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 |
|---|---|---|---|---|---|---|
36,901 | Are there two definitions of the word bias? | I agree that this terminology is confusing. Bias has one meaning in both of these contexts: distance from ideal or target values, but the interpretation depends on which space we are talking about. I'll explain what I mean with regard to the two quotes in your question.
By using mean-wise imputation, we are adding b... | Are there two definitions of the word bias? | I agree that this terminology is confusing. Bias has one meaning in both of these contexts: distance from ideal or target values, but the interpretation depends on which space we are talking about. | Are there two definitions of the word bias?
I agree that this terminology is confusing. Bias has one meaning in both of these contexts: distance from ideal or target values, but the interpretation depends on which space we are talking about. I'll explain what I mean with regard to the two quotes in your question.
By... | Are there two definitions of the word bias?
I agree that this terminology is confusing. Bias has one meaning in both of these contexts: distance from ideal or target values, but the interpretation depends on which space we are talking about. |
36,902 | Gradients of cross-entropy error in neural network | Use the chain rule,
$$
\frac{\partial C}{\partial W_1} = \frac{\partial C}{\partial z} \frac{\partial z}{\partial h} \frac{\partial h}{\partial a} \frac{\partial a}{\partial W_1} ,
$$
where
$$
a = W_1x+b_1 .
$$
$$
\frac{\partial C}{\partial z} = y-\hat{y},
$$
$$
\frac{\partial z}{\partial h} = W_2,
$$
$$
\frac{\parti... | Gradients of cross-entropy error in neural network | Use the chain rule,
$$
\frac{\partial C}{\partial W_1} = \frac{\partial C}{\partial z} \frac{\partial z}{\partial h} \frac{\partial h}{\partial a} \frac{\partial a}{\partial W_1} ,
$$
where
$$
a = W | Gradients of cross-entropy error in neural network
Use the chain rule,
$$
\frac{\partial C}{\partial W_1} = \frac{\partial C}{\partial z} \frac{\partial z}{\partial h} \frac{\partial h}{\partial a} \frac{\partial a}{\partial W_1} ,
$$
where
$$
a = W_1x+b_1 .
$$
$$
\frac{\partial C}{\partial z} = y-\hat{y},
$$
$$
\fra... | Gradients of cross-entropy error in neural network
Use the chain rule,
$$
\frac{\partial C}{\partial W_1} = \frac{\partial C}{\partial z} \frac{\partial z}{\partial h} \frac{\partial h}{\partial a} \frac{\partial a}{\partial W_1} ,
$$
where
$$
a = W |
36,903 | Help explaining (offering intuition/examples of) the score function and fisher's information to students | Buse, A (1982). The Likelihood Ratio, Wald, and Lagrange Multiplier Tests: An Expository Note. The American Statistician, 36:3a, 153-157 is an excellent reference with one major reservation: Lagrange multiplier test should have been called Rao's efficient score test. I wrote Prof. Rao about this when the paper came o... | Help explaining (offering intuition/examples of) the score function and fisher's information to stud | Buse, A (1982). The Likelihood Ratio, Wald, and Lagrange Multiplier Tests: An Expository Note. The American Statistician, 36:3a, 153-157 is an excellent reference with one major reservation: Lagrange | Help explaining (offering intuition/examples of) the score function and fisher's information to students
Buse, A (1982). The Likelihood Ratio, Wald, and Lagrange Multiplier Tests: An Expository Note. The American Statistician, 36:3a, 153-157 is an excellent reference with one major reservation: Lagrange multiplier tes... | Help explaining (offering intuition/examples of) the score function and fisher's information to stud
Buse, A (1982). The Likelihood Ratio, Wald, and Lagrange Multiplier Tests: An Expository Note. The American Statistician, 36:3a, 153-157 is an excellent reference with one major reservation: Lagrange |
36,904 | Can BIC be Used for Hypothesis Testing | You can construct just such an asymptotic approximation, but note that you can rewrite it in terms of the difference from (say) $BIC_0$ (or indeed any convenient constant). This can help avoid problems with underflow or overflow when exponentiating numbers which might be very far from 0.
Note further that (using a simi... | Can BIC be Used for Hypothesis Testing | You can construct just such an asymptotic approximation, but note that you can rewrite it in terms of the difference from (say) $BIC_0$ (or indeed any convenient constant). This can help avoid problem | Can BIC be Used for Hypothesis Testing
You can construct just such an asymptotic approximation, but note that you can rewrite it in terms of the difference from (say) $BIC_0$ (or indeed any convenient constant). This can help avoid problems with underflow or overflow when exponentiating numbers which might be very far ... | Can BIC be Used for Hypothesis Testing
You can construct just such an asymptotic approximation, but note that you can rewrite it in terms of the difference from (say) $BIC_0$ (or indeed any convenient constant). This can help avoid problem |
36,905 | Why do we deseasonalize data? | You deaseasonalize when the focus is on the secular trends. For instance, you're interested where the sales are going as opposed to what will be the sales in the next month. Sales are usually highly seasonal, e.g. home sales are up in summer and down in winter.
So, if your focus is on figuring out whether the general t... | Why do we deseasonalize data? | You deaseasonalize when the focus is on the secular trends. For instance, you're interested where the sales are going as opposed to what will be the sales in the next month. Sales are usually highly s | Why do we deseasonalize data?
You deaseasonalize when the focus is on the secular trends. For instance, you're interested where the sales are going as opposed to what will be the sales in the next month. Sales are usually highly seasonal, e.g. home sales are up in summer and down in winter.
So, if your focus is on figu... | Why do we deseasonalize data?
You deaseasonalize when the focus is on the secular trends. For instance, you're interested where the sales are going as opposed to what will be the sales in the next month. Sales are usually highly s |
36,906 | Why do we deseasonalize data? | You can only make a regression line using deseasonalised data. The Regression line equation can then be used to make deseasonalised future predictions. From this you can find the seasonalised future values. So perhaps this was done to forcast future values?
Though, i'm not too certain on how this correlates to stationa... | Why do we deseasonalize data? | You can only make a regression line using deseasonalised data. The Regression line equation can then be used to make deseasonalised future predictions. From this you can find the seasonalised future v | Why do we deseasonalize data?
You can only make a regression line using deseasonalised data. The Regression line equation can then be used to make deseasonalised future predictions. From this you can find the seasonalised future values. So perhaps this was done to forcast future values?
Though, i'm not too certain on h... | Why do we deseasonalize data?
You can only make a regression line using deseasonalised data. The Regression line equation can then be used to make deseasonalised future predictions. From this you can find the seasonalised future v |
36,907 | Regression Mixture in PYMC3 | An alternative is to use the marginalized mixture model (see also this SO answer). This utilizes the NUTS using ADVI and converges within 6000 samples.
import theano.tensore as tt
ncls = 2
with pm.Model() as basic_model:
w = pm.Dirichlet('w', np.ones(ncls))
alpha = pm.Normal('alpha', mu=0, sd=10)
beta = pm... | Regression Mixture in PYMC3 | An alternative is to use the marginalized mixture model (see also this SO answer). This utilizes the NUTS using ADVI and converges within 6000 samples.
import theano.tensore as tt
ncls = 2
with pm.Mo | Regression Mixture in PYMC3
An alternative is to use the marginalized mixture model (see also this SO answer). This utilizes the NUTS using ADVI and converges within 6000 samples.
import theano.tensore as tt
ncls = 2
with pm.Model() as basic_model:
w = pm.Dirichlet('w', np.ones(ncls))
alpha = pm.Normal('alpha'... | Regression Mixture in PYMC3
An alternative is to use the marginalized mixture model (see also this SO answer). This utilizes the NUTS using ADVI and converges within 6000 samples.
import theano.tensore as tt
ncls = 2
with pm.Mo |
36,908 | Regression Mixture in PYMC3 | So the problem with this was actually with the BinaryMetropolis sampler, a problem I only discovered by stumbling on this post.
I adjusted the scaling parameter of the sampler and after about 35k samples, it converged on the parameters.
with basic_model:
step1 = pm.Metropolis([p, alpha, beta_1, sigma])
step2 ... | Regression Mixture in PYMC3 | So the problem with this was actually with the BinaryMetropolis sampler, a problem I only discovered by stumbling on this post.
I adjusted the scaling parameter of the sampler and after about 35k samp | Regression Mixture in PYMC3
So the problem with this was actually with the BinaryMetropolis sampler, a problem I only discovered by stumbling on this post.
I adjusted the scaling parameter of the sampler and after about 35k samples, it converged on the parameters.
with basic_model:
step1 = pm.Metropolis([p, alpha... | Regression Mixture in PYMC3
So the problem with this was actually with the BinaryMetropolis sampler, a problem I only discovered by stumbling on this post.
I adjusted the scaling parameter of the sampler and after about 35k samp |
36,909 | (References) How to derive experimental design models, instead of just memorize them? | You're asking for a derivation, but I'd argue that this formula is not derivable. It stands on its own as a mathematical encoding of the outside world. The math doesn't care what a "block" is, but you do. And if you believe it can be modeled as an additive source of variation, then you'll likely end up with the linear ... | (References) How to derive experimental design models, instead of just memorize them? | You're asking for a derivation, but I'd argue that this formula is not derivable. It stands on its own as a mathematical encoding of the outside world. The math doesn't care what a "block" is, but you | (References) How to derive experimental design models, instead of just memorize them?
You're asking for a derivation, but I'd argue that this formula is not derivable. It stands on its own as a mathematical encoding of the outside world. The math doesn't care what a "block" is, but you do. And if you believe it can be ... | (References) How to derive experimental design models, instead of just memorize them?
You're asking for a derivation, but I'd argue that this formula is not derivable. It stands on its own as a mathematical encoding of the outside world. The math doesn't care what a "block" is, but you |
36,910 | Statistical anecdotes [closed] | Not sure if this is too serious, but there is the Berkeley gender bias case illustrating Simpson's paradox. A very recent nearly identical case illustrating the problem seems a PNAS study on gender bias in research funding, discussed, e.g., in this Science news article. | Statistical anecdotes [closed] | Not sure if this is too serious, but there is the Berkeley gender bias case illustrating Simpson's paradox. A very recent nearly identical case illustrating the problem seems a PNAS study on gender bi | Statistical anecdotes [closed]
Not sure if this is too serious, but there is the Berkeley gender bias case illustrating Simpson's paradox. A very recent nearly identical case illustrating the problem seems a PNAS study on gender bias in research funding, discussed, e.g., in this Science news article. | Statistical anecdotes [closed]
Not sure if this is too serious, but there is the Berkeley gender bias case illustrating Simpson's paradox. A very recent nearly identical case illustrating the problem seems a PNAS study on gender bi |
36,911 | expectation of $e^{-x}$ when x is log-normal | Suppose $X$ is log-normal random variable. The question is about the expectation
$\DeclareMathOperator{\E}{E} \E \exp(-X)$. This is related to the moment-generating function of $X$,
$$
M_X(t) = \E e^{tX}
$$
So you are asking for $M_X(-1)$, which do exist, but no closed expression is known. So, you could try numerica... | expectation of $e^{-x}$ when x is log-normal | Suppose $X$ is log-normal random variable. The question is about the expectation
$\DeclareMathOperator{\E}{E} \E \exp(-X)$. This is related to the moment-generating function of $X$,
$$
M_X(t) = \E | expectation of $e^{-x}$ when x is log-normal
Suppose $X$ is log-normal random variable. The question is about the expectation
$\DeclareMathOperator{\E}{E} \E \exp(-X)$. This is related to the moment-generating function of $X$,
$$
M_X(t) = \E e^{tX}
$$
So you are asking for $M_X(-1)$, which do exist, but no closed ex... | expectation of $e^{-x}$ when x is log-normal
Suppose $X$ is log-normal random variable. The question is about the expectation
$\DeclareMathOperator{\E}{E} \E \exp(-X)$. This is related to the moment-generating function of $X$,
$$
M_X(t) = \E |
36,912 | Maximum Likelihood Estimate of Infection Model Parameters | Here's a possibility in which the model is modified (1) to be explicitly probabilistic, and (2) to take place in discrete time.
The code below explains the modified model, simulates it, and then uses MLE to recover the parameters (whose true value is known in this toy example, since we simulated the data). Careful: m... | Maximum Likelihood Estimate of Infection Model Parameters | Here's a possibility in which the model is modified (1) to be explicitly probabilistic, and (2) to take place in discrete time.
The code below explains the modified model, simulates it, and then uses | Maximum Likelihood Estimate of Infection Model Parameters
Here's a possibility in which the model is modified (1) to be explicitly probabilistic, and (2) to take place in discrete time.
The code below explains the modified model, simulates it, and then uses MLE to recover the parameters (whose true value is known in th... | Maximum Likelihood Estimate of Infection Model Parameters
Here's a possibility in which the model is modified (1) to be explicitly probabilistic, and (2) to take place in discrete time.
The code below explains the modified model, simulates it, and then uses |
36,913 | Maximum Likelihood Estimate of Infection Model Parameters | These slides Provide a good initial start by doing iterative least squares fits, this is however only for the SI model.
This blog gives this problem a more extensive treatment. This seems to be similar to your approach. Fitting a Gaussian kernel via non-linear least squares might be a good way to get initial parameter ... | Maximum Likelihood Estimate of Infection Model Parameters | These slides Provide a good initial start by doing iterative least squares fits, this is however only for the SI model.
This blog gives this problem a more extensive treatment. This seems to be simila | Maximum Likelihood Estimate of Infection Model Parameters
These slides Provide a good initial start by doing iterative least squares fits, this is however only for the SI model.
This blog gives this problem a more extensive treatment. This seems to be similar to your approach. Fitting a Gaussian kernel via non-linear l... | Maximum Likelihood Estimate of Infection Model Parameters
These slides Provide a good initial start by doing iterative least squares fits, this is however only for the SI model.
This blog gives this problem a more extensive treatment. This seems to be simila |
36,914 | Statistical model to predict the next move on network only using movement history | Do you really want a statistical model, or just an algorithm for guessing the next node given all previous ones? If the latter then consider proceeding as follows.
Suppose you've gone $\ldots\rightarrow A\rightarrow B\rightarrow C$ and need to decide which of $X$, $Y$ or $Z$ is the most likely next node.
First-order ... | Statistical model to predict the next move on network only using movement history | Do you really want a statistical model, or just an algorithm for guessing the next node given all previous ones? If the latter then consider proceeding as follows.
Suppose you've gone $\ldots\rightar | Statistical model to predict the next move on network only using movement history
Do you really want a statistical model, or just an algorithm for guessing the next node given all previous ones? If the latter then consider proceeding as follows.
Suppose you've gone $\ldots\rightarrow A\rightarrow B\rightarrow C$ and n... | Statistical model to predict the next move on network only using movement history
Do you really want a statistical model, or just an algorithm for guessing the next node given all previous ones? If the latter then consider proceeding as follows.
Suppose you've gone $\ldots\rightar |
36,915 | Statistical model to predict the next move on network only using movement history | Hint for the non-time varying version: You can treat this as updating (use Bayes' theorem) probability estimates given some data. A multinomial likelihood and Dirichlet prior would be the standard approach. https://en.wikipedia.org/wiki/Dirichlet-multinomial_distribution
For the prior it sounds like you would want the ... | Statistical model to predict the next move on network only using movement history | Hint for the non-time varying version: You can treat this as updating (use Bayes' theorem) probability estimates given some data. A multinomial likelihood and Dirichlet prior would be the standard app | Statistical model to predict the next move on network only using movement history
Hint for the non-time varying version: You can treat this as updating (use Bayes' theorem) probability estimates given some data. A multinomial likelihood and Dirichlet prior would be the standard approach. https://en.wikipedia.org/wiki/D... | Statistical model to predict the next move on network only using movement history
Hint for the non-time varying version: You can treat this as updating (use Bayes' theorem) probability estimates given some data. A multinomial likelihood and Dirichlet prior would be the standard app |
36,916 | Statistical model to predict the next move on network only using movement history | A few answers and a few questions.
For simplicity let's start by assuming you're just seeing one long chain of movements. The simplest model would involve a Multinomial distribution for each node (essentially at each node there is a specific die to roll to determine where you go next). Our goal would be to estimate t... | Statistical model to predict the next move on network only using movement history | A few answers and a few questions.
For simplicity let's start by assuming you're just seeing one long chain of movements. The simplest model would involve a Multinomial distribution for each node (es | Statistical model to predict the next move on network only using movement history
A few answers and a few questions.
For simplicity let's start by assuming you're just seeing one long chain of movements. The simplest model would involve a Multinomial distribution for each node (essentially at each node there is a spec... | Statistical model to predict the next move on network only using movement history
A few answers and a few questions.
For simplicity let's start by assuming you're just seeing one long chain of movements. The simplest model would involve a Multinomial distribution for each node (es |
36,917 | What is the point of graphical models? | The value and power of graphical models of conditional probabilistic relations is that they convey information about the causal structure and inferential structure of the system. For example, rain or sprinklers can cause wet sidewalks, but wet sidewalks cannot cause rain or sprinklers spraying. If your evidence is "r... | What is the point of graphical models? | The value and power of graphical models of conditional probabilistic relations is that they convey information about the causal structure and inferential structure of the system. For example, rain or | What is the point of graphical models?
The value and power of graphical models of conditional probabilistic relations is that they convey information about the causal structure and inferential structure of the system. For example, rain or sprinklers can cause wet sidewalks, but wet sidewalks cannot cause rain or sprin... | What is the point of graphical models?
The value and power of graphical models of conditional probabilistic relations is that they convey information about the causal structure and inferential structure of the system. For example, rain or |
36,918 | Runs of the same type within a deck of cards - distribution of runs of different length | Let $I_i^c$ be an indicator variable such that:
$$
I_i^c =
\begin{cases}
1 & \text{run of length $c$ starts at $i^{th}$ position}, \\
0 & \text{otherwise}
\end{cases}
$$
To find $\mathbb{E}[R_c]$ where $R_c$ represents a run of length $c$ we simply make use of this identity(For a run to be of length $c$ it must start a... | Runs of the same type within a deck of cards - distribution of runs of different length | Let $I_i^c$ be an indicator variable such that:
$$
I_i^c =
\begin{cases}
1 & \text{run of length $c$ starts at $i^{th}$ position}, \\
0 & \text{otherwise}
\end{cases}
$$
To find $\mathbb{E}[R_c]$ wher | Runs of the same type within a deck of cards - distribution of runs of different length
Let $I_i^c$ be an indicator variable such that:
$$
I_i^c =
\begin{cases}
1 & \text{run of length $c$ starts at $i^{th}$ position}, \\
0 & \text{otherwise}
\end{cases}
$$
To find $\mathbb{E}[R_c]$ where $R_c$ represents a run of leng... | Runs of the same type within a deck of cards - distribution of runs of different length
Let $I_i^c$ be an indicator variable such that:
$$
I_i^c =
\begin{cases}
1 & \text{run of length $c$ starts at $i^{th}$ position}, \\
0 & \text{otherwise}
\end{cases}
$$
To find $\mathbb{E}[R_c]$ wher |
36,919 | How to test the difference in two proportions when the outcomes aren't binary? | The first part seems indeed reasonable.
Concerning the second part, I think these ratios can't be handled as proportions because they are not related to binary events, this imply that we have no clue how these ratios are distributed, which excludes z-test (well unless you have a lucky empirical normal distribution, but... | How to test the difference in two proportions when the outcomes aren't binary? | The first part seems indeed reasonable.
Concerning the second part, I think these ratios can't be handled as proportions because they are not related to binary events, this imply that we have no clue | How to test the difference in two proportions when the outcomes aren't binary?
The first part seems indeed reasonable.
Concerning the second part, I think these ratios can't be handled as proportions because they are not related to binary events, this imply that we have no clue how these ratios are distributed, which e... | How to test the difference in two proportions when the outcomes aren't binary?
The first part seems indeed reasonable.
Concerning the second part, I think these ratios can't be handled as proportions because they are not related to binary events, this imply that we have no clue |
36,920 | What is the term for the product of a probability and its complement? | (So this doesn't go completely unanswered)
I've never seen a term for it.
You could call it "the variance of a Bernoulli' I guess, or something similar referencing logistic regression, but I like what you called it in the title.
I expect it could have several names in particular application areas, but I really don't ... | What is the term for the product of a probability and its complement? | (So this doesn't go completely unanswered)
I've never seen a term for it.
You could call it "the variance of a Bernoulli' I guess, or something similar referencing logistic regression, but I like wha | What is the term for the product of a probability and its complement?
(So this doesn't go completely unanswered)
I've never seen a term for it.
You could call it "the variance of a Bernoulli' I guess, or something similar referencing logistic regression, but I like what you called it in the title.
I expect it could h... | What is the term for the product of a probability and its complement?
(So this doesn't go completely unanswered)
I've never seen a term for it.
You could call it "the variance of a Bernoulli' I guess, or something similar referencing logistic regression, but I like wha |
36,921 | Are aov() with Error() same as lmer() of lme4 package in R? | That the two models give identical $p$ values, and that $\sqrt{F}=\sqrt{45.85}=6.77=t$, is strong a priori evidence that models are indeed the same. Both end up fitting the model
$$
\begin{split}
\mu_{it} & = \beta_0 + b_{0,i} + (\beta_1 + b_{1,i}) t \\
Y_i & \sim \textrm{Normal}(\mu_{it}, \sigma^2) \\
\boldsymbol{b} &... | Are aov() with Error() same as lmer() of lme4 package in R? | That the two models give identical $p$ values, and that $\sqrt{F}=\sqrt{45.85}=6.77=t$, is strong a priori evidence that models are indeed the same. Both end up fitting the model
$$
\begin{split}
\mu_ | Are aov() with Error() same as lmer() of lme4 package in R?
That the two models give identical $p$ values, and that $\sqrt{F}=\sqrt{45.85}=6.77=t$, is strong a priori evidence that models are indeed the same. Both end up fitting the model
$$
\begin{split}
\mu_{it} & = \beta_0 + b_{0,i} + (\beta_1 + b_{1,i}) t \\
Y_i & ... | Are aov() with Error() same as lmer() of lme4 package in R?
That the two models give identical $p$ values, and that $\sqrt{F}=\sqrt{45.85}=6.77=t$, is strong a priori evidence that models are indeed the same. Both end up fitting the model
$$
\begin{split}
\mu_ |
36,922 | How to test if social structure is non-random and resulting from genetic relatedness – and how to deal with demography effect | Now I will create two distance matrices. First is association matrix derived from co-occurence data represented by OR-SP index. Observed Roost-Sharing Proportion is calculated for each pair of individuals by dividing the number of days two individuals were found together by the number of all possible days they could be... | How to test if social structure is non-random and resulting from genetic relatedness – and how to de | Now I will create two distance matrices. First is association matrix derived from co-occurence data represented by OR-SP index. Observed Roost-Sharing Proportion is calculated for each pair of individ | How to test if social structure is non-random and resulting from genetic relatedness – and how to deal with demography effect
Now I will create two distance matrices. First is association matrix derived from co-occurence data represented by OR-SP index. Observed Roost-Sharing Proportion is calculated for each pair of i... | How to test if social structure is non-random and resulting from genetic relatedness – and how to de
Now I will create two distance matrices. First is association matrix derived from co-occurence data represented by OR-SP index. Observed Roost-Sharing Proportion is calculated for each pair of individ |
36,923 | How to test if social structure is non-random and resulting from genetic relatedness – and how to deal with demography effect | I think your question might be less of a method question and more of a theoretical question about what you are trying to achieve with your data.
If you are interested in co-occurences only, does it really matters that some individuals have more time than other to form ties in order to find subgroups?
Now, you could th... | How to test if social structure is non-random and resulting from genetic relatedness – and how to de | I think your question might be less of a method question and more of a theoretical question about what you are trying to achieve with your data.
If you are interested in co-occurences only, does it r | How to test if social structure is non-random and resulting from genetic relatedness – and how to deal with demography effect
I think your question might be less of a method question and more of a theoretical question about what you are trying to achieve with your data.
If you are interested in co-occurences only, doe... | How to test if social structure is non-random and resulting from genetic relatedness – and how to de
I think your question might be less of a method question and more of a theoretical question about what you are trying to achieve with your data.
If you are interested in co-occurences only, does it r |
36,924 | Role of base measure in exponential family | Since $p(x|\theta)$ must integrate to 1, $h(x)$ must be non-negative, but that's the only restriction (according to page 111 in this book).
However, I think the question highlights a common confusion (at least one that I've had before). There isn't just one exponential family of distributions. Rather, there are many s... | Role of base measure in exponential family | Since $p(x|\theta)$ must integrate to 1, $h(x)$ must be non-negative, but that's the only restriction (according to page 111 in this book).
However, I think the question highlights a common confusion | Role of base measure in exponential family
Since $p(x|\theta)$ must integrate to 1, $h(x)$ must be non-negative, but that's the only restriction (according to page 111 in this book).
However, I think the question highlights a common confusion (at least one that I've had before). There isn't just one exponential family ... | Role of base measure in exponential family
Since $p(x|\theta)$ must integrate to 1, $h(x)$ must be non-negative, but that's the only restriction (according to page 111 in this book).
However, I think the question highlights a common confusion |
36,925 | Role of base measure in exponential family | The central restriction is that $h(x)$ cannot depend on the parameters $\theta$. Intuitively, the base measure is the distribution of $x$ when the exponential term is given no weight i.e. $\theta=0$.
As mentioned in a comment to your question, this is related to the distinction between a family of distributions being a... | Role of base measure in exponential family | The central restriction is that $h(x)$ cannot depend on the parameters $\theta$. Intuitively, the base measure is the distribution of $x$ when the exponential term is given no weight i.e. $\theta=0$.
| Role of base measure in exponential family
The central restriction is that $h(x)$ cannot depend on the parameters $\theta$. Intuitively, the base measure is the distribution of $x$ when the exponential term is given no weight i.e. $\theta=0$.
As mentioned in a comment to your question, this is related to the distinctio... | Role of base measure in exponential family
The central restriction is that $h(x)$ cannot depend on the parameters $\theta$. Intuitively, the base measure is the distribution of $x$ when the exponential term is given no weight i.e. $\theta=0$.
|
36,926 | Why variance of dependent variable differs from variance of error term in linear regression? | G. Seber assumes that $X\beta$ is constant. You do not assume that in your verification. If $X$ is random, then $Var(Y)=Var(X\beta+\varepsilon)=Var(X\beta)+Var(\varepsilon)$, with additional assumption that $X$ is independent from $\varepsilon$. In theory if $X$ is fixed then $Var(X\beta)=0$. Since you take a sample $X... | Why variance of dependent variable differs from variance of error term in linear regression? | G. Seber assumes that $X\beta$ is constant. You do not assume that in your verification. If $X$ is random, then $Var(Y)=Var(X\beta+\varepsilon)=Var(X\beta)+Var(\varepsilon)$, with additional assumptio | Why variance of dependent variable differs from variance of error term in linear regression?
G. Seber assumes that $X\beta$ is constant. You do not assume that in your verification. If $X$ is random, then $Var(Y)=Var(X\beta+\varepsilon)=Var(X\beta)+Var(\varepsilon)$, with additional assumption that $X$ is independent f... | Why variance of dependent variable differs from variance of error term in linear regression?
G. Seber assumes that $X\beta$ is constant. You do not assume that in your verification. If $X$ is random, then $Var(Y)=Var(X\beta+\varepsilon)=Var(X\beta)+Var(\varepsilon)$, with additional assumptio |
36,927 | Can bootstrap re-sampling be a re-sample of a smaller size [duplicate] | To your first question, yes. This is called block bootstrapping. Any time you think you have dependencies in your data, you should bootstrap groups of observations to capture the dependencies. The things you are bootstrapping over should be independent.
To your second question, the answer is also yes. You can make ... | Can bootstrap re-sampling be a re-sample of a smaller size [duplicate] | To your first question, yes. This is called block bootstrapping. Any time you think you have dependencies in your data, you should bootstrap groups of observations to capture the dependencies. The | Can bootstrap re-sampling be a re-sample of a smaller size [duplicate]
To your first question, yes. This is called block bootstrapping. Any time you think you have dependencies in your data, you should bootstrap groups of observations to capture the dependencies. The things you are bootstrapping over should be indep... | Can bootstrap re-sampling be a re-sample of a smaller size [duplicate]
To your first question, yes. This is called block bootstrapping. Any time you think you have dependencies in your data, you should bootstrap groups of observations to capture the dependencies. The |
36,928 | Can bootstrap re-sampling be a re-sample of a smaller size [duplicate] | This was asked a long time ago, but I wrote an answer for a very similar question (maybe these should be linked?) and will post it here as well in case anyone discovers this question in future.
For your first question, @Bill is right -- you should "block bootstrap" the individuals to ensure the dependence structures wi... | Can bootstrap re-sampling be a re-sample of a smaller size [duplicate] | This was asked a long time ago, but I wrote an answer for a very similar question (maybe these should be linked?) and will post it here as well in case anyone discovers this question in future.
For yo | Can bootstrap re-sampling be a re-sample of a smaller size [duplicate]
This was asked a long time ago, but I wrote an answer for a very similar question (maybe these should be linked?) and will post it here as well in case anyone discovers this question in future.
For your first question, @Bill is right -- you should "... | Can bootstrap re-sampling be a re-sample of a smaller size [duplicate]
This was asked a long time ago, but I wrote an answer for a very similar question (maybe these should be linked?) and will post it here as well in case anyone discovers this question in future.
For yo |
36,929 | What is a reasonable noninformative prior for quadratic and cubic coefficients in Bayesian polynomial regression? | To be honest, in the absence of a clear theory, I'd be inclined to frame the model in terms of orthogonal polynomials, and then put priors on the higher order terms that indicate that I expect them to be small -- which would tend to pull the posterior toward zero, rather than be uninformative.
If I wanted an uninforma... | What is a reasonable noninformative prior for quadratic and cubic coefficients in Bayesian polynomia | To be honest, in the absence of a clear theory, I'd be inclined to frame the model in terms of orthogonal polynomials, and then put priors on the higher order terms that indicate that I expect them t | What is a reasonable noninformative prior for quadratic and cubic coefficients in Bayesian polynomial regression?
To be honest, in the absence of a clear theory, I'd be inclined to frame the model in terms of orthogonal polynomials, and then put priors on the higher order terms that indicate that I expect them to be s... | What is a reasonable noninformative prior for quadratic and cubic coefficients in Bayesian polynomia
To be honest, in the absence of a clear theory, I'd be inclined to frame the model in terms of orthogonal polynomials, and then put priors on the higher order terms that indicate that I expect them t |
36,930 | What is a reasonable noninformative prior for quadratic and cubic coefficients in Bayesian polynomial regression? | Have you tried to use Jeffrey's prior? This is a standard method for generating non-informative priors (though I admit I have no experience with complicated likelihood functions you have mentioned)
http://en.wikipedia.org/wiki/Jeffreys_prior
The basic idea is that a non-informative prior will contain no information on ... | What is a reasonable noninformative prior for quadratic and cubic coefficients in Bayesian polynomia | Have you tried to use Jeffrey's prior? This is a standard method for generating non-informative priors (though I admit I have no experience with complicated likelihood functions you have mentioned)
ht | What is a reasonable noninformative prior for quadratic and cubic coefficients in Bayesian polynomial regression?
Have you tried to use Jeffrey's prior? This is a standard method for generating non-informative priors (though I admit I have no experience with complicated likelihood functions you have mentioned)
http://e... | What is a reasonable noninformative prior for quadratic and cubic coefficients in Bayesian polynomia
Have you tried to use Jeffrey's prior? This is a standard method for generating non-informative priors (though I admit I have no experience with complicated likelihood functions you have mentioned)
ht |
36,931 | Null deviance in glm R | Thanks to @jbaums.
y = c(2,3,6,7,8,9,10,12,15)
x = c(-1, -1, 0, 0, 0, 0, 1, 1, 1)
For the no intercept null model we have:
$$
Y \sim {\rm Poisson}(1)
$$
leading to the following null model likelihood term:
$$
\mathcal L(y) = \exp(-1)/y!
$$
or loglikelihood term:
$$
l(y) = -1 - \log(y!)
$$
The log-likehood for t... | Null deviance in glm R | Thanks to @jbaums.
y = c(2,3,6,7,8,9,10,12,15)
x = c(-1, -1, 0, 0, 0, 0, 1, 1, 1)
For the no intercept null model we have:
$$
Y \sim {\rm Poisson}(1)
$$
leading to the following null model likelih | Null deviance in glm R
Thanks to @jbaums.
y = c(2,3,6,7,8,9,10,12,15)
x = c(-1, -1, 0, 0, 0, 0, 1, 1, 1)
For the no intercept null model we have:
$$
Y \sim {\rm Poisson}(1)
$$
leading to the following null model likelihood term:
$$
\mathcal L(y) = \exp(-1)/y!
$$
or loglikelihood term:
$$
l(y) = -1 - \log(y!)
$$... | Null deviance in glm R
Thanks to @jbaums.
y = c(2,3,6,7,8,9,10,12,15)
x = c(-1, -1, 0, 0, 0, 0, 1, 1, 1)
For the no intercept null model we have:
$$
Y \sim {\rm Poisson}(1)
$$
leading to the following null model likelih |
36,932 | Updating bias with RBMs (Restricted Boltzmann Machines) | TLDR
For $n$-step Contrastive Divergence, update visible bias $b_j$, based on data vector $\mathbf{d}$ using:
$$
b_j^{(t)} \gets b_j^{(t-1)} + \eta \left( d_j - \hat{v}_j^{(n)} \right)
$$
Update hidden bias $h_i$ using:
$$
c_i^{(t)} \gets c_i^{(t-1)} + \eta \left( \hat{h}_{i}^{(0)} - \hat{h}_{i}^{(n)} \right)
$$
Where ... | Updating bias with RBMs (Restricted Boltzmann Machines) | TLDR
For $n$-step Contrastive Divergence, update visible bias $b_j$, based on data vector $\mathbf{d}$ using:
$$
b_j^{(t)} \gets b_j^{(t-1)} + \eta \left( d_j - \hat{v}_j^{(n)} \right)
$$
Update hidde | Updating bias with RBMs (Restricted Boltzmann Machines)
TLDR
For $n$-step Contrastive Divergence, update visible bias $b_j$, based on data vector $\mathbf{d}$ using:
$$
b_j^{(t)} \gets b_j^{(t-1)} + \eta \left( d_j - \hat{v}_j^{(n)} \right)
$$
Update hidden bias $h_i$ using:
$$
c_i^{(t)} \gets c_i^{(t-1)} + \eta \left(... | Updating bias with RBMs (Restricted Boltzmann Machines)
TLDR
For $n$-step Contrastive Divergence, update visible bias $b_j$, based on data vector $\mathbf{d}$ using:
$$
b_j^{(t)} \gets b_j^{(t-1)} + \eta \left( d_j - \hat{v}_j^{(n)} \right)
$$
Update hidde |
36,933 | Should I use epochs > 1 when training data is unlimited? | If you have access to unlimited data, unless the order in which that data is generated has an influence on the data, it is better not to have epochs and just train for as long as desired while synthetising examples on the fly. (You want each of your examples to be iid).
However, if your data generating process is bias... | Should I use epochs > 1 when training data is unlimited? | If you have access to unlimited data, unless the order in which that data is generated has an influence on the data, it is better not to have epochs and just train for as long as desired while synthet | Should I use epochs > 1 when training data is unlimited?
If you have access to unlimited data, unless the order in which that data is generated has an influence on the data, it is better not to have epochs and just train for as long as desired while synthetising examples on the fly. (You want each of your examples to b... | Should I use epochs > 1 when training data is unlimited?
If you have access to unlimited data, unless the order in which that data is generated has an influence on the data, it is better not to have epochs and just train for as long as desired while synthet |
36,934 | Should I use epochs > 1 when training data is unlimited? | For this issue you can use Online learning. Defenition you can find at Wikipedia. More information about online learning in NN you can check at this article. | Should I use epochs > 1 when training data is unlimited? | For this issue you can use Online learning. Defenition you can find at Wikipedia. More information about online learning in NN you can check at this article. | Should I use epochs > 1 when training data is unlimited?
For this issue you can use Online learning. Defenition you can find at Wikipedia. More information about online learning in NN you can check at this article. | Should I use epochs > 1 when training data is unlimited?
For this issue you can use Online learning. Defenition you can find at Wikipedia. More information about online learning in NN you can check at this article. |
36,935 | Distribution of the Levenshtein distance between two random strings | I guess it is not a direct answer, but you can try to simulate the scenario and check the empirical distribution to have a rough idea (R code below).
So it seems that for strings longer than ~ 100 the distribution is symmetric and quite narrow around .53 times the length of the string.
# dependencies
library(ggplot2... | Distribution of the Levenshtein distance between two random strings | I guess it is not a direct answer, but you can try to simulate the scenario and check the empirical distribution to have a rough idea (R code below).
So it seems that for strings longer than ~ 100 t | Distribution of the Levenshtein distance between two random strings
I guess it is not a direct answer, but you can try to simulate the scenario and check the empirical distribution to have a rough idea (R code below).
So it seems that for strings longer than ~ 100 the distribution is symmetric and quite narrow around... | Distribution of the Levenshtein distance between two random strings
I guess it is not a direct answer, but you can try to simulate the scenario and check the empirical distribution to have a rough idea (R code below).
So it seems that for strings longer than ~ 100 t |
36,936 | Distribution of the Levenshtein distance between two random strings | This looks a bit like the Tracy-Widom distribution perhaps? For longest common subsequences there is a "famous" result relating the distribution of LCS between random strings (under a bunch of limiting assumptions) to the Tracy-Widom distribution: https://arxiv.org/abs/q-bio/0410012. https://www.quantamagazine.org/beyo... | Distribution of the Levenshtein distance between two random strings | This looks a bit like the Tracy-Widom distribution perhaps? For longest common subsequences there is a "famous" result relating the distribution of LCS between random strings (under a bunch of limitin | Distribution of the Levenshtein distance between two random strings
This looks a bit like the Tracy-Widom distribution perhaps? For longest common subsequences there is a "famous" result relating the distribution of LCS between random strings (under a bunch of limiting assumptions) to the Tracy-Widom distribution: http... | Distribution of the Levenshtein distance between two random strings
This looks a bit like the Tracy-Widom distribution perhaps? For longest common subsequences there is a "famous" result relating the distribution of LCS between random strings (under a bunch of limitin |
36,937 | normalization effect on polynomial regression | Polynomial (least squares) regression of data $\newcommand{\y}{\mathrm{y}}\y$ (thought of as an $n$-vector $(y_i)$) against a variable $\newcommand{\x}{\mathrm{x}}\x$ (also an $n$-vector ($x_i)$) uses the variables $\mathrm {1} = \x^0$ (a constant $n$-vector), $\x = \x^1$, $\x^2 = (x_i^2)$, ... and $\x^d = (x_i^d)$. T... | normalization effect on polynomial regression | Polynomial (least squares) regression of data $\newcommand{\y}{\mathrm{y}}\y$ (thought of as an $n$-vector $(y_i)$) against a variable $\newcommand{\x}{\mathrm{x}}\x$ (also an $n$-vector ($x_i)$) uses | normalization effect on polynomial regression
Polynomial (least squares) regression of data $\newcommand{\y}{\mathrm{y}}\y$ (thought of as an $n$-vector $(y_i)$) against a variable $\newcommand{\x}{\mathrm{x}}\x$ (also an $n$-vector ($x_i)$) uses the variables $\mathrm {1} = \x^0$ (a constant $n$-vector), $\x = \x^1$, ... | normalization effect on polynomial regression
Polynomial (least squares) regression of data $\newcommand{\y}{\mathrm{y}}\y$ (thought of as an $n$-vector $(y_i)$) against a variable $\newcommand{\x}{\mathrm{x}}\x$ (also an $n$-vector ($x_i)$) uses |
36,938 | Working with the bootstrap sample vs the original sample | The estimator in #2 is the thing you're generating the interval for ... the sample mean. You're using the bootstrap to try to get at the sampling distribution of the sample mean, by using the resampling distribution to approximate it.
Since it's the exact same estimator in #1 and #2, #2 will have the same true properti... | Working with the bootstrap sample vs the original sample | The estimator in #2 is the thing you're generating the interval for ... the sample mean. You're using the bootstrap to try to get at the sampling distribution of the sample mean, by using the resampli | Working with the bootstrap sample vs the original sample
The estimator in #2 is the thing you're generating the interval for ... the sample mean. You're using the bootstrap to try to get at the sampling distribution of the sample mean, by using the resampling distribution to approximate it.
Since it's the exact same es... | Working with the bootstrap sample vs the original sample
The estimator in #2 is the thing you're generating the interval for ... the sample mean. You're using the bootstrap to try to get at the sampling distribution of the sample mean, by using the resampli |
36,939 | Best practice for ADF/KPSS unit root testing sequence? | The steps where the null hypothesis is rejected relates to the following processes:
Step 1.1 is related to (iii) is stationary around a linear trend,
Step 2.1 is related to (ii) is stationary around a non-zero mean,
Step 3.1 is related to (i) is stationary around a zero mean.
When the null is not rejected, then you m... | Best practice for ADF/KPSS unit root testing sequence? | The steps where the null hypothesis is rejected relates to the following processes:
Step 1.1 is related to (iii) is stationary around a linear trend,
Step 2.1 is related to (ii) is stationary around | Best practice for ADF/KPSS unit root testing sequence?
The steps where the null hypothesis is rejected relates to the following processes:
Step 1.1 is related to (iii) is stationary around a linear trend,
Step 2.1 is related to (ii) is stationary around a non-zero mean,
Step 3.1 is related to (i) is stationary around ... | Best practice for ADF/KPSS unit root testing sequence?
The steps where the null hypothesis is rejected relates to the following processes:
Step 1.1 is related to (iii) is stationary around a linear trend,
Step 2.1 is related to (ii) is stationary around |
36,940 | How to quickly identify participants responding randomly to self-report psychometric tests with many items? | Jeromy's own answer is more useful than mine, but since I am working on this myself, I have collected a few handy R code bits that can also be helpful or steer one in the right direction of detecting 'suspicious' responses.
The assumption here is that participants often (I find) respond in a pattern of some sort. Espe... | How to quickly identify participants responding randomly to self-report psychometric tests with many | Jeromy's own answer is more useful than mine, but since I am working on this myself, I have collected a few handy R code bits that can also be helpful or steer one in the right direction of detecting | How to quickly identify participants responding randomly to self-report psychometric tests with many items?
Jeromy's own answer is more useful than mine, but since I am working on this myself, I have collected a few handy R code bits that can also be helpful or steer one in the right direction of detecting 'suspicious'... | How to quickly identify participants responding randomly to self-report psychometric tests with many
Jeromy's own answer is more useful than mine, but since I am working on this myself, I have collected a few handy R code bits that can also be helpful or steer one in the right direction of detecting |
36,941 | How to quickly identify participants responding randomly to self-report psychometric tests with many items? | The careless R package on github includes a few nice functions.
https://github.com/ryentes/careless
Collection of Implementations for Indices of Careless Responding... [It] provides functions to support the computation of indices of careless
responding. Initial indices include even/odd, psychometric synonyms,
outlier,... | How to quickly identify participants responding randomly to self-report psychometric tests with many | The careless R package on github includes a few nice functions.
https://github.com/ryentes/careless
Collection of Implementations for Indices of Careless Responding... [It] provides functions to supp | How to quickly identify participants responding randomly to self-report psychometric tests with many items?
The careless R package on github includes a few nice functions.
https://github.com/ryentes/careless
Collection of Implementations for Indices of Careless Responding... [It] provides functions to support the comp... | How to quickly identify participants responding randomly to self-report psychometric tests with many
The careless R package on github includes a few nice functions.
https://github.com/ryentes/careless
Collection of Implementations for Indices of Careless Responding... [It] provides functions to supp |
36,942 | Distribution of Trace of non-centered Wishart matrix | It looks like you can find it in:
S. Kourouklis and P.G. Moschopoulos (1985) On the distribution of the trace of a non-central Wishart. Metron XLIII(1--2): 85--92.
It looks like they cover the case of general covariance matrix $\Sigma$ there.
They also give pointers to in the paper to:
Mathai, A.M. and Pillai, K.C.S. ... | Distribution of Trace of non-centered Wishart matrix | It looks like you can find it in:
S. Kourouklis and P.G. Moschopoulos (1985) On the distribution of the trace of a non-central Wishart. Metron XLIII(1--2): 85--92.
It looks like they cover the case o | Distribution of Trace of non-centered Wishart matrix
It looks like you can find it in:
S. Kourouklis and P.G. Moschopoulos (1985) On the distribution of the trace of a non-central Wishart. Metron XLIII(1--2): 85--92.
It looks like they cover the case of general covariance matrix $\Sigma$ there.
They also give pointers... | Distribution of Trace of non-centered Wishart matrix
It looks like you can find it in:
S. Kourouklis and P.G. Moschopoulos (1985) On the distribution of the trace of a non-central Wishart. Metron XLIII(1--2): 85--92.
It looks like they cover the case o |
36,943 | Longitudinal data: baseline effect versus random intercept | I assume $j=1,...,9$.
Yes, you can treat $\beta_1t_{0i}$ as object-specific intercept. The difference from random intercept is that $\beta_1t_{0i}$ is fixed. It is kind of like the difference between fixed and random effects in econometrics. All objects share the same $\beta_1$, which is then weighted by the baseline ... | Longitudinal data: baseline effect versus random intercept | I assume $j=1,...,9$.
Yes, you can treat $\beta_1t_{0i}$ as object-specific intercept. The difference from random intercept is that $\beta_1t_{0i}$ is fixed. It is kind of like the difference between | Longitudinal data: baseline effect versus random intercept
I assume $j=1,...,9$.
Yes, you can treat $\beta_1t_{0i}$ as object-specific intercept. The difference from random intercept is that $\beta_1t_{0i}$ is fixed. It is kind of like the difference between fixed and random effects in econometrics. All objects share ... | Longitudinal data: baseline effect versus random intercept
I assume $j=1,...,9$.
Yes, you can treat $\beta_1t_{0i}$ as object-specific intercept. The difference from random intercept is that $\beta_1t_{0i}$ is fixed. It is kind of like the difference between |
36,944 | Longitudinal data: baseline effect versus random intercept | First of all, I think your model specification is somewhat confusing. I would use $x_i=y_{i0}$ instead of $t_{0i}$ as $t_{ij}$ was used to represent time $j$ for individual $i$. You probably want to use baseline measurement rather than baseline time as covariate. So your model should be
$$y_{ij} = \beta_0 + \beta_1 x_i... | Longitudinal data: baseline effect versus random intercept | First of all, I think your model specification is somewhat confusing. I would use $x_i=y_{i0}$ instead of $t_{0i}$ as $t_{ij}$ was used to represent time $j$ for individual $i$. You probably want to u | Longitudinal data: baseline effect versus random intercept
First of all, I think your model specification is somewhat confusing. I would use $x_i=y_{i0}$ instead of $t_{0i}$ as $t_{ij}$ was used to represent time $j$ for individual $i$. You probably want to use baseline measurement rather than baseline time as covariat... | Longitudinal data: baseline effect versus random intercept
First of all, I think your model specification is somewhat confusing. I would use $x_i=y_{i0}$ instead of $t_{0i}$ as $t_{ij}$ was used to represent time $j$ for individual $i$. You probably want to u |
36,945 | Probabilistic interpretation from sigmoid functions | Why do we interpret the results of logistic regression as
probabilities?
Because the logistic regression model can be viewed as arising from a linear regression latent variable model, where the error term of this linear regression is assumed to follow the standard logistic distribution. See for example this post.
... | Probabilistic interpretation from sigmoid functions | Why do we interpret the results of logistic regression as
probabilities?
Because the logistic regression model can be viewed as arising from a linear regression latent variable model, where the e | Probabilistic interpretation from sigmoid functions
Why do we interpret the results of logistic regression as
probabilities?
Because the logistic regression model can be viewed as arising from a linear regression latent variable model, where the error term of this linear regression is assumed to follow the standar... | Probabilistic interpretation from sigmoid functions
Why do we interpret the results of logistic regression as
probabilities?
Because the logistic regression model can be viewed as arising from a linear regression latent variable model, where the e |
36,946 | Probabilistic interpretation from sigmoid functions | A probability is bounded between 0 and 1 (inclusive), and a sigmoid curve is a convenient curve that can be forced to respect those bounds. It is not the only one, but the sigmoid curve has proven to be the most popular one. So, not all probability models have a sigmoid cure, though many do.
Moreover, not all models wi... | Probabilistic interpretation from sigmoid functions | A probability is bounded between 0 and 1 (inclusive), and a sigmoid curve is a convenient curve that can be forced to respect those bounds. It is not the only one, but the sigmoid curve has proven to | Probabilistic interpretation from sigmoid functions
A probability is bounded between 0 and 1 (inclusive), and a sigmoid curve is a convenient curve that can be forced to respect those bounds. It is not the only one, but the sigmoid curve has proven to be the most popular one. So, not all probability models have a sigmo... | Probabilistic interpretation from sigmoid functions
A probability is bounded between 0 and 1 (inclusive), and a sigmoid curve is a convenient curve that can be forced to respect those bounds. It is not the only one, but the sigmoid curve has proven to |
36,947 | Persistence in GJR-GARCH (asymmetric GARCH) | I found an answer in the "vignette" to the "rugarch" package in R. Here is a quote from pages 7-8 (emphasis is mine):
Because of the presence of the indicator function, the persistence of
the model now crucially depends on the asymmetry of the conditional
distribution used. The persistence of the model $\hat P$ is... | Persistence in GJR-GARCH (asymmetric GARCH) | I found an answer in the "vignette" to the "rugarch" package in R. Here is a quote from pages 7-8 (emphasis is mine):
Because of the presence of the indicator function, the persistence of
the model | Persistence in GJR-GARCH (asymmetric GARCH)
I found an answer in the "vignette" to the "rugarch" package in R. Here is a quote from pages 7-8 (emphasis is mine):
Because of the presence of the indicator function, the persistence of
the model now crucially depends on the asymmetry of the conditional
distribution us... | Persistence in GJR-GARCH (asymmetric GARCH)
I found an answer in the "vignette" to the "rugarch" package in R. Here is a quote from pages 7-8 (emphasis is mine):
Because of the presence of the indicator function, the persistence of
the model |
36,948 | Interpretation of multiple logistic regression with interactions in R | The relation of age or Hip.Prox.Femhip to the probability of LENIpos depends on the value of the other variable. That is suggested by the interaction term in your second model. In the usual R presentaton of regression coefficients, the coefficient for age in the second model is the relation of LENIpos to age in the abs... | Interpretation of multiple logistic regression with interactions in R | The relation of age or Hip.Prox.Femhip to the probability of LENIpos depends on the value of the other variable. That is suggested by the interaction term in your second model. In the usual R presenta | Interpretation of multiple logistic regression with interactions in R
The relation of age or Hip.Prox.Femhip to the probability of LENIpos depends on the value of the other variable. That is suggested by the interaction term in your second model. In the usual R presentaton of regression coefficients, the coefficient fo... | Interpretation of multiple logistic regression with interactions in R
The relation of age or Hip.Prox.Femhip to the probability of LENIpos depends on the value of the other variable. That is suggested by the interaction term in your second model. In the usual R presenta |
36,949 | Interpretation of multiple logistic regression with interactions in R | @EdM is right. The fact that the interaction's p-value is .06 (i.e., 'not-significant') is meaningless; you have an interaction. Let me add a few more details to supplement his (?) answer:
A Mann-Whitney U-test of age~LENIpos isn't really the same as the univariate logistic regression of LENIpos~age (although the ... | Interpretation of multiple logistic regression with interactions in R | @EdM is right. The fact that the interaction's p-value is .06 (i.e., 'not-significant') is meaningless; you have an interaction. Let me add a few more details to supplement his (?) answer:
A Mann | Interpretation of multiple logistic regression with interactions in R
@EdM is right. The fact that the interaction's p-value is .06 (i.e., 'not-significant') is meaningless; you have an interaction. Let me add a few more details to supplement his (?) answer:
A Mann-Whitney U-test of age~LENIpos isn't really the sa... | Interpretation of multiple logistic regression with interactions in R
@EdM is right. The fact that the interaction's p-value is .06 (i.e., 'not-significant') is meaningless; you have an interaction. Let me add a few more details to supplement his (?) answer:
A Mann |
36,950 | Estimating $n$ and $p$ for Binomial distribution, repeated counting of partly hidden population | How could a Bayesian estimation proceed without additional information, is there any sensible prior for $n$?
Your question is almost exactly the same question that Adrian Raftery answers in his paper "Inference for the Binomial $N$ parameter." Instead of aquariums, the author was looking at counts of animals in a wild... | Estimating $n$ and $p$ for Binomial distribution, repeated counting of partly hidden population | How could a Bayesian estimation proceed without additional information, is there any sensible prior for $n$?
Your question is almost exactly the same question that Adrian Raftery answers in his paper | Estimating $n$ and $p$ for Binomial distribution, repeated counting of partly hidden population
How could a Bayesian estimation proceed without additional information, is there any sensible prior for $n$?
Your question is almost exactly the same question that Adrian Raftery answers in his paper "Inference for the Bino... | Estimating $n$ and $p$ for Binomial distribution, repeated counting of partly hidden population
How could a Bayesian estimation proceed without additional information, is there any sensible prior for $n$?
Your question is almost exactly the same question that Adrian Raftery answers in his paper |
36,951 | How does Vowpal Wabbit handle NA's or missing values? [closed] | To elaborate on my answer:
Lets say the first line of your data is:
y, v1, v2, v3
10, 5, NA, 3
The VW string encoding of that line is:
10 |v1:4 v2:NA v3:3
As you probably discovered v2:NA doesn't work for VW, as the part after the colon needs to be a number.
An easy solution to this is to find :NA in your VW string... | How does Vowpal Wabbit handle NA's or missing values? [closed] | To elaborate on my answer:
Lets say the first line of your data is:
y, v1, v2, v3
10, 5, NA, 3
The VW string encoding of that line is:
10 |v1:4 v2:NA v3:3
As you probably discovered v2:NA doesn't | How does Vowpal Wabbit handle NA's or missing values? [closed]
To elaborate on my answer:
Lets say the first line of your data is:
y, v1, v2, v3
10, 5, NA, 3
The VW string encoding of that line is:
10 |v1:4 v2:NA v3:3
As you probably discovered v2:NA doesn't work for VW, as the part after the colon needs to be a nu... | How does Vowpal Wabbit handle NA's or missing values? [closed]
To elaborate on my answer:
Lets say the first line of your data is:
y, v1, v2, v3
10, 5, NA, 3
The VW string encoding of that line is:
10 |v1:4 v2:NA v3:3
As you probably discovered v2:NA doesn't |
36,952 | two-sample Kolmogorov-Smirnov test p-value in R confusion | No, it's wrong. The default Kolmogorov-Smirnov in R is already two sided (i.e. already tests $F_X\neq F_Y$ rather than $F_X<F_Y$ or $F_X>F_Y$ (in all three cases, we should add "somewhere").
If you had done a one-tailed test but intended to do a two tail test (and if the sample turned out to have a difference in the di... | two-sample Kolmogorov-Smirnov test p-value in R confusion | No, it's wrong. The default Kolmogorov-Smirnov in R is already two sided (i.e. already tests $F_X\neq F_Y$ rather than $F_X<F_Y$ or $F_X>F_Y$ (in all three cases, we should add "somewhere").
If you ha | two-sample Kolmogorov-Smirnov test p-value in R confusion
No, it's wrong. The default Kolmogorov-Smirnov in R is already two sided (i.e. already tests $F_X\neq F_Y$ rather than $F_X<F_Y$ or $F_X>F_Y$ (in all three cases, we should add "somewhere").
If you had done a one-tailed test but intended to do a two tail test (a... | two-sample Kolmogorov-Smirnov test p-value in R confusion
No, it's wrong. The default Kolmogorov-Smirnov in R is already two sided (i.e. already tests $F_X\neq F_Y$ rather than $F_X<F_Y$ or $F_X>F_Y$ (in all three cases, we should add "somewhere").
If you ha |
36,953 | Combining data from different sources | Your model estimate would be a useful prior.
I have applied the following approach in LeBauer et al 2013, and have adapted code from priors_demo.Rmd below.
To parameterize this prior using simulation, consider your model
$$ \textrm{logLC}_{50} = b_0 X+b_1$$
Assume $b_0 \sim N(0.94, 0.03)$ and $b_1 \sim N(1.33, ... | Combining data from different sources | Your model estimate would be a useful prior.
I have applied the following approach in LeBauer et al 2013, and have adapted code from priors_demo.Rmd below.
To parameterize this prior using simu | Combining data from different sources
Your model estimate would be a useful prior.
I have applied the following approach in LeBauer et al 2013, and have adapted code from priors_demo.Rmd below.
To parameterize this prior using simulation, consider your model
$$ \textrm{logLC}_{50} = b_0 X+b_1$$
Assume $b_0 \sim... | Combining data from different sources
Your model estimate would be a useful prior.
I have applied the following approach in LeBauer et al 2013, and have adapted code from priors_demo.Rmd below.
To parameterize this prior using simu |
36,954 | Calculating Perplexity | I stumbled upon this searching how perplexity is calculated. I think applying the Jurafsky formula I find the right number (I used R):
P1 <- 1/4
P2 <- 1/4
P3 <- 1/4
P4 <- 1/120000
SP <- P1*P2*P3*P4
Result <- SP**(-1/4)
Result is 52.64296 | Calculating Perplexity | I stumbled upon this searching how perplexity is calculated. I think applying the Jurafsky formula I find the right number (I used R):
P1 <- 1/4
P2 <- 1/4
P3 <- 1/4
P4 <- 1/120000
SP <- P1*P2*P3*P4
R | Calculating Perplexity
I stumbled upon this searching how perplexity is calculated. I think applying the Jurafsky formula I find the right number (I used R):
P1 <- 1/4
P2 <- 1/4
P3 <- 1/4
P4 <- 1/120000
SP <- P1*P2*P3*P4
Result <- SP**(-1/4)
Result is 52.64296 | Calculating Perplexity
I stumbled upon this searching how perplexity is calculated. I think applying the Jurafsky formula I find the right number (I used R):
P1 <- 1/4
P2 <- 1/4
P3 <- 1/4
P4 <- 1/120000
SP <- P1*P2*P3*P4
R |
36,955 | Calculating Perplexity | I interpreted the probabilities here as:
Let's imagine there are 120000 words in total, where by probability distribution:
Operator, Sales and Technical Support each occur 30,000 times (P = 1/4)
Each of the name occur only once (P = 1/120000).
Perplexity can be calculated then, using the formula:
$(\frac{1}{4}^{30000}... | Calculating Perplexity | I interpreted the probabilities here as:
Let's imagine there are 120000 words in total, where by probability distribution:
Operator, Sales and Technical Support each occur 30,000 times (P = 1/4)
Each | Calculating Perplexity
I interpreted the probabilities here as:
Let's imagine there are 120000 words in total, where by probability distribution:
Operator, Sales and Technical Support each occur 30,000 times (P = 1/4)
Each of the name occur only once (P = 1/120000).
Perplexity can be calculated then, using the formula:... | Calculating Perplexity
I interpreted the probabilities here as:
Let's imagine there are 120000 words in total, where by probability distribution:
Operator, Sales and Technical Support each occur 30,000 times (P = 1/4)
Each |
36,956 | How to summarize GAM model result from multiple imputation data in R | First, GAM's are basically a combination of GLMs, splines, and ridge regression (loosely speaking). You might be well advised to work on your understanding of these three things before attempting to work with their combination.
Second, I've done multiple imputation with GAMs, but not with mice.
In general, you're inte... | How to summarize GAM model result from multiple imputation data in R | First, GAM's are basically a combination of GLMs, splines, and ridge regression (loosely speaking). You might be well advised to work on your understanding of these three things before attempting to | How to summarize GAM model result from multiple imputation data in R
First, GAM's are basically a combination of GLMs, splines, and ridge regression (loosely speaking). You might be well advised to work on your understanding of these three things before attempting to work with their combination.
Second, I've done mult... | How to summarize GAM model result from multiple imputation data in R
First, GAM's are basically a combination of GLMs, splines, and ridge regression (loosely speaking). You might be well advised to work on your understanding of these three things before attempting to |
36,957 | How to summarize GAM model result from multiple imputation data in R | See https://stat.ethz.ch/R-manual/R-devel/library/mgcv/html/missing.data.html
Or enter help(mgcv::missing.data) in an R session. An approach that can be effective, with sample code on the help page, is then to
substitute a simple random effects model in which the by variable
mechanism is used to set s(x) to zer... | How to summarize GAM model result from multiple imputation data in R | See https://stat.ethz.ch/R-manual/R-devel/library/mgcv/html/missing.data.html
Or enter help(mgcv::missing.data) in an R session. An approach that can be effective, with sample code on the help page, | How to summarize GAM model result from multiple imputation data in R
See https://stat.ethz.ch/R-manual/R-devel/library/mgcv/html/missing.data.html
Or enter help(mgcv::missing.data) in an R session. An approach that can be effective, with sample code on the help page, is then to
substitute a simple random effects mo... | How to summarize GAM model result from multiple imputation data in R
See https://stat.ethz.ch/R-manual/R-devel/library/mgcv/html/missing.data.html
Or enter help(mgcv::missing.data) in an R session. An approach that can be effective, with sample code on the help page, |
36,958 | MLE for mean of symmetric but otherwise unknown distribution | Consider the single-parameter Exponential Family of distributions, i.e. distributions whose probability density (or mass) function can be written as
$$f(x) = h(x)\cdot \exp{\big\{\eta(\theta)T(x)-A(\theta)\big\}}$$
The log-likelihood from an i.i.d sample of size $n$ is then
$$\tilde L = \sum_{i=1}^n\ln h(x_i) + \eta(\t... | MLE for mean of symmetric but otherwise unknown distribution | Consider the single-parameter Exponential Family of distributions, i.e. distributions whose probability density (or mass) function can be written as
$$f(x) = h(x)\cdot \exp{\big\{\eta(\theta)T(x)-A(\t | MLE for mean of symmetric but otherwise unknown distribution
Consider the single-parameter Exponential Family of distributions, i.e. distributions whose probability density (or mass) function can be written as
$$f(x) = h(x)\cdot \exp{\big\{\eta(\theta)T(x)-A(\theta)\big\}}$$
The log-likelihood from an i.i.d sample of s... | MLE for mean of symmetric but otherwise unknown distribution
Consider the single-parameter Exponential Family of distributions, i.e. distributions whose probability density (or mass) function can be written as
$$f(x) = h(x)\cdot \exp{\big\{\eta(\theta)T(x)-A(\t |
36,959 | Deviance Residuals | Any of the various forms of residuals used in connection with GLMs (raw, Pearson, deviance, Anscombe and even working residuals) can be difficult to interpret visually.
However, broadly speaking, your deviance residuals should be expected to have mean close to 0 and nearly constant variance, when plotted against any pr... | Deviance Residuals | Any of the various forms of residuals used in connection with GLMs (raw, Pearson, deviance, Anscombe and even working residuals) can be difficult to interpret visually.
However, broadly speaking, your | Deviance Residuals
Any of the various forms of residuals used in connection with GLMs (raw, Pearson, deviance, Anscombe and even working residuals) can be difficult to interpret visually.
However, broadly speaking, your deviance residuals should be expected to have mean close to 0 and nearly constant variance, when plo... | Deviance Residuals
Any of the various forms of residuals used in connection with GLMs (raw, Pearson, deviance, Anscombe and even working residuals) can be difficult to interpret visually.
However, broadly speaking, your |
36,960 | Can effective sample size in MCMC simulation be greater than the actual sample size? | For a particular definition of autocorrelation, negative autocorrelation can cause $N_{eff} > n$. This answer gives a MWE using coda. | Can effective sample size in MCMC simulation be greater than the actual sample size? | For a particular definition of autocorrelation, negative autocorrelation can cause $N_{eff} > n$. This answer gives a MWE using coda. | Can effective sample size in MCMC simulation be greater than the actual sample size?
For a particular definition of autocorrelation, negative autocorrelation can cause $N_{eff} > n$. This answer gives a MWE using coda. | Can effective sample size in MCMC simulation be greater than the actual sample size?
For a particular definition of autocorrelation, negative autocorrelation can cause $N_{eff} > n$. This answer gives a MWE using coda. |
36,961 | Can effective sample size in MCMC simulation be greater than the actual sample size? | In principle yes, you are right. The sample size should not be larger.
One possibility is that the package is using some optimization routine to improve the variance such as VEGAS.
As kjetil b halvorsen pointed out, it could be that autocorrelation is negative. But I'm not seeing how. | Can effective sample size in MCMC simulation be greater than the actual sample size? | In principle yes, you are right. The sample size should not be larger.
One possibility is that the package is using some optimization routine to improve the variance such as VEGAS.
As kjetil b halvor | Can effective sample size in MCMC simulation be greater than the actual sample size?
In principle yes, you are right. The sample size should not be larger.
One possibility is that the package is using some optimization routine to improve the variance such as VEGAS.
As kjetil b halvorsen pointed out, it could be that a... | Can effective sample size in MCMC simulation be greater than the actual sample size?
In principle yes, you are right. The sample size should not be larger.
One possibility is that the package is using some optimization routine to improve the variance such as VEGAS.
As kjetil b halvor |
36,962 | Averaging multiple distributions | (I expand this answer to cover more completely a setup that occurs frequently, and also, to focus on the estimation of the population variance).
The setup is as follows: from $K$ independent samples that all come from a normal i.i.d. population $N(\mu, \sigma^2)$ and have varying sizes, $n_1+...+n_K = N$, we are not g... | Averaging multiple distributions | (I expand this answer to cover more completely a setup that occurs frequently, and also, to focus on the estimation of the population variance).
The setup is as follows: from $K$ independent samples | Averaging multiple distributions
(I expand this answer to cover more completely a setup that occurs frequently, and also, to focus on the estimation of the population variance).
The setup is as follows: from $K$ independent samples that all come from a normal i.i.d. population $N(\mu, \sigma^2)$ and have varying sizes... | Averaging multiple distributions
(I expand this answer to cover more completely a setup that occurs frequently, and also, to focus on the estimation of the population variance).
The setup is as follows: from $K$ independent samples |
36,963 | T-test with sample standard deviation of zero. Possible? | Since this question is getting a fair number of hits, and I stumbled across it on Google when I was looking for similar information, I am going to expand on the comments above.
The Purpose Of The T Test
What we are doing when we do a t test is measuring the number of standard deviations our measured mean is from the ba... | T-test with sample standard deviation of zero. Possible? | Since this question is getting a fair number of hits, and I stumbled across it on Google when I was looking for similar information, I am going to expand on the comments above.
The Purpose Of The T Te | T-test with sample standard deviation of zero. Possible?
Since this question is getting a fair number of hits, and I stumbled across it on Google when I was looking for similar information, I am going to expand on the comments above.
The Purpose Of The T Test
What we are doing when we do a t test is measuring the numbe... | T-test with sample standard deviation of zero. Possible?
Since this question is getting a fair number of hits, and I stumbled across it on Google when I was looking for similar information, I am going to expand on the comments above.
The Purpose Of The T Te |
36,964 | Time Varying System Matrices in Kalman Filter | If your dynamic system is
$$ x_t = A_t x_{t-1} + \eta_t $$
$$ y_t = B_t x_t + \varepsilon_t $$
Then when people say system matrices $A_t, B_t$ should be deterministic, this means that Kalman Filter gives you an estimate of state $x_t$ conditional on past and current values of parameters $$\mathbf E\left(x_t|\,y_t,\dot... | Time Varying System Matrices in Kalman Filter | If your dynamic system is
$$ x_t = A_t x_{t-1} + \eta_t $$
$$ y_t = B_t x_t + \varepsilon_t $$
Then when people say system matrices $A_t, B_t$ should be deterministic, this means that Kalman Filter g | Time Varying System Matrices in Kalman Filter
If your dynamic system is
$$ x_t = A_t x_{t-1} + \eta_t $$
$$ y_t = B_t x_t + \varepsilon_t $$
Then when people say system matrices $A_t, B_t$ should be deterministic, this means that Kalman Filter gives you an estimate of state $x_t$ conditional on past and current values... | Time Varying System Matrices in Kalman Filter
If your dynamic system is
$$ x_t = A_t x_{t-1} + \eta_t $$
$$ y_t = B_t x_t + \varepsilon_t $$
Then when people say system matrices $A_t, B_t$ should be deterministic, this means that Kalman Filter g |
36,965 | Time Varying System Matrices in Kalman Filter | Can the evolution of time varying system matrices be stochastic?
Yes. If your model is
$$ x_t = A_t x_{t-1} + \eta_t $$
$$ y_t = B_t x_t + \varepsilon_t $$
and you assume further that $A_t$ and $B_t$ are themselves latent Markov processes, then you might have a model amenable to particle filtering, and in particular R... | Time Varying System Matrices in Kalman Filter | Can the evolution of time varying system matrices be stochastic?
Yes. If your model is
$$ x_t = A_t x_{t-1} + \eta_t $$
$$ y_t = B_t x_t + \varepsilon_t $$
and you assume further that $A_t$ and $B_t$ | Time Varying System Matrices in Kalman Filter
Can the evolution of time varying system matrices be stochastic?
Yes. If your model is
$$ x_t = A_t x_{t-1} + \eta_t $$
$$ y_t = B_t x_t + \varepsilon_t $$
and you assume further that $A_t$ and $B_t$ are themselves latent Markov processes, then you might have a model amena... | Time Varying System Matrices in Kalman Filter
Can the evolution of time varying system matrices be stochastic?
Yes. If your model is
$$ x_t = A_t x_{t-1} + \eta_t $$
$$ y_t = B_t x_t + \varepsilon_t $$
and you assume further that $A_t$ and $B_t$ |
36,966 | Standard errors from flexsurvreg | Getting the confidence interval directly
Firstly, printing an flexsurvreg object (or its res element) already shows the 95% confidence interval:
> expFit
Estimates:
est L95% U95% se
rate 0.007341 0.005746 0.009379 0.000918
Reproducing the the confidence interval manually
So I guess you... | Standard errors from flexsurvreg | Getting the confidence interval directly
Firstly, printing an flexsurvreg object (or its res element) already shows the 95% confidence interval:
> expFit
Estimates:
est L95% U95% | Standard errors from flexsurvreg
Getting the confidence interval directly
Firstly, printing an flexsurvreg object (or its res element) already shows the 95% confidence interval:
> expFit
Estimates:
est L95% U95% se
rate 0.007341 0.005746 0.009379 0.000918
Reproducing the the confidence... | Standard errors from flexsurvreg
Getting the confidence interval directly
Firstly, printing an flexsurvreg object (or its res element) already shows the 95% confidence interval:
> expFit
Estimates:
est L95% U95% |
36,967 | Weights in quantile regression for complex survey in R | i am not sure @Metrics answer will give the correct standard errors for a survey-weighted quantreg call. here's an example of what you're trying to do. you are certainly hitting a bug because the qr function nested within the withReplicates function at this point cannot handle multiple tau parameters at once (even th... | Weights in quantile regression for complex survey in R | i am not sure @Metrics answer will give the correct standard errors for a survey-weighted quantreg call. here's an example of what you're trying to do. you are certainly hitting a bug because the qr | Weights in quantile regression for complex survey in R
i am not sure @Metrics answer will give the correct standard errors for a survey-weighted quantreg call. here's an example of what you're trying to do. you are certainly hitting a bug because the qr function nested within the withReplicates function at this point... | Weights in quantile regression for complex survey in R
i am not sure @Metrics answer will give the correct standard errors for a survey-weighted quantreg call. here's an example of what you're trying to do. you are certainly hitting a bug because the qr |
36,968 | Weights in quantile regression for complex survey in R | The usage of rq in quantreg package
rq(formula, tau=.5, data, subset, weights, na.action,
method="br", model = TRUE, contrasts, ...)
where,
weights=vector of observation weights; if supplied, the algorithm fits to minimize the sum of the weights multiplied into the absolute residuals. The length of weights must be th... | Weights in quantile regression for complex survey in R | The usage of rq in quantreg package
rq(formula, tau=.5, data, subset, weights, na.action,
method="br", model = TRUE, contrasts, ...)
where,
weights=vector of observation weights; if supplied, the al | Weights in quantile regression for complex survey in R
The usage of rq in quantreg package
rq(formula, tau=.5, data, subset, weights, na.action,
method="br", model = TRUE, contrasts, ...)
where,
weights=vector of observation weights; if supplied, the algorithm fits to minimize the sum of the weights multiplied into t... | Weights in quantile regression for complex survey in R
The usage of rq in quantreg package
rq(formula, tau=.5, data, subset, weights, na.action,
method="br", model = TRUE, contrasts, ...)
where,
weights=vector of observation weights; if supplied, the al |
36,969 | Models for Generalized Estimating Equation? | I prefer to call GEE an estimation method compared to ML or REML, since it combines quasi-likelihood estimation with robust variance estimation to estimate generalized linear marginal models for longitudinal data. Some texts and papers also call "GEE models", e.g. Hedeker, D., & Gibbons, R. D. (2006). Longitudinal data... | Models for Generalized Estimating Equation? | I prefer to call GEE an estimation method compared to ML or REML, since it combines quasi-likelihood estimation with robust variance estimation to estimate generalized linear marginal models for longi | Models for Generalized Estimating Equation?
I prefer to call GEE an estimation method compared to ML or REML, since it combines quasi-likelihood estimation with robust variance estimation to estimate generalized linear marginal models for longitudinal data. Some texts and papers also call "GEE models", e.g. Hedeker, D.... | Models for Generalized Estimating Equation?
I prefer to call GEE an estimation method compared to ML or REML, since it combines quasi-likelihood estimation with robust variance estimation to estimate generalized linear marginal models for longi |
36,970 | Estimating the mean and variance of a stationary time series | On the question about the mean - yes, I would have thought so. Stationarity means $E[Y_t]=c$ for all $t$ and the sample mean should estimate $c$.
On the variance (I hope this helps):
Say you have a stationary, zero mean AR(1) series:
$Y_t = \phi Y_{t-1} + e_t$
Where $\{e_t\}$ is white noise. Then if you take Var$(Y_t)$... | Estimating the mean and variance of a stationary time series | On the question about the mean - yes, I would have thought so. Stationarity means $E[Y_t]=c$ for all $t$ and the sample mean should estimate $c$.
On the variance (I hope this helps):
Say you have a st | Estimating the mean and variance of a stationary time series
On the question about the mean - yes, I would have thought so. Stationarity means $E[Y_t]=c$ for all $t$ and the sample mean should estimate $c$.
On the variance (I hope this helps):
Say you have a stationary, zero mean AR(1) series:
$Y_t = \phi Y_{t-1} + e_t... | Estimating the mean and variance of a stationary time series
On the question about the mean - yes, I would have thought so. Stationarity means $E[Y_t]=c$ for all $t$ and the sample mean should estimate $c$.
On the variance (I hope this helps):
Say you have a st |
36,971 | Estimating the mean and variance of a stationary time series | If the time series is indeed stationary, you may take the sample variance. However, since your time series is auto-correlated, you may be more interested in the variance of the residuals.
Stationary means that the joint distribution of the time series is unaffected by time shifts. Thus, you can define a meaningful marg... | Estimating the mean and variance of a stationary time series | If the time series is indeed stationary, you may take the sample variance. However, since your time series is auto-correlated, you may be more interested in the variance of the residuals.
Stationary m | Estimating the mean and variance of a stationary time series
If the time series is indeed stationary, you may take the sample variance. However, since your time series is auto-correlated, you may be more interested in the variance of the residuals.
Stationary means that the joint distribution of the time series is unaf... | Estimating the mean and variance of a stationary time series
If the time series is indeed stationary, you may take the sample variance. However, since your time series is auto-correlated, you may be more interested in the variance of the residuals.
Stationary m |
36,972 | How statistical packages calculate power | You're correct that one way to perform a power analysis would be via simulation. You could repeatedly generate 100 observations from a distribution and test those observations against the null hypothesis. If it consistently reported a (true) difference, you could say the test has high power.
However, for many common te... | How statistical packages calculate power | You're correct that one way to perform a power analysis would be via simulation. You could repeatedly generate 100 observations from a distribution and test those observations against the null hypothe | How statistical packages calculate power
You're correct that one way to perform a power analysis would be via simulation. You could repeatedly generate 100 observations from a distribution and test those observations against the null hypothesis. If it consistently reported a (true) difference, you could say the test ha... | How statistical packages calculate power
You're correct that one way to perform a power analysis would be via simulation. You could repeatedly generate 100 observations from a distribution and test those observations against the null hypothe |
36,973 | Appropriate Application of Survival Analysis | I recently had a set of interval censored survival data, so I know exactly what you need. If you have ever used R, this should help.
If you don't want to assume a parametric form, how about an interval censored Cox proportional hazards model? The intcox package that would do this is no longer in the R repository. I wou... | Appropriate Application of Survival Analysis | I recently had a set of interval censored survival data, so I know exactly what you need. If you have ever used R, this should help.
If you don't want to assume a parametric form, how about an interva | Appropriate Application of Survival Analysis
I recently had a set of interval censored survival data, so I know exactly what you need. If you have ever used R, this should help.
If you don't want to assume a parametric form, how about an interval censored Cox proportional hazards model? The intcox package that would do... | Appropriate Application of Survival Analysis
I recently had a set of interval censored survival data, so I know exactly what you need. If you have ever used R, this should help.
If you don't want to assume a parametric form, how about an interva |
36,974 | Appropriate Application of Survival Analysis | Survival function is usually right-continuous since it is a distribution function, I will use $a_k:=[t_{k-1}, t_k),k=1,2,\cdots,n$ as the interval.
Let $T_{ij}$ and $C_{ij}$ be the true continuous survival and censoring time for subject $j$ in sample $i$, respectively. Both variables may not be observed directly, but ... | Appropriate Application of Survival Analysis | Survival function is usually right-continuous since it is a distribution function, I will use $a_k:=[t_{k-1}, t_k),k=1,2,\cdots,n$ as the interval.
Let $T_{ij}$ and $C_{ij}$ be the true continuous su | Appropriate Application of Survival Analysis
Survival function is usually right-continuous since it is a distribution function, I will use $a_k:=[t_{k-1}, t_k),k=1,2,\cdots,n$ as the interval.
Let $T_{ij}$ and $C_{ij}$ be the true continuous survival and censoring time for subject $j$ in sample $i$, respectively. Both... | Appropriate Application of Survival Analysis
Survival function is usually right-continuous since it is a distribution function, I will use $a_k:=[t_{k-1}, t_k),k=1,2,\cdots,n$ as the interval.
Let $T_{ij}$ and $C_{ij}$ be the true continuous su |
36,975 | Capture-recapture sampling valid in literary analysis? | Capture-recapture relies on random samples on both occasions. You somehow need to make a random sample from the unknown pool of characters, count them, then make another, totally independent sample, and count the overlap. In biology, capture-recapture works because you expect that marked fish mingle with others in the ... | Capture-recapture sampling valid in literary analysis? | Capture-recapture relies on random samples on both occasions. You somehow need to make a random sample from the unknown pool of characters, count them, then make another, totally independent sample, a | Capture-recapture sampling valid in literary analysis?
Capture-recapture relies on random samples on both occasions. You somehow need to make a random sample from the unknown pool of characters, count them, then make another, totally independent sample, and count the overlap. In biology, capture-recapture works because... | Capture-recapture sampling valid in literary analysis?
Capture-recapture relies on random samples on both occasions. You somehow need to make a random sample from the unknown pool of characters, count them, then make another, totally independent sample, a |
36,976 | What level to use when comparing subjects in a hierarchical Bayesian analysis? | Just to clarify your model
Let $y_{ij}$ be reaction time for participant $i$ on trial $j$.
$$y_{ij} \sim N(\mu_i, \sigma^2_i)$$
And then you model $\mu_i$ and $\sigma^2_i$ as coming from some other distribution with hyperparameters.
You ask if I would want to compare two subjects what distributions should I compare?
So... | What level to use when comparing subjects in a hierarchical Bayesian analysis? | Just to clarify your model
Let $y_{ij}$ be reaction time for participant $i$ on trial $j$.
$$y_{ij} \sim N(\mu_i, \sigma^2_i)$$
And then you model $\mu_i$ and $\sigma^2_i$ as coming from some other di | What level to use when comparing subjects in a hierarchical Bayesian analysis?
Just to clarify your model
Let $y_{ij}$ be reaction time for participant $i$ on trial $j$.
$$y_{ij} \sim N(\mu_i, \sigma^2_i)$$
And then you model $\mu_i$ and $\sigma^2_i$ as coming from some other distribution with hyperparameters.
You ask ... | What level to use when comparing subjects in a hierarchical Bayesian analysis?
Just to clarify your model
Let $y_{ij}$ be reaction time for participant $i$ on trial $j$.
$$y_{ij} \sim N(\mu_i, \sigma^2_i)$$
And then you model $\mu_i$ and $\sigma^2_i$ as coming from some other di |
36,977 | Can a neural network output represent a posterior probability? | The conditions under which the output of a neural net can be treated as estimates of posterior probabilities are fairly broad, I remember the following paper as being pretty interesting and informative (caveat: but I've not read it since 2002)
Marco Saerens, Patrice Latinne, Christine Decaestecker: Any reasonable cost ... | Can a neural network output represent a posterior probability? | The conditions under which the output of a neural net can be treated as estimates of posterior probabilities are fairly broad, I remember the following paper as being pretty interesting and informativ | Can a neural network output represent a posterior probability?
The conditions under which the output of a neural net can be treated as estimates of posterior probabilities are fairly broad, I remember the following paper as being pretty interesting and informative (caveat: but I've not read it since 2002)
Marco Saerens... | Can a neural network output represent a posterior probability?
The conditions under which the output of a neural net can be treated as estimates of posterior probabilities are fairly broad, I remember the following paper as being pretty interesting and informativ |
36,978 | Hyperplane problem in linear congruent generator | $\text{corr}(R_t,R_{t-1}) \leq \frac{1}{a}\left(1-\frac{6c}{m}+6(\frac{_{c}}{^m})^2\right)+\frac{a+6}{m}$
This formula is an adaptation from Greenberger, 1961$^{[1]}$, who gives the first term above in an initial approximation and later gives another approximation with an additional term.
The serial correlation is typi... | Hyperplane problem in linear congruent generator | $\text{corr}(R_t,R_{t-1}) \leq \frac{1}{a}\left(1-\frac{6c}{m}+6(\frac{_{c}}{^m})^2\right)+\frac{a+6}{m}$
This formula is an adaptation from Greenberger, 1961$^{[1]}$, who gives the first term above i | Hyperplane problem in linear congruent generator
$\text{corr}(R_t,R_{t-1}) \leq \frac{1}{a}\left(1-\frac{6c}{m}+6(\frac{_{c}}{^m})^2\right)+\frac{a+6}{m}$
This formula is an adaptation from Greenberger, 1961$^{[1]}$, who gives the first term above in an initial approximation and later gives another approximation with a... | Hyperplane problem in linear congruent generator
$\text{corr}(R_t,R_{t-1}) \leq \frac{1}{a}\left(1-\frac{6c}{m}+6(\frac{_{c}}{^m})^2\right)+\frac{a+6}{m}$
This formula is an adaptation from Greenberger, 1961$^{[1]}$, who gives the first term above i |
36,979 | Looking for a good followup to the Stanford AI course | I wanted to refer you to the Statistical Learning book but I wanted to be sure that it wasn't your text. It was written by Stanford Statistics faculty Trevor Hastie, Jerome Friedman and Rob Tibshirani. Here is a link to it on amazon. | Looking for a good followup to the Stanford AI course | I wanted to refer you to the Statistical Learning book but I wanted to be sure that it wasn't your text. It was written by Stanford Statistics faculty Trevor Hastie, Jerome Friedman and Rob Tibshiran | Looking for a good followup to the Stanford AI course
I wanted to refer you to the Statistical Learning book but I wanted to be sure that it wasn't your text. It was written by Stanford Statistics faculty Trevor Hastie, Jerome Friedman and Rob Tibshirani. Here is a link to it on amazon. | Looking for a good followup to the Stanford AI course
I wanted to refer you to the Statistical Learning book but I wanted to be sure that it wasn't your text. It was written by Stanford Statistics faculty Trevor Hastie, Jerome Friedman and Rob Tibshiran |
36,980 | Looking for a good followup to the Stanford AI course | I'm finding that the machine learning course from Coursera/Andrew Ng/Stanford is really great. It has a balance of statistics, AI, linear algebra, programming. The motivations/intuitions that are given in the video lectures get me pumped to solve some problems. | Looking for a good followup to the Stanford AI course | I'm finding that the machine learning course from Coursera/Andrew Ng/Stanford is really great. It has a balance of statistics, AI, linear algebra, programming. The motivations/intuitions that are give | Looking for a good followup to the Stanford AI course
I'm finding that the machine learning course from Coursera/Andrew Ng/Stanford is really great. It has a balance of statistics, AI, linear algebra, programming. The motivations/intuitions that are given in the video lectures get me pumped to solve some problems. | Looking for a good followup to the Stanford AI course
I'm finding that the machine learning course from Coursera/Andrew Ng/Stanford is really great. It has a balance of statistics, AI, linear algebra, programming. The motivations/intuitions that are give |
36,981 | Different random effects in nlme and nlmer | Short: It's lack of precision in nlmer
In order to obtain the same results as nlme I needed to move away form the laplacian approximatoin which is set with nAGQ=1. According to the nlmer manpage the nAGQ sets the number of points per axis for the evaluation of the adaptive Gauss-Hermite approximation. Basically, increa... | Different random effects in nlme and nlmer | Short: It's lack of precision in nlmer
In order to obtain the same results as nlme I needed to move away form the laplacian approximatoin which is set with nAGQ=1. According to the nlmer manpage the n | Different random effects in nlme and nlmer
Short: It's lack of precision in nlmer
In order to obtain the same results as nlme I needed to move away form the laplacian approximatoin which is set with nAGQ=1. According to the nlmer manpage the nAGQ sets the number of points per axis for the evaluation of the adaptive Gau... | Different random effects in nlme and nlmer
Short: It's lack of precision in nlmer
In order to obtain the same results as nlme I needed to move away form the laplacian approximatoin which is set with nAGQ=1. According to the nlmer manpage the n |
36,982 | Supervised approaches vs. topic models in sentiment analysis | One disadvantage of an unsupervised method like LDA is it will generally take considerably longer to train compared to supervised methods. I'm also confused about the 2% increase you mention, based on table 2 it looks like an 8% difference between the best supervised approach they compared against and their best unsupe... | Supervised approaches vs. topic models in sentiment analysis | One disadvantage of an unsupervised method like LDA is it will generally take considerably longer to train compared to supervised methods. I'm also confused about the 2% increase you mention, based on | Supervised approaches vs. topic models in sentiment analysis
One disadvantage of an unsupervised method like LDA is it will generally take considerably longer to train compared to supervised methods. I'm also confused about the 2% increase you mention, based on table 2 it looks like an 8% difference between the best su... | Supervised approaches vs. topic models in sentiment analysis
One disadvantage of an unsupervised method like LDA is it will generally take considerably longer to train compared to supervised methods. I'm also confused about the 2% increase you mention, based on |
36,983 | Supervised approaches vs. topic models in sentiment analysis | As an additional note, by using unsupervised model, possible to have more domain specific result, especially if you are interested in a outlier domain. In that case it is not easy to find a good dataset for supervised learning thus you might need to use one of the unsupervised method. Or an semi-unsupervied method like... | Supervised approaches vs. topic models in sentiment analysis | As an additional note, by using unsupervised model, possible to have more domain specific result, especially if you are interested in a outlier domain. In that case it is not easy to find a good datas | Supervised approaches vs. topic models in sentiment analysis
As an additional note, by using unsupervised model, possible to have more domain specific result, especially if you are interested in a outlier domain. In that case it is not easy to find a good dataset for supervised learning thus you might need to use one o... | Supervised approaches vs. topic models in sentiment analysis
As an additional note, by using unsupervised model, possible to have more domain specific result, especially if you are interested in a outlier domain. In that case it is not easy to find a good datas |
36,984 | Language modeling: why is adding up to 1 so important? | The main advantages of using strict probabilities are a) ease of interpretation of the numbers; and b) being able to use Bayes theorem and other probabilistic methods in subsequent analysis. In some situations though, it is unnecessary. For example if you just want to rank the results with no further analysis, then the... | Language modeling: why is adding up to 1 so important? | The main advantages of using strict probabilities are a) ease of interpretation of the numbers; and b) being able to use Bayes theorem and other probabilistic methods in subsequent analysis. In some s | Language modeling: why is adding up to 1 so important?
The main advantages of using strict probabilities are a) ease of interpretation of the numbers; and b) being able to use Bayes theorem and other probabilistic methods in subsequent analysis. In some situations though, it is unnecessary. For example if you just want... | Language modeling: why is adding up to 1 so important?
The main advantages of using strict probabilities are a) ease of interpretation of the numbers; and b) being able to use Bayes theorem and other probabilistic methods in subsequent analysis. In some s |
36,985 | Cluster clickstream data | It is a good question with many practical applications.
Your data are sequential so we need a similarity measure between any pair of sequences. I recommend Levensthein distance since it is very intuitive and very nicely defined. See also this nice bachelor thesis with an overview of more measures for sequential data.
F... | Cluster clickstream data | It is a good question with many practical applications.
Your data are sequential so we need a similarity measure between any pair of sequences. I recommend Levensthein distance since it is very intuit | Cluster clickstream data
It is a good question with many practical applications.
Your data are sequential so we need a similarity measure between any pair of sequences. I recommend Levensthein distance since it is very intuitive and very nicely defined. See also this nice bachelor thesis with an overview of more measur... | Cluster clickstream data
It is a good question with many practical applications.
Your data are sequential so we need a similarity measure between any pair of sequences. I recommend Levensthein distance since it is very intuit |
36,986 | Cluster clickstream data | Want to improve this post? Provide detailed answers to this question, including citations and an explanation of why your answer is correct. Answers without enough detail may be edited or deleted.
You can use package clickstream or clickclust in R lan... | Cluster clickstream data | Want to improve this post? Provide detailed answers to this question, including citations and an explanation of why your answer is correct. Answers without enough detail may be edited or deleted.
| Cluster clickstream data
Want to improve this post? Provide detailed answers to this question, including citations and an explanation of why your answer is correct. Answers without enough detail may be edited or deleted.
You can use package clickstre... | Cluster clickstream data
Want to improve this post? Provide detailed answers to this question, including citations and an explanation of why your answer is correct. Answers without enough detail may be edited or deleted.
|
36,987 | Hierarchical multinomial logit with R/JAGS | After a bit og Googling I found the following package which does the trick:
http://cran.r-project.org/web/packages/ChoiceModelR/index.html | Hierarchical multinomial logit with R/JAGS | After a bit og Googling I found the following package which does the trick:
http://cran.r-project.org/web/packages/ChoiceModelR/index.html | Hierarchical multinomial logit with R/JAGS
After a bit og Googling I found the following package which does the trick:
http://cran.r-project.org/web/packages/ChoiceModelR/index.html | Hierarchical multinomial logit with R/JAGS
After a bit og Googling I found the following package which does the trick:
http://cran.r-project.org/web/packages/ChoiceModelR/index.html |
36,988 | Hierarchical multinomial logit with R/JAGS | MCMCpack has implemented a multinomial logit which will probably be considerably faster than one you've implemented yourself in JAGS, presuming that it meets your needs.
MCMCmnl(formula, baseline=NULL, data=NULL,
burnin = 1000, mcmc = 10000, thin = 1,
mcmc.method = c("IndMH", "RWM", "slice"), tune = 1, ... | Hierarchical multinomial logit with R/JAGS | MCMCpack has implemented a multinomial logit which will probably be considerably faster than one you've implemented yourself in JAGS, presuming that it meets your needs.
MCMCmnl(formula, baseline=NULL | Hierarchical multinomial logit with R/JAGS
MCMCpack has implemented a multinomial logit which will probably be considerably faster than one you've implemented yourself in JAGS, presuming that it meets your needs.
MCMCmnl(formula, baseline=NULL, data=NULL,
burnin = 1000, mcmc = 10000, thin = 1,
mcmc.meth... | Hierarchical multinomial logit with R/JAGS
MCMCpack has implemented a multinomial logit which will probably be considerably faster than one you've implemented yourself in JAGS, presuming that it meets your needs.
MCMCmnl(formula, baseline=NULL |
36,989 | How to perform inter-rater reliability with multiple raters, different raters per participant, and possible changes over time? | How are you planning to account for the fact that some ratings were done by the same rater? Off the top of my head, I can't think of any measures that take that into account when it isn't consistently done. After all, if you compare the same rater twice, you're looking at consistency; if you compare two raters, you're ... | How to perform inter-rater reliability with multiple raters, different raters per participant, and p | How are you planning to account for the fact that some ratings were done by the same rater? Off the top of my head, I can't think of any measures that take that into account when it isn't consistently | How to perform inter-rater reliability with multiple raters, different raters per participant, and possible changes over time?
How are you planning to account for the fact that some ratings were done by the same rater? Off the top of my head, I can't think of any measures that take that into account when it isn't consi... | How to perform inter-rater reliability with multiple raters, different raters per participant, and p
How are you planning to account for the fact that some ratings were done by the same rater? Off the top of my head, I can't think of any measures that take that into account when it isn't consistently |
36,990 | How to evaluate quality of probability estimator for Bernoulli experiments? | You can quantify the quality of the estimator by calculating the total surprisal of all of the coin flips.
Suppose that your expert makes predictions $q_i$ for each coin. Then, given indicator variables for the coins coming up heads $x_i$, the total surprisal is:
\begin{align}
\sum_i\left[ -x_i\log q_i - (1-x_i)\log (... | How to evaluate quality of probability estimator for Bernoulli experiments? | You can quantify the quality of the estimator by calculating the total surprisal of all of the coin flips.
Suppose that your expert makes predictions $q_i$ for each coin. Then, given indicator variab | How to evaluate quality of probability estimator for Bernoulli experiments?
You can quantify the quality of the estimator by calculating the total surprisal of all of the coin flips.
Suppose that your expert makes predictions $q_i$ for each coin. Then, given indicator variables for the coins coming up heads $x_i$, the... | How to evaluate quality of probability estimator for Bernoulli experiments?
You can quantify the quality of the estimator by calculating the total surprisal of all of the coin flips.
Suppose that your expert makes predictions $q_i$ for each coin. Then, given indicator variab |
36,991 | How to evaluate quality of probability estimator for Bernoulli experiments? | If I understand your question correctly, you might want to check out this question. As I explained there, one way of assessing the calibration of probability predictions is with a scoring rule. A common example of a scoring rule is the Brier score: $$BS = \frac{1}{N}\sum\limits _{t=1}^{N}(f_t-o_t)^2$$ where $f_t$ is ... | How to evaluate quality of probability estimator for Bernoulli experiments? | If I understand your question correctly, you might want to check out this question. As I explained there, one way of assessing the calibration of probability predictions is with a scoring rule. A co | How to evaluate quality of probability estimator for Bernoulli experiments?
If I understand your question correctly, you might want to check out this question. As I explained there, one way of assessing the calibration of probability predictions is with a scoring rule. A common example of a scoring rule is the Brier ... | How to evaluate quality of probability estimator for Bernoulli experiments?
If I understand your question correctly, you might want to check out this question. As I explained there, one way of assessing the calibration of probability predictions is with a scoring rule. A co |
36,992 | How to evaluate quality of probability estimator for Bernoulli experiments? | The above answer may be useful but is complicated and I am not sure how to apply it. Thinking in simple terms this is a special case of testing whether or not a person has psychic powers (really no different from a scientific evaluation of the mechanics and physics of the coin flip). Obviously have psychic capability ... | How to evaluate quality of probability estimator for Bernoulli experiments? | The above answer may be useful but is complicated and I am not sure how to apply it. Thinking in simple terms this is a special case of testing whether or not a person has psychic powers (really no di | How to evaluate quality of probability estimator for Bernoulli experiments?
The above answer may be useful but is complicated and I am not sure how to apply it. Thinking in simple terms this is a special case of testing whether or not a person has psychic powers (really no different from a scientific evaluation of the ... | How to evaluate quality of probability estimator for Bernoulli experiments?
The above answer may be useful but is complicated and I am not sure how to apply it. Thinking in simple terms this is a special case of testing whether or not a person has psychic powers (really no di |
36,993 | How to evaluate quality of probability estimator for Bernoulli experiments? | Another way to evaluate the quality is to look at the Reliability Diagram.
This does not immediately yield a value between 0 and 1, but can be used for a first visual evaluation. | How to evaluate quality of probability estimator for Bernoulli experiments? | Another way to evaluate the quality is to look at the Reliability Diagram.
This does not immediately yield a value between 0 and 1, but can be used for a first visual evaluation. | How to evaluate quality of probability estimator for Bernoulli experiments?
Another way to evaluate the quality is to look at the Reliability Diagram.
This does not immediately yield a value between 0 and 1, but can be used for a first visual evaluation. | How to evaluate quality of probability estimator for Bernoulli experiments?
Another way to evaluate the quality is to look at the Reliability Diagram.
This does not immediately yield a value between 0 and 1, but can be used for a first visual evaluation. |
36,994 | How to fit the model for crossed and nested design using lme function in R? | The tricky part here is to specify the right formula.
library(nlme)
# Assume y is your response variable.
lme(fixed = y ~ A, random = ~ A | B/C)
Here B/C stands for C nested in B and is short for B + B:C. The interaction with A is present because A is repeated in the random part.
For a basic introduction to nlme, I re... | How to fit the model for crossed and nested design using lme function in R? | The tricky part here is to specify the right formula.
library(nlme)
# Assume y is your response variable.
lme(fixed = y ~ A, random = ~ A | B/C)
Here B/C stands for C nested in B and is short for B + | How to fit the model for crossed and nested design using lme function in R?
The tricky part here is to specify the right formula.
library(nlme)
# Assume y is your response variable.
lme(fixed = y ~ A, random = ~ A | B/C)
Here B/C stands for C nested in B and is short for B + B:C. The interaction with A is present beca... | How to fit the model for crossed and nested design using lme function in R?
The tricky part here is to specify the right formula.
library(nlme)
# Assume y is your response variable.
lme(fixed = y ~ A, random = ~ A | B/C)
Here B/C stands for C nested in B and is short for B + |
36,995 | Difference between survdiff log-rank and coxph log-rank | Without actual output it is difficult to tell, but generally an "overall logrank score" will test the null hypothesis that all of the coefficients are 0. Therefore a significant result could be due to one or more of your covariates being related to survival while your 2 groups are still identical (or they could be dif... | Difference between survdiff log-rank and coxph log-rank | Without actual output it is difficult to tell, but generally an "overall logrank score" will test the null hypothesis that all of the coefficients are 0. Therefore a significant result could be due t | Difference between survdiff log-rank and coxph log-rank
Without actual output it is difficult to tell, but generally an "overall logrank score" will test the null hypothesis that all of the coefficients are 0. Therefore a significant result could be due to one or more of your covariates being related to survival while... | Difference between survdiff log-rank and coxph log-rank
Without actual output it is difficult to tell, but generally an "overall logrank score" will test the null hypothesis that all of the coefficients are 0. Therefore a significant result could be due t |
36,996 | Confidence intervals for a polynomial | In my answer, I provide many links to background material to save space here. I'm going to write my answer taking the info in the links as given.
I think a Bayesian approach is a natural fit to this problem, especially since you seek to convince only yourself. It's a bit convoluted to use confidence intervals to answer... | Confidence intervals for a polynomial | In my answer, I provide many links to background material to save space here. I'm going to write my answer taking the info in the links as given.
I think a Bayesian approach is a natural fit to this p | Confidence intervals for a polynomial
In my answer, I provide many links to background material to save space here. I'm going to write my answer taking the info in the links as given.
I think a Bayesian approach is a natural fit to this problem, especially since you seek to convince only yourself. It's a bit convoluted... | Confidence intervals for a polynomial
In my answer, I provide many links to background material to save space here. I'm going to write my answer taking the info in the links as given.
I think a Bayesian approach is a natural fit to this p |
36,997 | Confidence intervals for a polynomial | I presume the z_k are not probabilities but sample frequencies. This is because, otherwise, Q_i(z_0, ..., z_i) is not a random variable. In that case, computing the variance of the Q_i's is straightforward algebra. Define, first, the event indicators Z_i which is 1 if Z == i, 0 otherwise. It's a Bernoulli random variab... | Confidence intervals for a polynomial | I presume the z_k are not probabilities but sample frequencies. This is because, otherwise, Q_i(z_0, ..., z_i) is not a random variable. In that case, computing the variance of the Q_i's is straightfo | Confidence intervals for a polynomial
I presume the z_k are not probabilities but sample frequencies. This is because, otherwise, Q_i(z_0, ..., z_i) is not a random variable. In that case, computing the variance of the Q_i's is straightforward algebra. Define, first, the event indicators Z_i which is 1 if Z == i, 0 oth... | Confidence intervals for a polynomial
I presume the z_k are not probabilities but sample frequencies. This is because, otherwise, Q_i(z_0, ..., z_i) is not a random variable. In that case, computing the variance of the Q_i's is straightfo |
36,998 | Confidence intervals for a polynomial | Kevin, please be carefull since I'll have to change your notation a little bit: your $z_i$'s are not my $z_i$'s.
I think the following Bayesian solution is worth a try. Cook a random parameter $\Lambda>0$ and let $Z_1,\dots,Z_n$ be conditionally i.i.d., given $\Lambda=\lambda$, with $Z_i\mid\Lambda = \lambda \sim \tex... | Confidence intervals for a polynomial | Kevin, please be carefull since I'll have to change your notation a little bit: your $z_i$'s are not my $z_i$'s.
I think the following Bayesian solution is worth a try. Cook a random parameter $\Lamb | Confidence intervals for a polynomial
Kevin, please be carefull since I'll have to change your notation a little bit: your $z_i$'s are not my $z_i$'s.
I think the following Bayesian solution is worth a try. Cook a random parameter $\Lambda>0$ and let $Z_1,\dots,Z_n$ be conditionally i.i.d., given $\Lambda=\lambda$, wi... | Confidence intervals for a polynomial
Kevin, please be carefull since I'll have to change your notation a little bit: your $z_i$'s are not my $z_i$'s.
I think the following Bayesian solution is worth a try. Cook a random parameter $\Lamb |
36,999 | Classification of conversations based on content | This is how I would approach it. You actually need to check if a text is in class I or III (else it would be class II).
First, define a bag of words for classes I and III. You can manually do this
For each text, calculate the tf-idf for the words in these two classes and sum it (get two sums).
If some of these two su... | Classification of conversations based on content | This is how I would approach it. You actually need to check if a text is in class I or III (else it would be class II).
First, define a bag of words for classes I and III. You can manually do this
F | Classification of conversations based on content
This is how I would approach it. You actually need to check if a text is in class I or III (else it would be class II).
First, define a bag of words for classes I and III. You can manually do this
For each text, calculate the tf-idf for the words in these two classes a... | Classification of conversations based on content
This is how I would approach it. You actually need to check if a text is in class I or III (else it would be class II).
First, define a bag of words for classes I and III. You can manually do this
F |
37,000 | Comparing a sample distribution to an implied distribution | That's a familiar problem from a previous life!
First, you're not going to be able to do exactly what you want, which is to come up with a probability that the observations could have come from a specified distribution etc. This is because you don't have a well-specified alternative distribution, one which the data ... | Comparing a sample distribution to an implied distribution | That's a familiar problem from a previous life!
First, you're not going to be able to do exactly what you want, which is to come up with a probability that the observations could have come from a sp | Comparing a sample distribution to an implied distribution
That's a familiar problem from a previous life!
First, you're not going to be able to do exactly what you want, which is to come up with a probability that the observations could have come from a specified distribution etc. This is because you don't have a w... | Comparing a sample distribution to an implied distribution
That's a familiar problem from a previous life!
First, you're not going to be able to do exactly what you want, which is to come up with a probability that the observations could have come from a sp |
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