some insight. | Intuitive explanation of PSIS-LOO cross-validation
I'm a scientist, not a statistician, but given that it has been almost a year since this question was first asked and it still has not received any answers, I will do my best to provide some insight. Revisions/corrections to my answer are welcome as I have also spent c... | Intuitive explanation of PSIS-LOO cross-validation
I'm a scientist, not a statistician, but given that it has been almost a year since this question was first asked and it still has not received any answers, I will do my best to provide some insight. |
41,857 | Why is bootstrapping p-values not just finding the null in the bootstrap samples? | Hi: I think what you're missing is that, for bootstrapping to work, not only does the distribution of the "thing" being bootstrapped have to converge to a distibution under the null but that "thing" has to be pivotal. By pivotal, it is meant that the statistic being bootstrapped doesn't depend on the parameter being ... | Why is bootstrapping p-values not just finding the null in the bootstrap samples? | Hi: I think what you're missing is that, for bootstrapping to work, not only does the distribution of the "thing" being bootstrapped have to converge to a distibution under the null but that "thing" | Why is bootstrapping p-values not just finding the null in the bootstrap samples?
Hi: I think what you're missing is that, for bootstrapping to work, not only does the distribution of the "thing" being bootstrapped have to converge to a distibution under the null but that "thing" has to be pivotal. By pivotal, it is ... | Why is bootstrapping p-values not just finding the null in the bootstrap samples?
Hi: I think what you're missing is that, for bootstrapping to work, not only does the distribution of the "thing" being bootstrapped have to converge to a distibution under the null but that "thing" |
41,858 | How do I find the UMVUE of $\sqrt{\alpha}$ here? | You are going down the correct path—when you are looking for the UMVUE in a parametric problem, the simplest method in most cases is to use the Lehmann–Scheffé theorem, which says that if you can form an unbiased estimator from a complete sufficient statistic, then that estimator is the unique UMVUE. Now, from your st... | How do I find the UMVUE of $\sqrt{\alpha}$ here? | You are going down the correct path—when you are looking for the UMVUE in a parametric problem, the simplest method in most cases is to use the Lehmann–Scheffé theorem, which says that if you can form | How do I find the UMVUE of $\sqrt{\alpha}$ here?
You are going down the correct path—when you are looking for the UMVUE in a parametric problem, the simplest method in most cases is to use the Lehmann–Scheffé theorem, which says that if you can form an unbiased estimator from a complete sufficient statistic, then that ... | How do I find the UMVUE of $\sqrt{\alpha}$ here?
You are going down the correct path—when you are looking for the UMVUE in a parametric problem, the simplest method in most cases is to use the Lehmann–Scheffé theorem, which says that if you can form |
41,859 | auto.arima vs arima.sim | No, you did not make an error in your code (that I can see).
It is unfortunately the case that automatic ARIMA model selection rarely recovers the model that was used to simulate the input data. This is simply a consequence of there usually being very little data compared to the number of parameters to be estimated. Af... | auto.arima vs arima.sim | No, you did not make an error in your code (that I can see).
It is unfortunately the case that automatic ARIMA model selection rarely recovers the model that was used to simulate the input data. This | auto.arima vs arima.sim
No, you did not make an error in your code (that I can see).
It is unfortunately the case that automatic ARIMA model selection rarely recovers the model that was used to simulate the input data. This is simply a consequence of there usually being very little data compared to the number of parame... | auto.arima vs arima.sim
No, you did not make an error in your code (that I can see).
It is unfortunately the case that automatic ARIMA model selection rarely recovers the model that was used to simulate the input data. This |
41,860 | Problem 2.4.1 part a) from Pearl et al. "Causal Inference in Statistics: A Primer" | I think your code for simulating the data has a typo. In the line beginning with set.seed(6) $Z_1$ should be $Z_3$. | Problem 2.4.1 part a) from Pearl et al. "Causal Inference in Statistics: A Primer" | I think your code for simulating the data has a typo. In the line beginning with set.seed(6) $Z_1$ should be $Z_3$. | Problem 2.4.1 part a) from Pearl et al. "Causal Inference in Statistics: A Primer"
I think your code for simulating the data has a typo. In the line beginning with set.seed(6) $Z_1$ should be $Z_3$. | Problem 2.4.1 part a) from Pearl et al. "Causal Inference in Statistics: A Primer"
I think your code for simulating the data has a typo. In the line beginning with set.seed(6) $Z_1$ should be $Z_3$. |
41,861 | Spelling out a detail in the gradient boosting machine algorithm for binary classification | I think your reasoning is basically correct: we could use an iterative solver like Newton's method to get a really good approximation to the optimal $\gamma$, but that's a lot of work.
The xgboost software uses a second-order Taylor expansion of $(3)$ because quadratics are easy to optimize. (Described in https://xgbo... | Spelling out a detail in the gradient boosting machine algorithm for binary classification | I think your reasoning is basically correct: we could use an iterative solver like Newton's method to get a really good approximation to the optimal $\gamma$, but that's a lot of work.
The xgboost so | Spelling out a detail in the gradient boosting machine algorithm for binary classification
I think your reasoning is basically correct: we could use an iterative solver like Newton's method to get a really good approximation to the optimal $\gamma$, but that's a lot of work.
The xgboost software uses a second-order Ta... | Spelling out a detail in the gradient boosting machine algorithm for binary classification
I think your reasoning is basically correct: we could use an iterative solver like Newton's method to get a really good approximation to the optimal $\gamma$, but that's a lot of work.
The xgboost so |
41,862 | Spelling out a detail in the gradient boosting machine algorithm for binary classification | I would say that expand equation 3 using taylor series until seconnd order polynomial and then set the derivative of this modified equation wrt gamma equal to zero to get the gamma optimal..this is equivalent to performing only one iteration of newtons method for optimization. you should get the gamma as sum(residuals)... | Spelling out a detail in the gradient boosting machine algorithm for binary classification | I would say that expand equation 3 using taylor series until seconnd order polynomial and then set the derivative of this modified equation wrt gamma equal to zero to get the gamma optimal..this is eq | Spelling out a detail in the gradient boosting machine algorithm for binary classification
I would say that expand equation 3 using taylor series until seconnd order polynomial and then set the derivative of this modified equation wrt gamma equal to zero to get the gamma optimal..this is equivalent to performing only o... | Spelling out a detail in the gradient boosting machine algorithm for binary classification
I would say that expand equation 3 using taylor series until seconnd order polynomial and then set the derivative of this modified equation wrt gamma equal to zero to get the gamma optimal..this is eq |
41,863 | Are dependent variables necessarily functions of one another? | This question is interesting because it concerns the general problem of regression in the sense of characterizing (or estimating based on data) the conditional distribution of one variable, $X_1,$ based on values of another variable $X_2.$ Their lack of statistical independence implies there is something to be gained ... | Are dependent variables necessarily functions of one another? | This question is interesting because it concerns the general problem of regression in the sense of characterizing (or estimating based on data) the conditional distribution of one variable, $X_1,$ bas | Are dependent variables necessarily functions of one another?
This question is interesting because it concerns the general problem of regression in the sense of characterizing (or estimating based on data) the conditional distribution of one variable, $X_1,$ based on values of another variable $X_2.$ Their lack of sta... | Are dependent variables necessarily functions of one another?
This question is interesting because it concerns the general problem of regression in the sense of characterizing (or estimating based on data) the conditional distribution of one variable, $X_1,$ bas |
41,864 | Are dependent variables necessarily functions of one another? | I think this is a good place to use a picture.
x0 <- x1 <- seq(-2,2,0.1)
y0 <- x0
y1 <- -x1
x <- c(x0,x1)
y <- c(y0,y1)
plot(x,y)
I think the lack of independence is evident. However, the relationship cannot be functional, as a large value of $X1$, say $X1=2$, results in either $X2=2$ or $X2=-2$, and there's the usu... | Are dependent variables necessarily functions of one another? | I think this is a good place to use a picture.
x0 <- x1 <- seq(-2,2,0.1)
y0 <- x0
y1 <- -x1
x <- c(x0,x1)
y <- c(y0,y1)
plot(x,y)
I think the lack of independence is evident. However, the relations | Are dependent variables necessarily functions of one another?
I think this is a good place to use a picture.
x0 <- x1 <- seq(-2,2,0.1)
y0 <- x0
y1 <- -x1
x <- c(x0,x1)
y <- c(y0,y1)
plot(x,y)
I think the lack of independence is evident. However, the relationship cannot be functional, as a large value of $X1$, say $X... | Are dependent variables necessarily functions of one another?
I think this is a good place to use a picture.
x0 <- x1 <- seq(-2,2,0.1)
y0 <- x0
y1 <- -x1
x <- c(x0,x1)
y <- c(y0,y1)
plot(x,y)
I think the lack of independence is evident. However, the relations |
41,865 | Are dependent variables necessarily functions of one another? | In common factor models, observed variables dependent on the same common factor covary and yet are conditionally independent given the common factor upon which they are jointly dependent. In the literature on graphical causal models, this structure--two variables jointly dependent on a third variable but with no relati... | Are dependent variables necessarily functions of one another? | In common factor models, observed variables dependent on the same common factor covary and yet are conditionally independent given the common factor upon which they are jointly dependent. In the liter | Are dependent variables necessarily functions of one another?
In common factor models, observed variables dependent on the same common factor covary and yet are conditionally independent given the common factor upon which they are jointly dependent. In the literature on graphical causal models, this structure--two vari... | Are dependent variables necessarily functions of one another?
In common factor models, observed variables dependent on the same common factor covary and yet are conditionally independent given the common factor upon which they are jointly dependent. In the liter |
41,866 | Mixed Effects Model | I fitted variables TEMPS (time) and GROUPE (Gender) like fixed effects and NUMERO (Subjects) like random effect. I am wondering if that is right.
Yes, you have repeated measures within individuals so fitting random intercepts for this factor accounts for the correlation between measurements within each individual.
No... | Mixed Effects Model | I fitted variables TEMPS (time) and GROUPE (Gender) like fixed effects and NUMERO (Subjects) like random effect. I am wondering if that is right.
Yes, you have repeated measures within individuals so | Mixed Effects Model
I fitted variables TEMPS (time) and GROUPE (Gender) like fixed effects and NUMERO (Subjects) like random effect. I am wondering if that is right.
Yes, you have repeated measures within individuals so fitting random intercepts for this factor accounts for the correlation between measurements within ... | Mixed Effects Model
I fitted variables TEMPS (time) and GROUPE (Gender) like fixed effects and NUMERO (Subjects) like random effect. I am wondering if that is right.
Yes, you have repeated measures within individuals so |
41,867 | Confidence interval for mean of Poisson with only zero counts | The standard procedure (Hahn & Meeker, section 7.2.2) exploits the basic relationship between Poisson and Chi-squared variates; namely, when $F_{\lambda}$ is the Poisson PDF of parameter $\lambda$ and $G_{\nu}$ is the Chi-squared PDF of parameter $\nu,$ then for any $k\in\{0,1,2,\ldots\},$
$$1-F_\lambda(k) = G_{2k+2}(2... | Confidence interval for mean of Poisson with only zero counts | The standard procedure (Hahn & Meeker, section 7.2.2) exploits the basic relationship between Poisson and Chi-squared variates; namely, when $F_{\lambda}$ is the Poisson PDF of parameter $\lambda$ and | Confidence interval for mean of Poisson with only zero counts
The standard procedure (Hahn & Meeker, section 7.2.2) exploits the basic relationship between Poisson and Chi-squared variates; namely, when $F_{\lambda}$ is the Poisson PDF of parameter $\lambda$ and $G_{\nu}$ is the Chi-squared PDF of parameter $\nu,$ then... | Confidence interval for mean of Poisson with only zero counts
The standard procedure (Hahn & Meeker, section 7.2.2) exploits the basic relationship between Poisson and Chi-squared variates; namely, when $F_{\lambda}$ is the Poisson PDF of parameter $\lambda$ and |
41,868 | Confidence interval for mean of Poisson with only zero counts | I answered my own question after some research. Please comment if something is wrong.
Frequentist confidence interval
An exact confidence interval can be derived based on the probability mass function for a Poisson distribution,
$$ P(X \le k) = \frac{\lambda^ke^{-\lambda}}{k!} $$
in which $k$ is some possible count and... | Confidence interval for mean of Poisson with only zero counts | I answered my own question after some research. Please comment if something is wrong.
Frequentist confidence interval
An exact confidence interval can be derived based on the probability mass function | Confidence interval for mean of Poisson with only zero counts
I answered my own question after some research. Please comment if something is wrong.
Frequentist confidence interval
An exact confidence interval can be derived based on the probability mass function for a Poisson distribution,
$$ P(X \le k) = \frac{\lambda... | Confidence interval for mean of Poisson with only zero counts
I answered my own question after some research. Please comment if something is wrong.
Frequentist confidence interval
An exact confidence interval can be derived based on the probability mass function |
41,869 | Is the sample correlation always positively correlated with the sample variance? | TL;dr
The off-diagonal entries of the sample covariance will generally be correlated with the diagonal entries because $E(XY^3) - E(XY)E(Y^2) = 0$ only when special conditions of the mixed 4th order moments hold. When $(X,Y)$ is bivariate Gaussian, these conditions hold only when $X$ is independent of $Y$.
Details
The... | Is the sample correlation always positively correlated with the sample variance? | TL;dr
The off-diagonal entries of the sample covariance will generally be correlated with the diagonal entries because $E(XY^3) - E(XY)E(Y^2) = 0$ only when special conditions of the mixed 4th order m | Is the sample correlation always positively correlated with the sample variance?
TL;dr
The off-diagonal entries of the sample covariance will generally be correlated with the diagonal entries because $E(XY^3) - E(XY)E(Y^2) = 0$ only when special conditions of the mixed 4th order moments hold. When $(X,Y)$ is bivariate... | Is the sample correlation always positively correlated with the sample variance?
TL;dr
The off-diagonal entries of the sample covariance will generally be correlated with the diagonal entries because $E(XY^3) - E(XY)E(Y^2) = 0$ only when special conditions of the mixed 4th order m |
41,870 | Is the sample correlation always positively correlated with the sample variance? | Edit: This answer is incorrect. I'm not sure whether it's better to leave it here for the record, or to just delete it.
Yes, it does hold asymptotically regardless of the distribution of X and Y. I was on the right track with the Taylor expansion: | Is the sample correlation always positively correlated with the sample variance? | Edit: This answer is incorrect. I'm not sure whether it's better to leave it here for the record, or to just delete it.
Yes, it does hold asymptotically regardless of the distribution of X and Y. I wa | Is the sample correlation always positively correlated with the sample variance?
Edit: This answer is incorrect. I'm not sure whether it's better to leave it here for the record, or to just delete it.
Yes, it does hold asymptotically regardless of the distribution of X and Y. I was on the right track with the Taylor ex... | Is the sample correlation always positively correlated with the sample variance?
Edit: This answer is incorrect. I'm not sure whether it's better to leave it here for the record, or to just delete it.
Yes, it does hold asymptotically regardless of the distribution of X and Y. I wa |
41,871 | Is the sample correlation always positively correlated with the sample variance? | It will depend on the joint distribution. For the example you mention, the bivariate (zero-mean) Normal distribution is characterized by the $\rho, \sigma_x, \sigma_y$. It follows that one can have all possible combinations of values of these three parameters, implying that no relation between $\rho$ and the standard d... | Is the sample correlation always positively correlated with the sample variance? | It will depend on the joint distribution. For the example you mention, the bivariate (zero-mean) Normal distribution is characterized by the $\rho, \sigma_x, \sigma_y$. It follows that one can have al | Is the sample correlation always positively correlated with the sample variance?
It will depend on the joint distribution. For the example you mention, the bivariate (zero-mean) Normal distribution is characterized by the $\rho, \sigma_x, \sigma_y$. It follows that one can have all possible combinations of values of th... | Is the sample correlation always positively correlated with the sample variance?
It will depend on the joint distribution. For the example you mention, the bivariate (zero-mean) Normal distribution is characterized by the $\rho, \sigma_x, \sigma_y$. It follows that one can have al |
41,872 | Can AdaBoost be used for regression? | AdaBoost is a meta-algorithm, which means it can be used together with other algorithms for perfomance improvement. Indeed, the concept of boosting is a type of linear regression.
Now, specifically answering your question, AdaBoost is actually intented for classification and regression problems. Scikit-Learn, for examp... | Can AdaBoost be used for regression? | AdaBoost is a meta-algorithm, which means it can be used together with other algorithms for perfomance improvement. Indeed, the concept of boosting is a type of linear regression.
Now, specifically an | Can AdaBoost be used for regression?
AdaBoost is a meta-algorithm, which means it can be used together with other algorithms for perfomance improvement. Indeed, the concept of boosting is a type of linear regression.
Now, specifically answering your question, AdaBoost is actually intented for classification and regress... | Can AdaBoost be used for regression?
AdaBoost is a meta-algorithm, which means it can be used together with other algorithms for perfomance improvement. Indeed, the concept of boosting is a type of linear regression.
Now, specifically an |
41,873 | Do there exist adaptive step size methods for Newton-Raphson optimization? | In a sense, Newton Raphson is automatically doing the adaptive step size; it's adapting the step in each dimension (which changes the direction) according to the rate of change of the gradient. If the function is quadratic, this the "optimal" update in that in converges in one step.
Of course, generally the target func... | Do there exist adaptive step size methods for Newton-Raphson optimization? | In a sense, Newton Raphson is automatically doing the adaptive step size; it's adapting the step in each dimension (which changes the direction) according to the rate of change of the gradient. If the | Do there exist adaptive step size methods for Newton-Raphson optimization?
In a sense, Newton Raphson is automatically doing the adaptive step size; it's adapting the step in each dimension (which changes the direction) according to the rate of change of the gradient. If the function is quadratic, this the "optimal" up... | Do there exist adaptive step size methods for Newton-Raphson optimization?
In a sense, Newton Raphson is automatically doing the adaptive step size; it's adapting the step in each dimension (which changes the direction) according to the rate of change of the gradient. If the |
41,874 | What is the PDF for a log-log-normal distribution? | With $\mu$ and $\sigma$ being the mean and standard deviation of the underlying normal process:
$f(x) = \displaystyle \frac{1}{\sqrt{2\pi\sigma}x\ln(x)}\exp\Bigg({\frac{-\big(\ln(\ln(x)) - \mu\big)^2}{2\sigma^2}}\Bigg) \quad x \geq 1$ | What is the PDF for a log-log-normal distribution? | With $\mu$ and $\sigma$ being the mean and standard deviation of the underlying normal process:
$f(x) = \displaystyle \frac{1}{\sqrt{2\pi\sigma}x\ln(x)}\exp\Bigg({\frac{-\big(\ln(\ln(x)) - \mu\big)^2} | What is the PDF for a log-log-normal distribution?
With $\mu$ and $\sigma$ being the mean and standard deviation of the underlying normal process:
$f(x) = \displaystyle \frac{1}{\sqrt{2\pi\sigma}x\ln(x)}\exp\Bigg({\frac{-\big(\ln(\ln(x)) - \mu\big)^2}{2\sigma^2}}\Bigg) \quad x \geq 1$ | What is the PDF for a log-log-normal distribution?
With $\mu$ and $\sigma$ being the mean and standard deviation of the underlying normal process:
$f(x) = \displaystyle \frac{1}{\sqrt{2\pi\sigma}x\ln(x)}\exp\Bigg({\frac{-\big(\ln(\ln(x)) - \mu\big)^2} |
41,875 | Does AUC/ROC curve return a p-value? | No, it doesn't. p-values from ROC areas are new to me, but I read the following:
Mason and Graham (2002) show that the ROC area is equivalent to the Mann–Whitney U-statistic testing the significance of forecast event probabilities for cases where events actually occurred with those where events did not occur.
Function ... | Does AUC/ROC curve return a p-value? | No, it doesn't. p-values from ROC areas are new to me, but I read the following:
Mason and Graham (2002) show that the ROC area is equivalent to the Mann–Whitney U-statistic testing the significance o | Does AUC/ROC curve return a p-value?
No, it doesn't. p-values from ROC areas are new to me, but I read the following:
Mason and Graham (2002) show that the ROC area is equivalent to the Mann–Whitney U-statistic testing the significance of forecast event probabilities for cases where events actually occurred with those ... | Does AUC/ROC curve return a p-value?
No, it doesn't. p-values from ROC areas are new to me, but I read the following:
Mason and Graham (2002) show that the ROC area is equivalent to the Mann–Whitney U-statistic testing the significance o |
41,876 | Who invented the independence notation $\perp \!\!\! \perp$? | I have often seen it associated with AP Dawid 1979, "Conditional Independence in Statistical Theory." For example page 373 of these notes. I have no idea if Dawid actually invented it or popularized it.
Update 8/17/19: According to Wikipedia, the symbol was introduced by Elfving: "Elfving introduced the statistical sym... | Who invented the independence notation $\perp \!\!\! \perp$? | I have often seen it associated with AP Dawid 1979, "Conditional Independence in Statistical Theory." For example page 373 of these notes. I have no idea if Dawid actually invented it or popularized i | Who invented the independence notation $\perp \!\!\! \perp$?
I have often seen it associated with AP Dawid 1979, "Conditional Independence in Statistical Theory." For example page 373 of these notes. I have no idea if Dawid actually invented it or popularized it.
Update 8/17/19: According to Wikipedia, the symbol was i... | Who invented the independence notation $\perp \!\!\! \perp$?
I have often seen it associated with AP Dawid 1979, "Conditional Independence in Statistical Theory." For example page 373 of these notes. I have no idea if Dawid actually invented it or popularized i |
41,877 | Where is my mistake in this definition of Bayes Factor? | My deepest apologies, there is a typo in the final expression! Indeed, here is the complete text from my book (p.231):
Definition 5.5. The Bayes factor is the ratio of the posterior probabilities of the null and the alternative hypotheses over the
ratio of the prior probabilities of the null and the alternative
... | Where is my mistake in this definition of Bayes Factor? | My deepest apologies, there is a typo in the final expression! Indeed, here is the complete text from my book (p.231):
Definition 5.5. The Bayes factor is the ratio of the posterior probabilities of | Where is my mistake in this definition of Bayes Factor?
My deepest apologies, there is a typo in the final expression! Indeed, here is the complete text from my book (p.231):
Definition 5.5. The Bayes factor is the ratio of the posterior probabilities of the null and the alternative hypotheses over the
ratio of th... | Where is my mistake in this definition of Bayes Factor?
My deepest apologies, there is a typo in the final expression! Indeed, here is the complete text from my book (p.231):
Definition 5.5. The Bayes factor is the ratio of the posterior probabilities of |
41,878 | Gradient boosting regression trained on skewed data | I think we must first consider if the outliers are "true data" or just simply noise/corrupted input.
If they are corrupted data (e.g. an adult human weighting 775 kg) then it is perfectly reasonable to exclude these instances from further analysis. If these instances though are reasonable data we might want to work wi... | Gradient boosting regression trained on skewed data | I think we must first consider if the outliers are "true data" or just simply noise/corrupted input.
If they are corrupted data (e.g. an adult human weighting 775 kg) then it is perfectly reasonable | Gradient boosting regression trained on skewed data
I think we must first consider if the outliers are "true data" or just simply noise/corrupted input.
If they are corrupted data (e.g. an adult human weighting 775 kg) then it is perfectly reasonable to exclude these instances from further analysis. If these instances... | Gradient boosting regression trained on skewed data
I think we must first consider if the outliers are "true data" or just simply noise/corrupted input.
If they are corrupted data (e.g. an adult human weighting 775 kg) then it is perfectly reasonable |
41,879 | huge difference between estimates of binomial regresssion when including random effect vs when not | There is enough information in the question to clear this up. lsmeans is simply using the coefficients to obtain the group predicted probabilities.
So for the GLM, OP's implied model is:
\begin{equation}
\hat\pi=\frac{1}{1+e^{-(-1.9684+0.2139\times d)}}
\end{equation}
where $d$ is an indicator for membership in group 2... | huge difference between estimates of binomial regresssion when including random effect vs when not | There is enough information in the question to clear this up. lsmeans is simply using the coefficients to obtain the group predicted probabilities.
So for the GLM, OP's implied model is:
\begin{equati | huge difference between estimates of binomial regresssion when including random effect vs when not
There is enough information in the question to clear this up. lsmeans is simply using the coefficients to obtain the group predicted probabilities.
So for the GLM, OP's implied model is:
\begin{equation}
\hat\pi=\frac{1}{... | huge difference between estimates of binomial regresssion when including random effect vs when not
There is enough information in the question to clear this up. lsmeans is simply using the coefficients to obtain the group predicted probabilities.
So for the GLM, OP's implied model is:
\begin{equati |
41,880 | huge difference between estimates of binomial regresssion when including random effect vs when not | Model 1, Logistic regression without random effect:
$$\mathrm{Logit}(\Pr(Y=1)) = X\beta$$
We know MLE $\hat \beta$ is asymptotically unbiased. But
$$\hat Pr(Y=1) = \mathrm{Logit}^{-1}(X\hat\beta)$$ is biased estimate of $\Pr(Y=1)$, because the non-linearity of the logit function. But asymptotically it is unbiased. So f... | huge difference between estimates of binomial regresssion when including random effect vs when not | Model 1, Logistic regression without random effect:
$$\mathrm{Logit}(\Pr(Y=1)) = X\beta$$
We know MLE $\hat \beta$ is asymptotically unbiased. But
$$\hat Pr(Y=1) = \mathrm{Logit}^{-1}(X\hat\beta)$$ is | huge difference between estimates of binomial regresssion when including random effect vs when not
Model 1, Logistic regression without random effect:
$$\mathrm{Logit}(\Pr(Y=1)) = X\beta$$
We know MLE $\hat \beta$ is asymptotically unbiased. But
$$\hat Pr(Y=1) = \mathrm{Logit}^{-1}(X\hat\beta)$$ is biased estimate of $... | huge difference between estimates of binomial regresssion when including random effect vs when not
Model 1, Logistic regression without random effect:
$$\mathrm{Logit}(\Pr(Y=1)) = X\beta$$
We know MLE $\hat \beta$ is asymptotically unbiased. But
$$\hat Pr(Y=1) = \mathrm{Logit}^{-1}(X\hat\beta)$$ is |
41,881 | RKHS norm and Fourier transform link | I'm also learning this stuff and was unable to find a proof so I took a swing at one.
There's a couple things we need to know about RKHS and Fourier analysis before we start (that I think are well established online if you're unfamiliar):
The word "reproducing" in RKHS comes from the fact that if we take the inner pro... | RKHS norm and Fourier transform link | I'm also learning this stuff and was unable to find a proof so I took a swing at one.
There's a couple things we need to know about RKHS and Fourier analysis before we start (that I think are well est | RKHS norm and Fourier transform link
I'm also learning this stuff and was unable to find a proof so I took a swing at one.
There's a couple things we need to know about RKHS and Fourier analysis before we start (that I think are well established online if you're unfamiliar):
The word "reproducing" in RKHS comes from t... | RKHS norm and Fourier transform link
I'm also learning this stuff and was unable to find a proof so I took a swing at one.
There's a couple things we need to know about RKHS and Fourier analysis before we start (that I think are well est |
41,882 | Effective sample size of a weighted sample | Can weights be regarded as introducing some kind of correlation into the data?
Assume you have two uncorrelated standard normal variables with lots of samples. If all points on / closest to a positively sloped line are heavily weighted relative to other points, you would induce positive correlation. Similarly, if all... | Effective sample size of a weighted sample | Can weights be regarded as introducing some kind of correlation into the data?
Assume you have two uncorrelated standard normal variables with lots of samples. If all points on / closest to a positi | Effective sample size of a weighted sample
Can weights be regarded as introducing some kind of correlation into the data?
Assume you have two uncorrelated standard normal variables with lots of samples. If all points on / closest to a positively sloped line are heavily weighted relative to other points, you would ind... | Effective sample size of a weighted sample
Can weights be regarded as introducing some kind of correlation into the data?
Assume you have two uncorrelated standard normal variables with lots of samples. If all points on / closest to a positi |
41,883 | Significance vs. goodness-of-fit in regression | Yes, the p-values that come with standard regression output are testing if the associated beta (slope coefficient) is $0$. (It is possible to get p-values for tests against other values, but you have to know how to set that up—it isn't what software does by default, and it really isn't very common.)
Yes, you can hav... | Significance vs. goodness-of-fit in regression | Yes, the p-values that come with standard regression output are testing if the associated beta (slope coefficient) is $0$. (It is possible to get p-values for tests against other values, but you have | Significance vs. goodness-of-fit in regression
Yes, the p-values that come with standard regression output are testing if the associated beta (slope coefficient) is $0$. (It is possible to get p-values for tests against other values, but you have to know how to set that up—it isn't what software does by default, and i... | Significance vs. goodness-of-fit in regression
Yes, the p-values that come with standard regression output are testing if the associated beta (slope coefficient) is $0$. (It is possible to get p-values for tests against other values, but you have |
41,884 | Significance vs. goodness-of-fit in regression | To add to the answer by @gung let's assume a simpler model of
$$
Y=\beta_0 + \beta_1 X + e
$$
where we are estimating $Y$ using
$$
\hat Y=\hat \beta_0 + \hat \beta_1 X.
$$
we have $n$ data points $x_i$ and $y_i$, $i=1,...,n$.
p-values for coefficients are calculated as:
$$
PV_i = Pr(t>t_i )
$$
where
$$
t_i=\frac{|\... | Significance vs. goodness-of-fit in regression | To add to the answer by @gung let's assume a simpler model of
$$
Y=\beta_0 + \beta_1 X + e
$$
where we are estimating $Y$ using
$$
\hat Y=\hat \beta_0 + \hat \beta_1 X.
$$
we have $n$ data points $ | Significance vs. goodness-of-fit in regression
To add to the answer by @gung let's assume a simpler model of
$$
Y=\beta_0 + \beta_1 X + e
$$
where we are estimating $Y$ using
$$
\hat Y=\hat \beta_0 + \hat \beta_1 X.
$$
we have $n$ data points $x_i$ and $y_i$, $i=1,...,n$.
p-values for coefficients are calculated as:... | Significance vs. goodness-of-fit in regression
To add to the answer by @gung let's assume a simpler model of
$$
Y=\beta_0 + \beta_1 X + e
$$
where we are estimating $Y$ using
$$
\hat Y=\hat \beta_0 + \hat \beta_1 X.
$$
we have $n$ data points $ |
41,885 | Using partial measurements of output variable in modeling | Fun question. The key problem as noted by @MartijnWeterings is that the number of trees at phase 2 is only a partial measurement of the total number of trees. If we knew the total number of trees, however, we could solve the problem by building a model of the number of nuts observed at stage 1 given the number of trees... | Using partial measurements of output variable in modeling | Fun question. The key problem as noted by @MartijnWeterings is that the number of trees at phase 2 is only a partial measurement of the total number of trees. If we knew the total number of trees, how | Using partial measurements of output variable in modeling
Fun question. The key problem as noted by @MartijnWeterings is that the number of trees at phase 2 is only a partial measurement of the total number of trees. If we knew the total number of trees, however, we could solve the problem by building a model of the nu... | Using partial measurements of output variable in modeling
Fun question. The key problem as noted by @MartijnWeterings is that the number of trees at phase 2 is only a partial measurement of the total number of trees. If we knew the total number of trees, how |
41,886 | Using partial measurements of output variable in modeling | In phase 1 you could make a model that relates the behavior of a squirrel to the total number of nuts.
In phase 2 you do not observe the exact same full information as in phase 1. For instance, you do not know how many trees in total are used by a specific squirrel. But you do observe some of the squirel's behavior, n... | Using partial measurements of output variable in modeling | In phase 1 you could make a model that relates the behavior of a squirrel to the total number of nuts.
In phase 2 you do not observe the exact same full information as in phase 1. For instance, you d | Using partial measurements of output variable in modeling
In phase 1 you could make a model that relates the behavior of a squirrel to the total number of nuts.
In phase 2 you do not observe the exact same full information as in phase 1. For instance, you do not know how many trees in total are used by a specific squi... | Using partial measurements of output variable in modeling
In phase 1 you could make a model that relates the behavior of a squirrel to the total number of nuts.
In phase 2 you do not observe the exact same full information as in phase 1. For instance, you d |
41,887 | Difference between Mean/average accuracy and Overall accuracy | What the paper describes
I trust you are referring to the following quote
Each experiment is repeated ten times with a different training set to make the comparison fair, and both the mean accuracies and standard deviation are reported. For the evaluation metrics, overall accuracy (OA) and kappa coefficient (κ) are ad... | Difference between Mean/average accuracy and Overall accuracy | What the paper describes
I trust you are referring to the following quote
Each experiment is repeated ten times with a different training set to make the comparison fair, and both the mean accuracies | Difference between Mean/average accuracy and Overall accuracy
What the paper describes
I trust you are referring to the following quote
Each experiment is repeated ten times with a different training set to make the comparison fair, and both the mean accuracies and standard deviation are reported. For the evaluation m... | Difference between Mean/average accuracy and Overall accuracy
What the paper describes
I trust you are referring to the following quote
Each experiment is repeated ten times with a different training set to make the comparison fair, and both the mean accuracies |
41,888 | Difference between Mean/average accuracy and Overall accuracy | The mean accuracy and overall accuracy are nearly what you defined. But the mean accuracy is the average across all classes not just 1 like you listed. In fact they can be computed from each other given k target class labels where k >= 2:
avgaccuracy = (2*overallaccuracy + k-2)/k =2(overallaccuracy-1)/k+1
overallacc... | Difference between Mean/average accuracy and Overall accuracy | The mean accuracy and overall accuracy are nearly what you defined. But the mean accuracy is the average across all classes not just 1 like you listed. In fact they can be computed from each other g | Difference between Mean/average accuracy and Overall accuracy
The mean accuracy and overall accuracy are nearly what you defined. But the mean accuracy is the average across all classes not just 1 like you listed. In fact they can be computed from each other given k target class labels where k >= 2:
avgaccuracy = (2*... | Difference between Mean/average accuracy and Overall accuracy
The mean accuracy and overall accuracy are nearly what you defined. But the mean accuracy is the average across all classes not just 1 like you listed. In fact they can be computed from each other g |
41,889 | Robust Principal Component Analysis for Anomaly Detection | I went through this papers and others, and used Robust PCA for my own needs. Additionaly to Candes et al., you can take a look to the implementation suggested by Lin et al. (2013): https://arxiv.org/pdf/1009.5055.pdf. Besides detecting outliers, one of the problem formulation also allows you to complete missing entries... | Robust Principal Component Analysis for Anomaly Detection | I went through this papers and others, and used Robust PCA for my own needs. Additionaly to Candes et al., you can take a look to the implementation suggested by Lin et al. (2013): https://arxiv.org/p | Robust Principal Component Analysis for Anomaly Detection
I went through this papers and others, and used Robust PCA for my own needs. Additionaly to Candes et al., you can take a look to the implementation suggested by Lin et al. (2013): https://arxiv.org/pdf/1009.5055.pdf. Besides detecting outliers, one of the probl... | Robust Principal Component Analysis for Anomaly Detection
I went through this papers and others, and used Robust PCA for my own needs. Additionaly to Candes et al., you can take a look to the implementation suggested by Lin et al. (2013): https://arxiv.org/p |
41,890 | How to report: large sample sizes (10000+), significant small difference (1%) | Ideally and theoretically, you should decide on the test before seeing any data, and then report only on that test.
In your situation, I would say that you should report the test that makes sense based on what you know about your data generating process. It makes no sense to report on a simple $\chi^2$ test that does n... | How to report: large sample sizes (10000+), significant small difference (1%) | Ideally and theoretically, you should decide on the test before seeing any data, and then report only on that test.
In your situation, I would say that you should report the test that makes sense base | How to report: large sample sizes (10000+), significant small difference (1%)
Ideally and theoretically, you should decide on the test before seeing any data, and then report only on that test.
In your situation, I would say that you should report the test that makes sense based on what you know about your data generat... | How to report: large sample sizes (10000+), significant small difference (1%)
Ideally and theoretically, you should decide on the test before seeing any data, and then report only on that test.
In your situation, I would say that you should report the test that makes sense base |
41,891 | Why are PhD programs in statistics coursework heavy relative to PhD programs in the basic sciences? | I don't think the coursework is intended to be there as busywork in case you prove the Riemann hypothesis on your first day. More likely, the faculty has made the decision that it wants to get all of its graduate students up to some minimal level of mathematical/statistical competence prior to research training, and a... | Why are PhD programs in statistics coursework heavy relative to PhD programs in the basic sciences? | I don't think the coursework is intended to be there as busywork in case you prove the Riemann hypothesis on your first day. More likely, the faculty has made the decision that it wants to get all of | Why are PhD programs in statistics coursework heavy relative to PhD programs in the basic sciences?
I don't think the coursework is intended to be there as busywork in case you prove the Riemann hypothesis on your first day. More likely, the faculty has made the decision that it wants to get all of its graduate studen... | Why are PhD programs in statistics coursework heavy relative to PhD programs in the basic sciences?
I don't think the coursework is intended to be there as busywork in case you prove the Riemann hypothesis on your first day. More likely, the faculty has made the decision that it wants to get all of |
41,892 | Why are PhD programs in statistics coursework heavy relative to PhD programs in the basic sciences? | That's a very country specific thing and I suspect that it did just grow historically. Many other countries are much more focussed on doing research leading to publications and/or a monograph. This mirrors differences that you can also see in undergraduate education (application first vs. "thou shalt not touch a real d... | Why are PhD programs in statistics coursework heavy relative to PhD programs in the basic sciences? | That's a very country specific thing and I suspect that it did just grow historically. Many other countries are much more focussed on doing research leading to publications and/or a monograph. This mi | Why are PhD programs in statistics coursework heavy relative to PhD programs in the basic sciences?
That's a very country specific thing and I suspect that it did just grow historically. Many other countries are much more focussed on doing research leading to publications and/or a monograph. This mirrors differences th... | Why are PhD programs in statistics coursework heavy relative to PhD programs in the basic sciences?
That's a very country specific thing and I suspect that it did just grow historically. Many other countries are much more focussed on doing research leading to publications and/or a monograph. This mi |
41,893 | Does more training data help lower the bias of a high bias model? | However, what impact does training data size have on a high bias model? Generally, will more training data lower the bias, will it have no effect, or will it cause a further increase in the bias?
You mean a model with prediction errors due to high bias?
Bias, is defined as $\operatorname{Bias}[\hat{f}(x)]=\mathrm{E}[... | Does more training data help lower the bias of a high bias model? | However, what impact does training data size have on a high bias model? Generally, will more training data lower the bias, will it have no effect, or will it cause a further increase in the bias?
You | Does more training data help lower the bias of a high bias model?
However, what impact does training data size have on a high bias model? Generally, will more training data lower the bias, will it have no effect, or will it cause a further increase in the bias?
You mean a model with prediction errors due to high bias?... | Does more training data help lower the bias of a high bias model?
However, what impact does training data size have on a high bias model? Generally, will more training data lower the bias, will it have no effect, or will it cause a further increase in the bias?
You |
41,894 | Does more training data help lower the bias of a high bias model? | 1- Increasing training data size leads to decrease variance.
2- Decrease the variance leads to increase the bias.
so increase the training data size leads to decrease variance and increase variance. | Does more training data help lower the bias of a high bias model? | 1- Increasing training data size leads to decrease variance.
2- Decrease the variance leads to increase the bias.
so increase the training data size leads to decrease variance and increase variance. | Does more training data help lower the bias of a high bias model?
1- Increasing training data size leads to decrease variance.
2- Decrease the variance leads to increase the bias.
so increase the training data size leads to decrease variance and increase variance. | Does more training data help lower the bias of a high bias model?
1- Increasing training data size leads to decrease variance.
2- Decrease the variance leads to increase the bias.
so increase the training data size leads to decrease variance and increase variance. |
41,895 | How to test if the process that generated a time-series has changed over time | Structural change can be tested not only with Chow test mentioned by @John Stax Jakobsen.
There are plenty other tests, especially family of fluctuation tests usually works well.
Here you have nice introduction to R package strucchange that computes them. If you're not R user, read just theory, it is well described the... | How to test if the process that generated a time-series has changed over time | Structural change can be tested not only with Chow test mentioned by @John Stax Jakobsen.
There are plenty other tests, especially family of fluctuation tests usually works well.
Here you have nice in | How to test if the process that generated a time-series has changed over time
Structural change can be tested not only with Chow test mentioned by @John Stax Jakobsen.
There are plenty other tests, especially family of fluctuation tests usually works well.
Here you have nice introduction to R package strucchange that c... | How to test if the process that generated a time-series has changed over time
Structural change can be tested not only with Chow test mentioned by @John Stax Jakobsen.
There are plenty other tests, especially family of fluctuation tests usually works well.
Here you have nice in |
41,896 | How to test if the process that generated a time-series has changed over time | If it is reasonable to model the relationship with a linear regression, then an easy way to test for a structural break is the chow test.
see the wiki article here | How to test if the process that generated a time-series has changed over time | If it is reasonable to model the relationship with a linear regression, then an easy way to test for a structural break is the chow test.
see the wiki article here | How to test if the process that generated a time-series has changed over time
If it is reasonable to model the relationship with a linear regression, then an easy way to test for a structural break is the chow test.
see the wiki article here | How to test if the process that generated a time-series has changed over time
If it is reasonable to model the relationship with a linear regression, then an easy way to test for a structural break is the chow test.
see the wiki article here |
41,897 | How to test if the process that generated a time-series has changed over time | First, I would just fit some black box models (e.g. GBM or random forest) which directly take into account the time variable $T$, e.g. $Y_t=F(X_t^1, \ldots, X_d^t; T)$. It might be helpful to test various granularity of $T$, such as measured in calendar years (2016, 2018), months passed since 2016, etc. Then, in order ... | How to test if the process that generated a time-series has changed over time | First, I would just fit some black box models (e.g. GBM or random forest) which directly take into account the time variable $T$, e.g. $Y_t=F(X_t^1, \ldots, X_d^t; T)$. It might be helpful to test var | How to test if the process that generated a time-series has changed over time
First, I would just fit some black box models (e.g. GBM or random forest) which directly take into account the time variable $T$, e.g. $Y_t=F(X_t^1, \ldots, X_d^t; T)$. It might be helpful to test various granularity of $T$, such as measured ... | How to test if the process that generated a time-series has changed over time
First, I would just fit some black box models (e.g. GBM or random forest) which directly take into account the time variable $T$, e.g. $Y_t=F(X_t^1, \ldots, X_d^t; T)$. It might be helpful to test var |
41,898 | How to test if the process that generated a time-series has changed over time | One of the features that I put into my favorite forecasting package was the CHOW Test to investigate that breakpoint in parameters that was the most significant. Before I did that I had to treat/adjust for pulses/seasonal pulses.
Of course if there are identified level Shifts or Time Trends this test is bypassed.
The ... | How to test if the process that generated a time-series has changed over time | One of the features that I put into my favorite forecasting package was the CHOW Test to investigate that breakpoint in parameters that was the most significant. Before I did that I had to treat/adjus | How to test if the process that generated a time-series has changed over time
One of the features that I put into my favorite forecasting package was the CHOW Test to investigate that breakpoint in parameters that was the most significant. Before I did that I had to treat/adjust for pulses/seasonal pulses.
Of course i... | How to test if the process that generated a time-series has changed over time
One of the features that I put into my favorite forecasting package was the CHOW Test to investigate that breakpoint in parameters that was the most significant. Before I did that I had to treat/adjus |
41,899 | When modeling a copula, you need to generate "pseudo observations"? Why? What is a pseudo observation? [closed] | Copula models based on pseudo-observation (normalized ranked data), not on the original dataset. That due to the Sklar's theorem (the backbone of the copula model). From Sklar's theorem, copula is a function of uniform margins.
Hence, you need to transform the margins of your dataset to the standard uniform margins, i... | When modeling a copula, you need to generate "pseudo observations"? Why? What is a pseudo observatio | Copula models based on pseudo-observation (normalized ranked data), not on the original dataset. That due to the Sklar's theorem (the backbone of the copula model). From Sklar's theorem, copula is a f | When modeling a copula, you need to generate "pseudo observations"? Why? What is a pseudo observation? [closed]
Copula models based on pseudo-observation (normalized ranked data), not on the original dataset. That due to the Sklar's theorem (the backbone of the copula model). From Sklar's theorem, copula is a function ... | When modeling a copula, you need to generate "pseudo observations"? Why? What is a pseudo observatio
Copula models based on pseudo-observation (normalized ranked data), not on the original dataset. That due to the Sklar's theorem (the backbone of the copula model). From Sklar's theorem, copula is a f |
41,900 | Fitting distributions on censored data | A short answer which might be expanded: This is really about how the likelihood function is defined, see for instance How to rigorously define the likelihood?. It doesn't really matter if you use probability densities or probability mass functions to define your likelihood. The likelihood function is always defined w... | Fitting distributions on censored data | A short answer which might be expanded: This is really about how the likelihood function is defined, see for instance How to rigorously define the likelihood?. It doesn't really matter if you use pr | Fitting distributions on censored data
A short answer which might be expanded: This is really about how the likelihood function is defined, see for instance How to rigorously define the likelihood?. It doesn't really matter if you use probability densities or probability mass functions to define your likelihood. The ... | Fitting distributions on censored data
A short answer which might be expanded: This is really about how the likelihood function is defined, see for instance How to rigorously define the likelihood?. It doesn't really matter if you use pr |
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