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 |
|---|---|---|---|---|---|---|
36,001 | Understanding the different formulations for SVM | C-SVM:
$$
\begin{align}
&\text{minimize}
&t(\mathbf w,b,\xi)=
{1\over2}\|\mathbf w\|_2^2+{C\over m}\sum_{i = 1}^{m}\xi_i \\
&\text{subject to}
&\left\{\begin{matrix}
y_i(\langle\Phi(x_i),\mathbf w\rangle+b)\ge1-\xi_i &(\forall i=1,\dots,m)
\\
\xi_i \ge0
\end{matrix}\right.
\end{align}
$$
C-svc is the common SVM. The d... | Understanding the different formulations for SVM | C-SVM:
$$
\begin{align}
&\text{minimize}
&t(\mathbf w,b,\xi)=
{1\over2}\|\mathbf w\|_2^2+{C\over m}\sum_{i = 1}^{m}\xi_i \\
&\text{subject to}
&\left\{\begin{matrix}
y_i(\langle\Phi(x_i),\mathbf w\ran | Understanding the different formulations for SVM
C-SVM:
$$
\begin{align}
&\text{minimize}
&t(\mathbf w,b,\xi)=
{1\over2}\|\mathbf w\|_2^2+{C\over m}\sum_{i = 1}^{m}\xi_i \\
&\text{subject to}
&\left\{\begin{matrix}
y_i(\langle\Phi(x_i),\mathbf w\rangle+b)\ge1-\xi_i &(\forall i=1,\dots,m)
\\
\xi_i \ge0
\end{matrix}\rig... | Understanding the different formulations for SVM
C-SVM:
$$
\begin{align}
&\text{minimize}
&t(\mathbf w,b,\xi)=
{1\over2}\|\mathbf w\|_2^2+{C\over m}\sum_{i = 1}^{m}\xi_i \\
&\text{subject to}
&\left\{\begin{matrix}
y_i(\langle\Phi(x_i),\mathbf w\ran |
36,002 | How to explain KNN in Bayesian probability? | kNN from a Bayesian viewpoint
Let suppose that we have a data set comprising $N_{k}$ points in class $\mathcal{C}_{k}$ with $N$ total points, so that $\sum_{k}N_{k} = N$.
We want to classify a new point $\mathbf{x}$ by drawing a sphere centred on $\mathbf{x}$ containing precisely $K$ points irrespective of their class... | How to explain KNN in Bayesian probability? | kNN from a Bayesian viewpoint
Let suppose that we have a data set comprising $N_{k}$ points in class $\mathcal{C}_{k}$ with $N$ total points, so that $\sum_{k}N_{k} = N$.
We want to classify a new po | How to explain KNN in Bayesian probability?
kNN from a Bayesian viewpoint
Let suppose that we have a data set comprising $N_{k}$ points in class $\mathcal{C}_{k}$ with $N$ total points, so that $\sum_{k}N_{k} = N$.
We want to classify a new point $\mathbf{x}$ by drawing a sphere centred on $\mathbf{x}$ containing prec... | How to explain KNN in Bayesian probability?
kNN from a Bayesian viewpoint
Let suppose that we have a data set comprising $N_{k}$ points in class $\mathcal{C}_{k}$ with $N$ total points, so that $\sum_{k}N_{k} = N$.
We want to classify a new po |
36,003 | How to explain KNN in Bayesian probability? | As explained in detail in this other answer, kNN is a discriminative approach. In order to cast it in the Bayesian framework, we need a generative model, i.e. a model that tells how samples are generated. This question is developed in detail in this paper (Revisiting k-means: New Algorithms via Bayesian Nonparametrics)... | How to explain KNN in Bayesian probability? | As explained in detail in this other answer, kNN is a discriminative approach. In order to cast it in the Bayesian framework, we need a generative model, i.e. a model that tells how samples are genera | How to explain KNN in Bayesian probability?
As explained in detail in this other answer, kNN is a discriminative approach. In order to cast it in the Bayesian framework, we need a generative model, i.e. a model that tells how samples are generated. This question is developed in detail in this paper (Revisiting k-means:... | How to explain KNN in Bayesian probability?
As explained in detail in this other answer, kNN is a discriminative approach. In order to cast it in the Bayesian framework, we need a generative model, i.e. a model that tells how samples are genera |
36,004 | What is the intuitive (geometric?) meaning of minimizing the log determinant of a matrix? | Short answer is: The determinant plays a role because it is tied to the jacobian of the multivariate change of variables and the logarithm is tied to taking the log-likelihood.
Long Answer: Let's start with the univariate standard normal density (parameter free) which is $$\frac{1}{\sqrt{2\pi}} \exp\left(-\frac{1}{2}t... | What is the intuitive (geometric?) meaning of minimizing the log determinant of a matrix? | Short answer is: The determinant plays a role because it is tied to the jacobian of the multivariate change of variables and the logarithm is tied to taking the log-likelihood.
Long Answer: Let's sta | What is the intuitive (geometric?) meaning of minimizing the log determinant of a matrix?
Short answer is: The determinant plays a role because it is tied to the jacobian of the multivariate change of variables and the logarithm is tied to taking the log-likelihood.
Long Answer: Let's start with the univariate standar... | What is the intuitive (geometric?) meaning of minimizing the log determinant of a matrix?
Short answer is: The determinant plays a role because it is tied to the jacobian of the multivariate change of variables and the logarithm is tied to taking the log-likelihood.
Long Answer: Let's sta |
36,005 | Censored regression in R | The predict() and fitted() methods for tobit objects compute the estimates for the latent mean $\mu = E[y^*] = x^\top \beta$. Additionally, the scale parameter $\sigma$ is available as $scale in the objects:
mu <- fitted(fit)
sigma <- fit$scale
The probability of a non-zero observation is then $P(y > 0) = \Phi(\mu/\si... | Censored regression in R | The predict() and fitted() methods for tobit objects compute the estimates for the latent mean $\mu = E[y^*] = x^\top \beta$. Additionally, the scale parameter $\sigma$ is available as $scale in the o | Censored regression in R
The predict() and fitted() methods for tobit objects compute the estimates for the latent mean $\mu = E[y^*] = x^\top \beta$. Additionally, the scale parameter $\sigma$ is available as $scale in the objects:
mu <- fitted(fit)
sigma <- fit$scale
The probability of a non-zero observation is then... | Censored regression in R
The predict() and fitted() methods for tobit objects compute the estimates for the latent mean $\mu = E[y^*] = x^\top \beta$. Additionally, the scale parameter $\sigma$ is available as $scale in the o |
36,006 | Multicollinearity in polynomial regression | Don't use polynomial transformations "as such", because they will be collinear, as you note. Instead, transform them into orthogonal polynomials. In R, use the poly() command.
Even better, don't use higher order polynomials at all, since they will become unstable at the boundaries of your data space. Instead, use splin... | Multicollinearity in polynomial regression | Don't use polynomial transformations "as such", because they will be collinear, as you note. Instead, transform them into orthogonal polynomials. In R, use the poly() command.
Even better, don't use h | Multicollinearity in polynomial regression
Don't use polynomial transformations "as such", because they will be collinear, as you note. Instead, transform them into orthogonal polynomials. In R, use the poly() command.
Even better, don't use higher order polynomials at all, since they will become unstable at the bounda... | Multicollinearity in polynomial regression
Don't use polynomial transformations "as such", because they will be collinear, as you note. Instead, transform them into orthogonal polynomials. In R, use the poly() command.
Even better, don't use h |
36,007 | Cauchy distribution (likelihood and Fisher information) | The Fisher information for one observation is given by\begin{align*}I(\theta) &= -\mathbb{E}_\theta\left[\frac{\partial^2 \log f(X;\theta)}{\partial\theta^2}\right]\\ &=\mathbb{E}_\theta\left[ \frac{\partial^2 \log \{1+(X-\theta)^2\}}{\partial\theta^2}\right]\\
&=2\mathbb{E}_\theta\left[ -\frac{\partial }{\partial\thet... | Cauchy distribution (likelihood and Fisher information) | The Fisher information for one observation is given by\begin{align*}I(\theta) &= -\mathbb{E}_\theta\left[\frac{\partial^2 \log f(X;\theta)}{\partial\theta^2}\right]\\ &=\mathbb{E}_\theta\left[ \frac{\ | Cauchy distribution (likelihood and Fisher information)
The Fisher information for one observation is given by\begin{align*}I(\theta) &= -\mathbb{E}_\theta\left[\frac{\partial^2 \log f(X;\theta)}{\partial\theta^2}\right]\\ &=\mathbb{E}_\theta\left[ \frac{\partial^2 \log \{1+(X-\theta)^2\}}{\partial\theta^2}\right]\\
&=... | Cauchy distribution (likelihood and Fisher information)
The Fisher information for one observation is given by\begin{align*}I(\theta) &= -\mathbb{E}_\theta\left[\frac{\partial^2 \log f(X;\theta)}{\partial\theta^2}\right]\\ &=\mathbb{E}_\theta\left[ \frac{\ |
36,008 | Optimal number of bins in histogram by the Freedman–Diaconis rule: difference between theoretical rate and actual number | The reason comes from the fact that the histogram function is expected to include all the data, so it must span the range of the data.
The Freedman-Diaconis rule gives a formula for the width of the bins.
The function gives a formula for the number of bins.
The relationship between number of bins and the width of bins... | Optimal number of bins in histogram by the Freedman–Diaconis rule: difference between theoretical ra | The reason comes from the fact that the histogram function is expected to include all the data, so it must span the range of the data.
The Freedman-Diaconis rule gives a formula for the width of the | Optimal number of bins in histogram by the Freedman–Diaconis rule: difference between theoretical rate and actual number
The reason comes from the fact that the histogram function is expected to include all the data, so it must span the range of the data.
The Freedman-Diaconis rule gives a formula for the width of the... | Optimal number of bins in histogram by the Freedman–Diaconis rule: difference between theoretical ra
The reason comes from the fact that the histogram function is expected to include all the data, so it must span the range of the data.
The Freedman-Diaconis rule gives a formula for the width of the |
36,009 | Zero-inflated Poisson and Gibbs sampling, proofs and sampling | For the first question, given that you have a hierarchical model, you simply have to start from the higher level and proceed downwards:
$(r_i|p, \lambda )\sim\mathcal{B}(p)$ for $i=1,\ldots,n$
$(x_i|r, \lambda, p)\sim\mathcal{P}(\lambda r_i)$ for $i=1,\ldots,n$
Note that only the $x_i$'s for which $r_i=1$ need to be ... | Zero-inflated Poisson and Gibbs sampling, proofs and sampling | For the first question, given that you have a hierarchical model, you simply have to start from the higher level and proceed downwards:
$(r_i|p, \lambda )\sim\mathcal{B}(p)$ for $i=1,\ldots,n$
$(x_i| | Zero-inflated Poisson and Gibbs sampling, proofs and sampling
For the first question, given that you have a hierarchical model, you simply have to start from the higher level and proceed downwards:
$(r_i|p, \lambda )\sim\mathcal{B}(p)$ for $i=1,\ldots,n$
$(x_i|r, \lambda, p)\sim\mathcal{P}(\lambda r_i)$ for $i=1,\ldot... | Zero-inflated Poisson and Gibbs sampling, proofs and sampling
For the first question, given that you have a hierarchical model, you simply have to start from the higher level and proceed downwards:
$(r_i|p, \lambda )\sim\mathcal{B}(p)$ for $i=1,\ldots,n$
$(x_i| |
36,010 | Problems with time series prediction | You are attempting to forecast a compositional time series. That is, you have three components that are all constrained to lie between 0 and 1 and to add up to 1.
You can address this issue using standard exponential smoothing, by using an appropriate generalized logistic transformation. There was a presentation on thi... | Problems with time series prediction | You are attempting to forecast a compositional time series. That is, you have three components that are all constrained to lie between 0 and 1 and to add up to 1.
You can address this issue using stan | Problems with time series prediction
You are attempting to forecast a compositional time series. That is, you have three components that are all constrained to lie between 0 and 1 and to add up to 1.
You can address this issue using standard exponential smoothing, by using an appropriate generalized logistic transforma... | Problems with time series prediction
You are attempting to forecast a compositional time series. That is, you have three components that are all constrained to lie between 0 and 1 and to add up to 1.
You can address this issue using stan |
36,011 | Does a prediction interval have to contain the mean? | No, a prediction interval need not contain the mean. I think some of your confusion might be mixing prediction intervals and confidence intervals. While the goal of a prediction interval is to contain with some certainty future values of the random variable, the goal of a confidence interval is to contain the true me... | Does a prediction interval have to contain the mean? | No, a prediction interval need not contain the mean. I think some of your confusion might be mixing prediction intervals and confidence intervals. While the goal of a prediction interval is to conta | Does a prediction interval have to contain the mean?
No, a prediction interval need not contain the mean. I think some of your confusion might be mixing prediction intervals and confidence intervals. While the goal of a prediction interval is to contain with some certainty future values of the random variable, the go... | Does a prediction interval have to contain the mean?
No, a prediction interval need not contain the mean. I think some of your confusion might be mixing prediction intervals and confidence intervals. While the goal of a prediction interval is to conta |
36,012 | Does a prediction interval have to contain the mean? | Consider the distribution of possible returns in the St Petersburg paradox:
Prob(1)=1/2
Prob(2)=1/4
Prob(4)=1/8
...
Prob(2^n)=1/2^(n+1)
The mean diverges and is outside of any reasonable prediction interval. (The median is 1 in this case, but I don't know what I'd use for my point forecast. Maybe Stephan Kolassa, se... | Does a prediction interval have to contain the mean? | Consider the distribution of possible returns in the St Petersburg paradox:
Prob(1)=1/2
Prob(2)=1/4
Prob(4)=1/8
...
Prob(2^n)=1/2^(n+1)
The mean diverges and is outside of any reasonable prediction i | Does a prediction interval have to contain the mean?
Consider the distribution of possible returns in the St Petersburg paradox:
Prob(1)=1/2
Prob(2)=1/4
Prob(4)=1/8
...
Prob(2^n)=1/2^(n+1)
The mean diverges and is outside of any reasonable prediction interval. (The median is 1 in this case, but I don't know what I'd ... | Does a prediction interval have to contain the mean?
Consider the distribution of possible returns in the St Petersburg paradox:
Prob(1)=1/2
Prob(2)=1/4
Prob(4)=1/8
...
Prob(2^n)=1/2^(n+1)
The mean diverges and is outside of any reasonable prediction i |
36,013 | Why is the standard deviation defined using differences^2 instead of differences^4? [duplicate] | It has to do with moment generating functions. Specifically, variance is defined to be the second moment about the mean, and the third moment generating function is called the skewness. All of these things are called shape parameters, because they describe the shape of the distribution. The 4th moment, Kurtosis which ... | Why is the standard deviation defined using differences^2 instead of differences^4? [duplicate] | It has to do with moment generating functions. Specifically, variance is defined to be the second moment about the mean, and the third moment generating function is called the skewness. All of these t | Why is the standard deviation defined using differences^2 instead of differences^4? [duplicate]
It has to do with moment generating functions. Specifically, variance is defined to be the second moment about the mean, and the third moment generating function is called the skewness. All of these things are called shape p... | Why is the standard deviation defined using differences^2 instead of differences^4? [duplicate]
It has to do with moment generating functions. Specifically, variance is defined to be the second moment about the mean, and the third moment generating function is called the skewness. All of these t |
36,014 | Why is the standard deviation defined using differences^2 instead of differences^4? [duplicate] | The mean is in a sense the natural partner of the standard deviation: if you want to minimise $\sqrt{\frac{1}{N} \sum_{i=1}^N (x_i - m)^2}$ then this is achieved when $m = \frac{1}{N} \sum_{i=1}^N x_i$. For example, if you have $x_1=1, x_2=6, x_3=2$, then the minimum comes when $m=3$.
This is not true when you have ot... | Why is the standard deviation defined using differences^2 instead of differences^4? [duplicate] | The mean is in a sense the natural partner of the standard deviation: if you want to minimise $\sqrt{\frac{1}{N} \sum_{i=1}^N (x_i - m)^2}$ then this is achieved when $m = \frac{1}{N} \sum_{i=1}^N x_i | Why is the standard deviation defined using differences^2 instead of differences^4? [duplicate]
The mean is in a sense the natural partner of the standard deviation: if you want to minimise $\sqrt{\frac{1}{N} \sum_{i=1}^N (x_i - m)^2}$ then this is achieved when $m = \frac{1}{N} \sum_{i=1}^N x_i$. For example, if you ... | Why is the standard deviation defined using differences^2 instead of differences^4? [duplicate]
The mean is in a sense the natural partner of the standard deviation: if you want to minimise $\sqrt{\frac{1}{N} \sum_{i=1}^N (x_i - m)^2}$ then this is achieved when $m = \frac{1}{N} \sum_{i=1}^N x_i |
36,015 | What is re-randomization? | Rerandomization, as used by Morgan and Rubin (Annals of Statistics 2012), is a form of restricted randomization. Suppose you had all of your subjects available for randomization, e.g. you are randomizing 20 hospitals into two arms. You would like the two arms to be similar in terms of important covariates, e.g. hospita... | What is re-randomization? | Rerandomization, as used by Morgan and Rubin (Annals of Statistics 2012), is a form of restricted randomization. Suppose you had all of your subjects available for randomization, e.g. you are randomiz | What is re-randomization?
Rerandomization, as used by Morgan and Rubin (Annals of Statistics 2012), is a form of restricted randomization. Suppose you had all of your subjects available for randomization, e.g. you are randomizing 20 hospitals into two arms. You would like the two arms to be similar in terms of importan... | What is re-randomization?
Rerandomization, as used by Morgan and Rubin (Annals of Statistics 2012), is a form of restricted randomization. Suppose you had all of your subjects available for randomization, e.g. you are randomiz |
36,016 | Stepwise Model Selection in Logistic Regression in R | Using stepwise selection to find a model is a very bad thing to do. Your hypothesis tests will be invalid, and your out of sample predictive accuracy will be very poor due to overfitting. To understand these points more fully, it may help you to read my answer here: Algorithms for automatic model selection.
The ste... | Stepwise Model Selection in Logistic Regression in R | Using stepwise selection to find a model is a very bad thing to do. Your hypothesis tests will be invalid, and your out of sample predictive accuracy will be very poor due to overfitting. To underst | Stepwise Model Selection in Logistic Regression in R
Using stepwise selection to find a model is a very bad thing to do. Your hypothesis tests will be invalid, and your out of sample predictive accuracy will be very poor due to overfitting. To understand these points more fully, it may help you to read my answer here... | Stepwise Model Selection in Logistic Regression in R
Using stepwise selection to find a model is a very bad thing to do. Your hypothesis tests will be invalid, and your out of sample predictive accuracy will be very poor due to overfitting. To underst |
36,017 | CV for model parameter tuning AND then model evaluation | The simple rule is that data used for evaluating the performance of a model should not have been used to optimize the model in any way. If you split all of the available data into k disjoint subsets to use to tune the hyper-parameters of a model (e.g. the kernel and regularization parameters of an SVM), then you canno... | CV for model parameter tuning AND then model evaluation | The simple rule is that data used for evaluating the performance of a model should not have been used to optimize the model in any way. If you split all of the available data into k disjoint subsets | CV for model parameter tuning AND then model evaluation
The simple rule is that data used for evaluating the performance of a model should not have been used to optimize the model in any way. If you split all of the available data into k disjoint subsets to use to tune the hyper-parameters of a model (e.g. the kernel ... | CV for model parameter tuning AND then model evaluation
The simple rule is that data used for evaluating the performance of a model should not have been used to optimize the model in any way. If you split all of the available data into k disjoint subsets |
36,018 | Self-study: Finding the maximum likelihood estimates of the parameters of a density function - UPDATED | [Note: This is my answer to the Dec. 19, 2014, version of the question.]
If you operate the change of variable $y=x^2$ in your density
$$f_X(x|\alpha,\beta,\sigma)=\frac{1}{\Gamma \left( \alpha \right)\beta^{\alpha}}\exp\left\{{-\frac{x^2}{2\sigma^{2}}\frac{1}{\beta}}\right\}\frac{x^{2\alpha-1}}{2^{\alpha-1}\sigma^{2\a... | Self-study: Finding the maximum likelihood estimates of the parameters of a density function - UPDAT | [Note: This is my answer to the Dec. 19, 2014, version of the question.]
If you operate the change of variable $y=x^2$ in your density
$$f_X(x|\alpha,\beta,\sigma)=\frac{1}{\Gamma \left( \alpha \right | Self-study: Finding the maximum likelihood estimates of the parameters of a density function - UPDATED
[Note: This is my answer to the Dec. 19, 2014, version of the question.]
If you operate the change of variable $y=x^2$ in your density
$$f_X(x|\alpha,\beta,\sigma)=\frac{1}{\Gamma \left( \alpha \right)\beta^{\alpha}}\... | Self-study: Finding the maximum likelihood estimates of the parameters of a density function - UPDAT
[Note: This is my answer to the Dec. 19, 2014, version of the question.]
If you operate the change of variable $y=x^2$ in your density
$$f_X(x|\alpha,\beta,\sigma)=\frac{1}{\Gamma \left( \alpha \right |
36,019 | Self-study: Finding the maximum likelihood estimates of the parameters of a density function - UPDATED | In the case of the EM algorithm, the initial values can be set arbitrarily since the iterations are guaranteed to converge to the maximum:
We have seen that both the E and the M steps of the EM algorithm are increasing
the value of a well-defined bound on the log likelihood function and that the complete EM cycle wi... | Self-study: Finding the maximum likelihood estimates of the parameters of a density function - UPDAT | In the case of the EM algorithm, the initial values can be set arbitrarily since the iterations are guaranteed to converge to the maximum:
We have seen that both the E and the M steps of the EM algor | Self-study: Finding the maximum likelihood estimates of the parameters of a density function - UPDATED
In the case of the EM algorithm, the initial values can be set arbitrarily since the iterations are guaranteed to converge to the maximum:
We have seen that both the E and the M steps of the EM algorithm are increasi... | Self-study: Finding the maximum likelihood estimates of the parameters of a density function - UPDAT
In the case of the EM algorithm, the initial values can be set arbitrarily since the iterations are guaranteed to converge to the maximum:
We have seen that both the E and the M steps of the EM algor |
36,020 | In Max. Likelihood the expected score is zero for the true values. Is it also true for any other values? | Verbal formulation: "the expected value of the derivative of the log-likelihood of the sample evaluated (the derivative) at the true value, equals zero".
Innocent question-crucial remark: what is the "expected value" of a function? (informal) A: it is an integral through which we weigh a function using as weight the t... | In Max. Likelihood the expected score is zero for the true values. Is it also true for any other val | Verbal formulation: "the expected value of the derivative of the log-likelihood of the sample evaluated (the derivative) at the true value, equals zero".
Innocent question-crucial remark: what is the | In Max. Likelihood the expected score is zero for the true values. Is it also true for any other values?
Verbal formulation: "the expected value of the derivative of the log-likelihood of the sample evaluated (the derivative) at the true value, equals zero".
Innocent question-crucial remark: what is the "expected valu... | In Max. Likelihood the expected score is zero for the true values. Is it also true for any other val
Verbal formulation: "the expected value of the derivative of the log-likelihood of the sample evaluated (the derivative) at the true value, equals zero".
Innocent question-crucial remark: what is the |
36,021 | Chi-squared Vs Mutual information | They are related, so I don't suspect there to be a big difference (hence, go for mutual information if it's easier to calculate).
I haven't seen a formal argument for this, but my logic is:
A g-test is a derivate of mutual information ($G=2\cdot N \cdot MI(r,c)$, cfr. wiki link)
A Chi-squared leads
to the same conclus... | Chi-squared Vs Mutual information | They are related, so I don't suspect there to be a big difference (hence, go for mutual information if it's easier to calculate).
I haven't seen a formal argument for this, but my logic is:
A g-test | Chi-squared Vs Mutual information
They are related, so I don't suspect there to be a big difference (hence, go for mutual information if it's easier to calculate).
I haven't seen a formal argument for this, but my logic is:
A g-test is a derivate of mutual information ($G=2\cdot N \cdot MI(r,c)$, cfr. wiki link)
A Chi... | Chi-squared Vs Mutual information
They are related, so I don't suspect there to be a big difference (hence, go for mutual information if it's easier to calculate).
I haven't seen a formal argument for this, but my logic is:
A g-test |
36,022 | Chi-squared Vs Mutual information | Just as a follow up to @ciri answer, the same arguments have been developed in the following paper:
Richter et al., 2018 | Chi-squared Vs Mutual information | Just as a follow up to @ciri answer, the same arguments have been developed in the following paper:
Richter et al., 2018 | Chi-squared Vs Mutual information
Just as a follow up to @ciri answer, the same arguments have been developed in the following paper:
Richter et al., 2018 | Chi-squared Vs Mutual information
Just as a follow up to @ciri answer, the same arguments have been developed in the following paper:
Richter et al., 2018 |
36,023 | A person repeatedly selects the two most similar items out of three. How to model/estimate a perceptual distance between the items? | A good approach to this kind of problem can be found in section 4 of the paper The Bayesian Image Retrieval System, PicHunter by Cox et al (2000). The data is a set of integer outcomes $A_1, ..., A_N$ where $N$ is the number of trials. In your case, there are 3 possible outcomes per trial. I will let $A_i$ be the in... | A person repeatedly selects the two most similar items out of three. How to model/estimate a percept | A good approach to this kind of problem can be found in section 4 of the paper The Bayesian Image Retrieval System, PicHunter by Cox et al (2000). The data is a set of integer outcomes $A_1, ..., A_N | A person repeatedly selects the two most similar items out of three. How to model/estimate a perceptual distance between the items?
A good approach to this kind of problem can be found in section 4 of the paper The Bayesian Image Retrieval System, PicHunter by Cox et al (2000). The data is a set of integer outcomes $A... | A person repeatedly selects the two most similar items out of three. How to model/estimate a percept
A good approach to this kind of problem can be found in section 4 of the paper The Bayesian Image Retrieval System, PicHunter by Cox et al (2000). The data is a set of integer outcomes $A_1, ..., A_N |
36,024 | A person repeatedly selects the two most similar items out of three. How to model/estimate a perceptual distance between the items? | Thought:
I think eigenfaces is a decent way to convert what can be million-dimensional spaces to a few tens of dimensions.
Premise:
So lets assume that you are using a decent eigenfaces tool, or one that:
does preprocessing to align appropriate features
handles colors in an appropriate way
makes sure the pictures used... | A person repeatedly selects the two most similar items out of three. How to model/estimate a percept | Thought:
I think eigenfaces is a decent way to convert what can be million-dimensional spaces to a few tens of dimensions.
Premise:
So lets assume that you are using a decent eigenfaces tool, or one t | A person repeatedly selects the two most similar items out of three. How to model/estimate a perceptual distance between the items?
Thought:
I think eigenfaces is a decent way to convert what can be million-dimensional spaces to a few tens of dimensions.
Premise:
So lets assume that you are using a decent eigenfaces to... | A person repeatedly selects the two most similar items out of three. How to model/estimate a percept
Thought:
I think eigenfaces is a decent way to convert what can be million-dimensional spaces to a few tens of dimensions.
Premise:
So lets assume that you are using a decent eigenfaces tool, or one t |
36,025 | Posterior predictive check following ABC inference for multiple parameters | Great question for a newcomer!!!
Your ABC algorithm provides you with a sample $\theta_1,\ldots,\theta_M$ from the ABC-posterior distribution. For each component of the vector $\theta$, you thus get a sample of size $M$ from the marginal ABC-posterior. For instance here is a toy example about the mean-variance normal p... | Posterior predictive check following ABC inference for multiple parameters | Great question for a newcomer!!!
Your ABC algorithm provides you with a sample $\theta_1,\ldots,\theta_M$ from the ABC-posterior distribution. For each component of the vector $\theta$, you thus get a | Posterior predictive check following ABC inference for multiple parameters
Great question for a newcomer!!!
Your ABC algorithm provides you with a sample $\theta_1,\ldots,\theta_M$ from the ABC-posterior distribution. For each component of the vector $\theta$, you thus get a sample of size $M$ from the marginal ABC-pos... | Posterior predictive check following ABC inference for multiple parameters
Great question for a newcomer!!!
Your ABC algorithm provides you with a sample $\theta_1,\ldots,\theta_M$ from the ABC-posterior distribution. For each component of the vector $\theta$, you thus get a |
36,026 | $\bar{X}$ versus $\mathbb{E}(\bar{X})$? | First of all, $\bar{X}$ is not an estimator of the Normal distribution. The true mean $\mu$ (as well as the true variance $\sigma^2$) is a parameter of the Normal distribution. $\bar{X}$ is an estimator for $\mu$ and this distinction is extremely important.
It sounds like that your confusion stems from not understandin... | $\bar{X}$ versus $\mathbb{E}(\bar{X})$? | First of all, $\bar{X}$ is not an estimator of the Normal distribution. The true mean $\mu$ (as well as the true variance $\sigma^2$) is a parameter of the Normal distribution. $\bar{X}$ is an estimat | $\bar{X}$ versus $\mathbb{E}(\bar{X})$?
First of all, $\bar{X}$ is not an estimator of the Normal distribution. The true mean $\mu$ (as well as the true variance $\sigma^2$) is a parameter of the Normal distribution. $\bar{X}$ is an estimator for $\mu$ and this distinction is extremely important.
It sounds like that yo... | $\bar{X}$ versus $\mathbb{E}(\bar{X})$?
First of all, $\bar{X}$ is not an estimator of the Normal distribution. The true mean $\mu$ (as well as the true variance $\sigma^2$) is a parameter of the Normal distribution. $\bar{X}$ is an estimat |
36,027 | Under what circumstances is the log likelihood function of a point process concave? | This depends on the parameterization of the conditional intensity function. The (regular) point process likelihood is given by,
$L = \left[ \prod_i \lambda^\ast(t_i) \right] \exp\left(-\int \lambda^\ast(u) \,\mathrm{d}u \right) $
with the conditional intensity function $\lambda^\ast(t)$ (from Daley & Vere-Jones, 2002).... | Under what circumstances is the log likelihood function of a point process concave? | This depends on the parameterization of the conditional intensity function. The (regular) point process likelihood is given by,
$L = \left[ \prod_i \lambda^\ast(t_i) \right] \exp\left(-\int \lambda^\a | Under what circumstances is the log likelihood function of a point process concave?
This depends on the parameterization of the conditional intensity function. The (regular) point process likelihood is given by,
$L = \left[ \prod_i \lambda^\ast(t_i) \right] \exp\left(-\int \lambda^\ast(u) \,\mathrm{d}u \right) $
with t... | Under what circumstances is the log likelihood function of a point process concave?
This depends on the parameterization of the conditional intensity function. The (regular) point process likelihood is given by,
$L = \left[ \prod_i \lambda^\ast(t_i) \right] \exp\left(-\int \lambda^\a |
36,028 | Under what circumstances is the log likelihood function of a point process concave? | The likelihood function, as a functional form, is also a density. Since we are interested in the logarithm of the likelihood, the issue can be broken in two:
a) Is the density "log-concave"? (is its logarithm a concave function of the random variable?)
b) Is the density (viewed as a function of the paramaters) log-conc... | Under what circumstances is the log likelihood function of a point process concave? | The likelihood function, as a functional form, is also a density. Since we are interested in the logarithm of the likelihood, the issue can be broken in two:
a) Is the density "log-concave"? (is its l | Under what circumstances is the log likelihood function of a point process concave?
The likelihood function, as a functional form, is also a density. Since we are interested in the logarithm of the likelihood, the issue can be broken in two:
a) Is the density "log-concave"? (is its logarithm a concave function of the r... | Under what circumstances is the log likelihood function of a point process concave?
The likelihood function, as a functional form, is also a density. Since we are interested in the logarithm of the likelihood, the issue can be broken in two:
a) Is the density "log-concave"? (is its l |
36,029 | Simulation involving conditioning on sum of random variables | My comment in the referenced thread suggests one efficient approach: because $X=A+B$ and $Y=A-B$ are jointly Normal with zero covariance, they are independent, whence the simulation only needs to generate $Y$ (which has mean $0$ and variance $2$) and construct $A = (X+Y)/2$. In this example the distribution of $A^2|(A... | Simulation involving conditioning on sum of random variables | My comment in the referenced thread suggests one efficient approach: because $X=A+B$ and $Y=A-B$ are jointly Normal with zero covariance, they are independent, whence the simulation only needs to gene | Simulation involving conditioning on sum of random variables
My comment in the referenced thread suggests one efficient approach: because $X=A+B$ and $Y=A-B$ are jointly Normal with zero covariance, they are independent, whence the simulation only needs to generate $Y$ (which has mean $0$ and variance $2$) and construc... | Simulation involving conditioning on sum of random variables
My comment in the referenced thread suggests one efficient approach: because $X=A+B$ and $Y=A-B$ are jointly Normal with zero covariance, they are independent, whence the simulation only needs to gene |
36,030 | Simulation involving conditioning on sum of random variables | A generic way to solve this problem is to consider the change of variables from $(A,B)$ to $(A,A+B=S)$. The Jacobian of this transform being equal to one (1), the density of $(A,S)$ is
$$f_{A,S}(a,s)=f_A(a)f_B(s-a)$$
Therefore the density of $A$ conditional on $S=s$ is
$$f_{A|S}(a|s)\propto f_A(a)f_B(s-a)$$
with the pr... | Simulation involving conditioning on sum of random variables | A generic way to solve this problem is to consider the change of variables from $(A,B)$ to $(A,A+B=S)$. The Jacobian of this transform being equal to one (1), the density of $(A,S)$ is
$$f_{A,S}(a,s)= | Simulation involving conditioning on sum of random variables
A generic way to solve this problem is to consider the change of variables from $(A,B)$ to $(A,A+B=S)$. The Jacobian of this transform being equal to one (1), the density of $(A,S)$ is
$$f_{A,S}(a,s)=f_A(a)f_B(s-a)$$
Therefore the density of $A$ conditional o... | Simulation involving conditioning on sum of random variables
A generic way to solve this problem is to consider the change of variables from $(A,B)$ to $(A,A+B=S)$. The Jacobian of this transform being equal to one (1), the density of $(A,S)$ is
$$f_{A,S}(a,s)= |
36,031 | Simulation involving conditioning on sum of random variables | You could solve this problem using bootstrap samples. For example,
n <- 1000000
A <- rnorm(n)
B <- rnorm(n)
AB <- cbind(A,B)
boots <- 100
bootstrap_data <- matrix(NA,nrow=boots*n,ncol=2)
for(i in 1:boots){
index <- sample(1:n,n,replace=TRUE)
bootstrap_data[(i*n-n+1):(i*n),] <- cbind(A[index],B[index])
}
... | Simulation involving conditioning on sum of random variables | You could solve this problem using bootstrap samples. For example,
n <- 1000000
A <- rnorm(n)
B <- rnorm(n)
AB <- cbind(A,B)
boots <- 100
bootstrap_data <- matrix(NA,nrow=boots*n,ncol=2)
for(i i | Simulation involving conditioning on sum of random variables
You could solve this problem using bootstrap samples. For example,
n <- 1000000
A <- rnorm(n)
B <- rnorm(n)
AB <- cbind(A,B)
boots <- 100
bootstrap_data <- matrix(NA,nrow=boots*n,ncol=2)
for(i in 1:boots){
index <- sample(1:n,n,replace=TRUE)
boo... | Simulation involving conditioning on sum of random variables
You could solve this problem using bootstrap samples. For example,
n <- 1000000
A <- rnorm(n)
B <- rnorm(n)
AB <- cbind(A,B)
boots <- 100
bootstrap_data <- matrix(NA,nrow=boots*n,ncol=2)
for(i i |
36,032 | Simulation involving conditioning on sum of random variables | it seems to me that the question becomes this:
how to simulate (X,Y) conditional on X+Y=k and then
use monte carlo
to estimate EU(X,Y) for some function U(x,y)
let's start by reviewing importance sampling :
$E V(Z_1) = \int V(z) f_1(z) = \int V(z) \frac{f_1(z)}{f_2(z)} f_2(z) = E V(Z_2)\frac{f_1(Z_2)}{f_2(Z_2)}$
whe... | Simulation involving conditioning on sum of random variables | it seems to me that the question becomes this:
how to simulate (X,Y) conditional on X+Y=k and then
use monte carlo
to estimate EU(X,Y) for some function U(x,y)
let's start by reviewing importance s | Simulation involving conditioning on sum of random variables
it seems to me that the question becomes this:
how to simulate (X,Y) conditional on X+Y=k and then
use monte carlo
to estimate EU(X,Y) for some function U(x,y)
let's start by reviewing importance sampling :
$E V(Z_1) = \int V(z) f_1(z) = \int V(z) \frac{f_... | Simulation involving conditioning on sum of random variables
it seems to me that the question becomes this:
how to simulate (X,Y) conditional on X+Y=k and then
use monte carlo
to estimate EU(X,Y) for some function U(x,y)
let's start by reviewing importance s |
36,033 | Is there a test/technique/method for comparing principal components decompositions between samples? | So as far as I understood, you imagine that you have two clouds of $n$ points each, in a $d$-dimensional space; you do PCA on each cloud separately and then want to compare the PCA results between clouds, and to test for significant differences in some of the more important PCA features.
I don't think there are any sta... | Is there a test/technique/method for comparing principal components decompositions between samples? | So as far as I understood, you imagine that you have two clouds of $n$ points each, in a $d$-dimensional space; you do PCA on each cloud separately and then want to compare the PCA results between clo | Is there a test/technique/method for comparing principal components decompositions between samples?
So as far as I understood, you imagine that you have two clouds of $n$ points each, in a $d$-dimensional space; you do PCA on each cloud separately and then want to compare the PCA results between clouds, and to test for... | Is there a test/technique/method for comparing principal components decompositions between samples?
So as far as I understood, you imagine that you have two clouds of $n$ points each, in a $d$-dimensional space; you do PCA on each cloud separately and then want to compare the PCA results between clo |
36,034 | Is there a test/technique/method for comparing principal components decompositions between samples? | say you have the sample set2 1 and 2, and you found their 1 through nth principle components which are able to map out 90% of the information ( n may be different for both, and 90 is arbitrary).
You can calculate how much of the information in set1 can be retained after mapping to their principal components space and ... | Is there a test/technique/method for comparing principal components decompositions between samples? | say you have the sample set2 1 and 2, and you found their 1 through nth principle components which are able to map out 90% of the information ( n may be different for both, and 90 is arbitrary).
You | Is there a test/technique/method for comparing principal components decompositions between samples?
say you have the sample set2 1 and 2, and you found their 1 through nth principle components which are able to map out 90% of the information ( n may be different for both, and 90 is arbitrary).
You can calculate how mu... | Is there a test/technique/method for comparing principal components decompositions between samples?
say you have the sample set2 1 and 2, and you found their 1 through nth principle components which are able to map out 90% of the information ( n may be different for both, and 90 is arbitrary).
You |
36,035 | What is sparse regression model | I am working on a research project using Sparse Regression, and what I learned and understood so far is that $\mathbf{A}$ is the input matrix, such that $ \mathbf{A} \in \mathbb{R}^{n \times p}$ where $n$ is number of samples, and $p$ is number of features.
you are trying to find a set of optimal projection vectors $\v... | What is sparse regression model | I am working on a research project using Sparse Regression, and what I learned and understood so far is that $\mathbf{A}$ is the input matrix, such that $ \mathbf{A} \in \mathbb{R}^{n \times p}$ where | What is sparse regression model
I am working on a research project using Sparse Regression, and what I learned and understood so far is that $\mathbf{A}$ is the input matrix, such that $ \mathbf{A} \in \mathbb{R}^{n \times p}$ where $n$ is number of samples, and $p$ is number of features.
you are trying to find a set o... | What is sparse regression model
I am working on a research project using Sparse Regression, and what I learned and understood so far is that $\mathbf{A}$ is the input matrix, such that $ \mathbf{A} \in \mathbb{R}^{n \times p}$ where |
36,036 | What is sparse regression model | I have been searching for the answer to this question myself and keeping ending up on this thread. I wanted to address your question #2 in case you're still interested or in case others stumble on this post.
I think your understanding of sparse regressions is wrong. I believe that sparse regression is an umbrella term ... | What is sparse regression model | I have been searching for the answer to this question myself and keeping ending up on this thread. I wanted to address your question #2 in case you're still interested or in case others stumble on thi | What is sparse regression model
I have been searching for the answer to this question myself and keeping ending up on this thread. I wanted to address your question #2 in case you're still interested or in case others stumble on this post.
I think your understanding of sparse regressions is wrong. I believe that sparse... | What is sparse regression model
I have been searching for the answer to this question myself and keeping ending up on this thread. I wanted to address your question #2 in case you're still interested or in case others stumble on thi |
36,037 | $E[e^{cX}]$ where $c < 0$ and $X$ is lognormally distributed | What you want is the moment generating function of a lognormal variable, which is known to be a hard problem. Alternatively, this is the Laplace transform, which is your expression with $c$ replaced by $-c$. You should have a look at https://en.wikipedia.org/wiki/Log-normal_distribution which do have some useful in... | $E[e^{cX}]$ where $c < 0$ and $X$ is lognormally distributed | What you want is the moment generating function of a lognormal variable, which is known to be a hard problem. Alternatively, this is the Laplace transform, which is your expression with $c$ replaced b | $E[e^{cX}]$ where $c < 0$ and $X$ is lognormally distributed
What you want is the moment generating function of a lognormal variable, which is known to be a hard problem. Alternatively, this is the Laplace transform, which is your expression with $c$ replaced by $-c$. You should have a look at https://en.wikipedia.org/... | $E[e^{cX}]$ where $c < 0$ and $X$ is lognormally distributed
What you want is the moment generating function of a lognormal variable, which is known to be a hard problem. Alternatively, this is the Laplace transform, which is your expression with $c$ replaced b |
36,038 | comparing OLS, ridge and lasso | Since the goal is prediction you can choose some distance measure and then calculate the distance between your predictions $\hat{Y}$ and the true values $Y$, choosing the method with the minimum distance. The most common distance measurement for this setting is the mean squared error: MSE = $\sum_{i=1}^n \left(\hat{Y_i... | comparing OLS, ridge and lasso | Since the goal is prediction you can choose some distance measure and then calculate the distance between your predictions $\hat{Y}$ and the true values $Y$, choosing the method with the minimum dista | comparing OLS, ridge and lasso
Since the goal is prediction you can choose some distance measure and then calculate the distance between your predictions $\hat{Y}$ and the true values $Y$, choosing the method with the minimum distance. The most common distance measurement for this setting is the mean squared error: MSE... | comparing OLS, ridge and lasso
Since the goal is prediction you can choose some distance measure and then calculate the distance between your predictions $\hat{Y}$ and the true values $Y$, choosing the method with the minimum dista |
36,039 | Required: Method of moments fitting routine for the two-parameter generalized Pareto | As the case when $\xi = 0$ simply corresponds to an exponential distribution with scale parameter $\beta$, it is trivial to compute the method of moments estimator given $\overline y$, the first sample raw moment (the second is not needed since there is only one parameter to estimate in this case). For the case $\xi <... | Required: Method of moments fitting routine for the two-parameter generalized Pareto | As the case when $\xi = 0$ simply corresponds to an exponential distribution with scale parameter $\beta$, it is trivial to compute the method of moments estimator given $\overline y$, the first sampl | Required: Method of moments fitting routine for the two-parameter generalized Pareto
As the case when $\xi = 0$ simply corresponds to an exponential distribution with scale parameter $\beta$, it is trivial to compute the method of moments estimator given $\overline y$, the first sample raw moment (the second is not nee... | Required: Method of moments fitting routine for the two-parameter generalized Pareto
As the case when $\xi = 0$ simply corresponds to an exponential distribution with scale parameter $\beta$, it is trivial to compute the method of moments estimator given $\overline y$, the first sampl |
36,040 | Background subtraction for signal and error analysis | Estimating that error correctly will be tricky. But I would like to suggest it is more important first to find a better procedure to subtract background. Only once a good procedure is available would it be worthwhile analyzing the amount of error.
In this case, using the mean is biased upwards by the contributions fr... | Background subtraction for signal and error analysis | Estimating that error correctly will be tricky. But I would like to suggest it is more important first to find a better procedure to subtract background. Only once a good procedure is available woul | Background subtraction for signal and error analysis
Estimating that error correctly will be tricky. But I would like to suggest it is more important first to find a better procedure to subtract background. Only once a good procedure is available would it be worthwhile analyzing the amount of error.
In this case, usi... | Background subtraction for signal and error analysis
Estimating that error correctly will be tricky. But I would like to suggest it is more important first to find a better procedure to subtract background. Only once a good procedure is available woul |
36,041 | Background subtraction for signal and error analysis | On the background computation:
Since what you are doing is to measure the background by calculating the average of some values with backgroung only, you can use the error on the average ($\sigma_{Bckg}/\sqrt{n_{avg}}$) and this should estimate correctly the background variation, taking into account the variation of the... | Background subtraction for signal and error analysis | On the background computation:
Since what you are doing is to measure the background by calculating the average of some values with backgroung only, you can use the error on the average ($\sigma_{Bckg | Background subtraction for signal and error analysis
On the background computation:
Since what you are doing is to measure the background by calculating the average of some values with backgroung only, you can use the error on the average ($\sigma_{Bckg}/\sqrt{n_{avg}}$) and this should estimate correctly the backgroun... | Background subtraction for signal and error analysis
On the background computation:
Since what you are doing is to measure the background by calculating the average of some values with backgroung only, you can use the error on the average ($\sigma_{Bckg |
36,042 | Estimating Failure Rate from Observed Data | This does seem like a good model, implemented correctly in PyMC. There are two Bayesian stats facts that we can use to confirm your answer with another method:
$\textrm{Beta}(1,1)$ is equivalent to the uniform distribution on the interval $[0,1]$;
The beta and binomial distributions are conjugate.
This means that th... | Estimating Failure Rate from Observed Data | This does seem like a good model, implemented correctly in PyMC. There are two Bayesian stats facts that we can use to confirm your answer with another method:
$\textrm{Beta}(1,1)$ is equivalent to | Estimating Failure Rate from Observed Data
This does seem like a good model, implemented correctly in PyMC. There are two Bayesian stats facts that we can use to confirm your answer with another method:
$\textrm{Beta}(1,1)$ is equivalent to the uniform distribution on the interval $[0,1]$;
The beta and binomial distr... | Estimating Failure Rate from Observed Data
This does seem like a good model, implemented correctly in PyMC. There are two Bayesian stats facts that we can use to confirm your answer with another method:
$\textrm{Beta}(1,1)$ is equivalent to |
36,043 | Why is variability measured relative to a point? | Actually, not all measures of dispersion are calculated relative to some central point. Examples include the $Q_n$ and $S_n$ statistics. Your intuition is sharp, as indeed, the calculation of these only relies on pairwise differences.
A downside of these two estimators is that they are less efficient at the gaussian di... | Why is variability measured relative to a point? | Actually, not all measures of dispersion are calculated relative to some central point. Examples include the $Q_n$ and $S_n$ statistics. Your intuition is sharp, as indeed, the calculation of these on | Why is variability measured relative to a point?
Actually, not all measures of dispersion are calculated relative to some central point. Examples include the $Q_n$ and $S_n$ statistics. Your intuition is sharp, as indeed, the calculation of these only relies on pairwise differences.
A downside of these two estimators i... | Why is variability measured relative to a point?
Actually, not all measures of dispersion are calculated relative to some central point. Examples include the $Q_n$ and $S_n$ statistics. Your intuition is sharp, as indeed, the calculation of these on |
36,044 | What is MA(q) model input in real world? | When the unobserved error terms are autocorrelated, there are at least 4 possible strategies since you can't just add the errors into your model:
Use OLS with a corrected variance-covariance matrix (such as Newey-West)
Transformation of the model
Feasible Generalized Least Squares
Instrumental Variables
(2) is probab... | What is MA(q) model input in real world? | When the unobserved error terms are autocorrelated, there are at least 4 possible strategies since you can't just add the errors into your model:
Use OLS with a corrected variance-covariance matrix ( | What is MA(q) model input in real world?
When the unobserved error terms are autocorrelated, there are at least 4 possible strategies since you can't just add the errors into your model:
Use OLS with a corrected variance-covariance matrix (such as Newey-West)
Transformation of the model
Feasible Generalized Least Squa... | What is MA(q) model input in real world?
When the unobserved error terms are autocorrelated, there are at least 4 possible strategies since you can't just add the errors into your model:
Use OLS with a corrected variance-covariance matrix ( |
36,045 | What is MA(q) model input in real world? | When trying to get an intuitive real world picture of MA or AR (or ARMA or ARIMA if you are extending it) I often find it useful to think of carry over effects, that is something happening in one period carries over into the next.
Here's an example: say you are modelling newspaper sales. The noise (random error) in su... | What is MA(q) model input in real world? | When trying to get an intuitive real world picture of MA or AR (or ARMA or ARIMA if you are extending it) I often find it useful to think of carry over effects, that is something happening in one peri | What is MA(q) model input in real world?
When trying to get an intuitive real world picture of MA or AR (or ARMA or ARIMA if you are extending it) I often find it useful to think of carry over effects, that is something happening in one period carries over into the next.
Here's an example: say you are modelling newspa... | What is MA(q) model input in real world?
When trying to get an intuitive real world picture of MA or AR (or ARMA or ARIMA if you are extending it) I often find it useful to think of carry over effects, that is something happening in one peri |
36,046 | What to do when I have expected count <5 warning for a chi squared test? | A lot of the time, you may not need to do anything. The "5" rule is overly conservative, and there are a number of less restrictive (but somewhat more complex) guidelines to be found in the more recent literature (where 'more recent' means 'over the last half century or more').
For example, if all your cells have expec... | What to do when I have expected count <5 warning for a chi squared test? | A lot of the time, you may not need to do anything. The "5" rule is overly conservative, and there are a number of less restrictive (but somewhat more complex) guidelines to be found in the more recen | What to do when I have expected count <5 warning for a chi squared test?
A lot of the time, you may not need to do anything. The "5" rule is overly conservative, and there are a number of less restrictive (but somewhat more complex) guidelines to be found in the more recent literature (where 'more recent' means 'over t... | What to do when I have expected count <5 warning for a chi squared test?
A lot of the time, you may not need to do anything. The "5" rule is overly conservative, and there are a number of less restrictive (but somewhat more complex) guidelines to be found in the more recen |
36,047 | What to do when I have expected count <5 warning for a chi squared test? | First let me try to clarify the question:
You have a bunch of chi-square tests to run, specifically 12 answers to questions against several different demographic variables. All the demographic variables are nominal, with different numbers of levels (e.g. could be 2 (Male vs. female), 5 for race (or fewer depending on ... | What to do when I have expected count <5 warning for a chi squared test? | First let me try to clarify the question:
You have a bunch of chi-square tests to run, specifically 12 answers to questions against several different demographic variables. All the demographic variab | What to do when I have expected count <5 warning for a chi squared test?
First let me try to clarify the question:
You have a bunch of chi-square tests to run, specifically 12 answers to questions against several different demographic variables. All the demographic variables are nominal, with different numbers of leve... | What to do when I have expected count <5 warning for a chi squared test?
First let me try to clarify the question:
You have a bunch of chi-square tests to run, specifically 12 answers to questions against several different demographic variables. All the demographic variab |
36,048 | What to do when I have expected count <5 warning for a chi squared test? | You have two options:
ignore the warning
combine/merge the bins | What to do when I have expected count <5 warning for a chi squared test? | You have two options:
ignore the warning
combine/merge the bins | What to do when I have expected count <5 warning for a chi squared test?
You have two options:
ignore the warning
combine/merge the bins | What to do when I have expected count <5 warning for a chi squared test?
You have two options:
ignore the warning
combine/merge the bins |
36,049 | Standardizing inputs for CART | My answer at this stage is based on my intuitive understanding of how CART works, so take it face value.
Standardization does not add or subtract information contained in a given variable and does not distort its relationship to a target variable. For example, if you had a variable "age" which was a predictor for "purc... | Standardizing inputs for CART | My answer at this stage is based on my intuitive understanding of how CART works, so take it face value.
Standardization does not add or subtract information contained in a given variable and does not | Standardizing inputs for CART
My answer at this stage is based on my intuitive understanding of how CART works, so take it face value.
Standardization does not add or subtract information contained in a given variable and does not distort its relationship to a target variable. For example, if you had a variable "age" w... | Standardizing inputs for CART
My answer at this stage is based on my intuitive understanding of how CART works, so take it face value.
Standardization does not add or subtract information contained in a given variable and does not |
36,050 | Standardizing inputs for CART | I will try to give a formal proof here to clarify things.
Step 1
We denote with $x = {x_1, x_2, .., x_n}$ a vector, and with $var(x)=\frac{1}{n}\sum_{i=1}^{n}(x_i-\frac{1}{n}\sum_{j=1}^{n}x_j)^2$ the biased sample variance.
We denote with $y = \frac{x-m}{sd}$ the scaled version.
We work out a formula for $var(y)$ in te... | Standardizing inputs for CART | I will try to give a formal proof here to clarify things.
Step 1
We denote with $x = {x_1, x_2, .., x_n}$ a vector, and with $var(x)=\frac{1}{n}\sum_{i=1}^{n}(x_i-\frac{1}{n}\sum_{j=1}^{n}x_j)^2$ the | Standardizing inputs for CART
I will try to give a formal proof here to clarify things.
Step 1
We denote with $x = {x_1, x_2, .., x_n}$ a vector, and with $var(x)=\frac{1}{n}\sum_{i=1}^{n}(x_i-\frac{1}{n}\sum_{j=1}^{n}x_j)^2$ the biased sample variance.
We denote with $y = \frac{x-m}{sd}$ the scaled version.
We work ou... | Standardizing inputs for CART
I will try to give a formal proof here to clarify things.
Step 1
We denote with $x = {x_1, x_2, .., x_n}$ a vector, and with $var(x)=\frac{1}{n}\sum_{i=1}^{n}(x_i-\frac{1}{n}\sum_{j=1}^{n}x_j)^2$ the |
36,051 | Statistics Modelling Question | Quick Intuitive Solution
The best approach is to accept any offer exceeding a threshold $t$ to be determined.
The expected value of such offers is $(1+t)/2$ while the expected waiting time before such an offer is seen is $1/(1-t)$, which is multiplied by the daily cost $c$. Thus we must find $t$ that maximizes the net ... | Statistics Modelling Question | Quick Intuitive Solution
The best approach is to accept any offer exceeding a threshold $t$ to be determined.
The expected value of such offers is $(1+t)/2$ while the expected waiting time before such | Statistics Modelling Question
Quick Intuitive Solution
The best approach is to accept any offer exceeding a threshold $t$ to be determined.
The expected value of such offers is $(1+t)/2$ while the expected waiting time before such an offer is seen is $1/(1-t)$, which is multiplied by the daily cost $c$. Thus we must fi... | Statistics Modelling Question
Quick Intuitive Solution
The best approach is to accept any offer exceeding a threshold $t$ to be determined.
The expected value of such offers is $(1+t)/2$ while the expected waiting time before such |
36,052 | time series dimensionality reduction | You might want to consider forecastable component analysis (ForeCA), which is a dimension reduction technique for time series, specifically designed to obtaina lower dimensional space that is easier to forecast than the original time series.
Let's look at an example of monthly sunspot numbers and for computational effi... | time series dimensionality reduction | You might want to consider forecastable component analysis (ForeCA), which is a dimension reduction technique for time series, specifically designed to obtaina lower dimensional space that is easier t | time series dimensionality reduction
You might want to consider forecastable component analysis (ForeCA), which is a dimension reduction technique for time series, specifically designed to obtaina lower dimensional space that is easier to forecast than the original time series.
Let's look at an example of monthly sunsp... | time series dimensionality reduction
You might want to consider forecastable component analysis (ForeCA), which is a dimension reduction technique for time series, specifically designed to obtaina lower dimensional space that is easier t |
36,053 | time series dimensionality reduction | We see data like this from a number of fast food franchises that want to predict demand in 15 minute intervals. You can construct a daily model that incorporates day-of-the-week effects, weekly effects, monthly effects , week of the-month effects , day-of-the month effects, weekend effects , holiday lead and lag effect... | time series dimensionality reduction | We see data like this from a number of fast food franchises that want to predict demand in 15 minute intervals. You can construct a daily model that incorporates day-of-the-week effects, weekly effect | time series dimensionality reduction
We see data like this from a number of fast food franchises that want to predict demand in 15 minute intervals. You can construct a daily model that incorporates day-of-the-week effects, weekly effects, monthly effects , week of the-month effects , day-of-the month effects, weekend ... | time series dimensionality reduction
We see data like this from a number of fast food franchises that want to predict demand in 15 minute intervals. You can construct a daily model that incorporates day-of-the-week effects, weekly effect |
36,054 | What does it mean to sample a probability vector from a Dirichlet distribution? | A Dirichlet distribution is often used to probabilistically categorize events among several categories. Suppose that weather events take a Dirichlet distribution. We might then think that tomorrow's weather has probability of being sunny equal to 0.25, probability of rain equal to 0.5, and probability of snow equal to ... | What does it mean to sample a probability vector from a Dirichlet distribution? | A Dirichlet distribution is often used to probabilistically categorize events among several categories. Suppose that weather events take a Dirichlet distribution. We might then think that tomorrow's w | What does it mean to sample a probability vector from a Dirichlet distribution?
A Dirichlet distribution is often used to probabilistically categorize events among several categories. Suppose that weather events take a Dirichlet distribution. We might then think that tomorrow's weather has probability of being sunny eq... | What does it mean to sample a probability vector from a Dirichlet distribution?
A Dirichlet distribution is often used to probabilistically categorize events among several categories. Suppose that weather events take a Dirichlet distribution. We might then think that tomorrow's w |
36,055 | Why only the mean value is used in (K-means) clustering method? | There a literally thousands of k-means variations. Including soft assignment, variance and covariance (usually referred to as Gaussian Mixture Modeling or EM algorithm).
However, I'd like to point out a few things:
K-means is not based on Euclidean distance. It's based on variance minimization. Since the variance is t... | Why only the mean value is used in (K-means) clustering method? | There a literally thousands of k-means variations. Including soft assignment, variance and covariance (usually referred to as Gaussian Mixture Modeling or EM algorithm).
However, I'd like to point out | Why only the mean value is used in (K-means) clustering method?
There a literally thousands of k-means variations. Including soft assignment, variance and covariance (usually referred to as Gaussian Mixture Modeling or EM algorithm).
However, I'd like to point out a few things:
K-means is not based on Euclidean distan... | Why only the mean value is used in (K-means) clustering method?
There a literally thousands of k-means variations. Including soft assignment, variance and covariance (usually referred to as Gaussian Mixture Modeling or EM algorithm).
However, I'd like to point out |
36,056 | Why only the mean value is used in (K-means) clustering method? | There are lots of different clustering techniques out there, and K-means is just one approach. As DL Dahly commented, EM algorithms can be used for clustering in much the way you described. It's worth noting that the main difference between K-means and using EM with a guassian mixture model for clustering is the shape ... | Why only the mean value is used in (K-means) clustering method? | There are lots of different clustering techniques out there, and K-means is just one approach. As DL Dahly commented, EM algorithms can be used for clustering in much the way you described. It's worth | Why only the mean value is used in (K-means) clustering method?
There are lots of different clustering techniques out there, and K-means is just one approach. As DL Dahly commented, EM algorithms can be used for clustering in much the way you described. It's worth noting that the main difference between K-means and usi... | Why only the mean value is used in (K-means) clustering method?
There are lots of different clustering techniques out there, and K-means is just one approach. As DL Dahly commented, EM algorithms can be used for clustering in much the way you described. It's worth |
36,057 | Confusion over Lagged Dependent and HAC Standard Errors | Question 3)
In notation to be understood as matrix-vector, assume that the correct specification is
$$y = X\beta + \gamma y_{-1}+ e$$
(where $X$ contains the constant and the $X_1$ variable and $e$ is white noise, and $E(e\mid X) =0$), but you specify and estimate instead
$$y = X\beta + u$$
i.e. without including the ... | Confusion over Lagged Dependent and HAC Standard Errors | Question 3)
In notation to be understood as matrix-vector, assume that the correct specification is
$$y = X\beta + \gamma y_{-1}+ e$$
(where $X$ contains the constant and the $X_1$ variable and $e$ i | Confusion over Lagged Dependent and HAC Standard Errors
Question 3)
In notation to be understood as matrix-vector, assume that the correct specification is
$$y = X\beta + \gamma y_{-1}+ e$$
(where $X$ contains the constant and the $X_1$ variable and $e$ is white noise, and $E(e\mid X) =0$), but you specify and estimat... | Confusion over Lagged Dependent and HAC Standard Errors
Question 3)
In notation to be understood as matrix-vector, assume that the correct specification is
$$y = X\beta + \gamma y_{-1}+ e$$
(where $X$ contains the constant and the $X_1$ variable and $e$ i |
36,058 | Does more variables mean tighter confidence intervals? | do I ALWAYS get a tighter confidence interval if I include more variables in my model?
Yes, you do (EDIT: ...basically. Subject to some caveats. See comments below). Here's why: adding more variables reduces the SSE and thereby the variance of the model, on which your confidence and prediction intervals depend. This e... | Does more variables mean tighter confidence intervals? | do I ALWAYS get a tighter confidence interval if I include more variables in my model?
Yes, you do (EDIT: ...basically. Subject to some caveats. See comments below). Here's why: adding more variables | Does more variables mean tighter confidence intervals?
do I ALWAYS get a tighter confidence interval if I include more variables in my model?
Yes, you do (EDIT: ...basically. Subject to some caveats. See comments below). Here's why: adding more variables reduces the SSE and thereby the variance of the model, on which ... | Does more variables mean tighter confidence intervals?
do I ALWAYS get a tighter confidence interval if I include more variables in my model?
Yes, you do (EDIT: ...basically. Subject to some caveats. See comments below). Here's why: adding more variables |
36,059 | Question on the consequences of the Kolmogorov axioms | Let X be a standard normal random variable with $S=(-\infty,\infty)$. Here, $P(X=1)=0$ but $\{1\}\neq \emptyset$.
To show that $P(A)=1$ does not imply that $A=S$, consider the following. You flip a coin an infinite number of times. The event of getting all heads $\{H,H,H,H,...\}$ is in the sample space because it is p... | Question on the consequences of the Kolmogorov axioms | Let X be a standard normal random variable with $S=(-\infty,\infty)$. Here, $P(X=1)=0$ but $\{1\}\neq \emptyset$.
To show that $P(A)=1$ does not imply that $A=S$, consider the following. You flip a c | Question on the consequences of the Kolmogorov axioms
Let X be a standard normal random variable with $S=(-\infty,\infty)$. Here, $P(X=1)=0$ but $\{1\}\neq \emptyset$.
To show that $P(A)=1$ does not imply that $A=S$, consider the following. You flip a coin an infinite number of times. The event of getting all heads $\... | Question on the consequences of the Kolmogorov axioms
Let X be a standard normal random variable with $S=(-\infty,\infty)$. Here, $P(X=1)=0$ but $\{1\}\neq \emptyset$.
To show that $P(A)=1$ does not imply that $A=S$, consider the following. You flip a c |
36,060 | Question on the consequences of the Kolmogorov axioms | Following the arguments from @TrynnaDoStat:
Let $X$ be a standard normal random distribution, and therefore $X$ has support on whole $\mathbb{R}$. $P(X=1) = 0$ but $\{1\} \neq \emptyset$
Then using the principle that
$P(\Omega \backslash E) = 1 - P(E)$
$P(X \in \mathbb{R} \backslash ${1}$) = 1 - 0 = 1$, but $\mathbb{R}... | Question on the consequences of the Kolmogorov axioms | Following the arguments from @TrynnaDoStat:
Let $X$ be a standard normal random distribution, and therefore $X$ has support on whole $\mathbb{R}$. $P(X=1) = 0$ but $\{1\} \neq \emptyset$
Then using th | Question on the consequences of the Kolmogorov axioms
Following the arguments from @TrynnaDoStat:
Let $X$ be a standard normal random distribution, and therefore $X$ has support on whole $\mathbb{R}$. $P(X=1) = 0$ but $\{1\} \neq \emptyset$
Then using the principle that
$P(\Omega \backslash E) = 1 - P(E)$
$P(X \in \mat... | Question on the consequences of the Kolmogorov axioms
Following the arguments from @TrynnaDoStat:
Let $X$ be a standard normal random distribution, and therefore $X$ has support on whole $\mathbb{R}$. $P(X=1) = 0$ but $\{1\} \neq \emptyset$
Then using th |
36,061 | Question on the consequences of the Kolmogorov axioms | Take the uniform distribution on $S=[0,1]$. Now, $P[S]=1$, but also $P[S\setminus \{1\}]=1$ and $P[S \setminus \{1,1/2,1/3,\ldots\}] = 1$ as well even though both of the latter two are strict subsets of $S$. (Here the notation $A \setminus B$ means all elements belonging to set $A$ and not belonging to $B$.)
To answer ... | Question on the consequences of the Kolmogorov axioms | Take the uniform distribution on $S=[0,1]$. Now, $P[S]=1$, but also $P[S\setminus \{1\}]=1$ and $P[S \setminus \{1,1/2,1/3,\ldots\}] = 1$ as well even though both of the latter two are strict subsets | Question on the consequences of the Kolmogorov axioms
Take the uniform distribution on $S=[0,1]$. Now, $P[S]=1$, but also $P[S\setminus \{1\}]=1$ and $P[S \setminus \{1,1/2,1/3,\ldots\}] = 1$ as well even though both of the latter two are strict subsets of $S$. (Here the notation $A \setminus B$ means all elements belo... | Question on the consequences of the Kolmogorov axioms
Take the uniform distribution on $S=[0,1]$. Now, $P[S]=1$, but also $P[S\setminus \{1\}]=1$ and $P[S \setminus \{1,1/2,1/3,\ldots\}] = 1$ as well even though both of the latter two are strict subsets |
36,062 | Cause of singularity in matrix for quantile regression | I believe the reason it is coming up as singular is your second reason, that the data are binned. Duplicating observations (for a single x value, multiple responses) increases chances of singularity.
I had the same error message as you with a similarly structured dataset. I have multiple observations for each x value,... | Cause of singularity in matrix for quantile regression | I believe the reason it is coming up as singular is your second reason, that the data are binned. Duplicating observations (for a single x value, multiple responses) increases chances of singularity. | Cause of singularity in matrix for quantile regression
I believe the reason it is coming up as singular is your second reason, that the data are binned. Duplicating observations (for a single x value, multiple responses) increases chances of singularity.
I had the same error message as you with a similarly structured ... | Cause of singularity in matrix for quantile regression
I believe the reason it is coming up as singular is your second reason, that the data are binned. Duplicating observations (for a single x value, multiple responses) increases chances of singularity. |
36,063 | Cause of singularity in matrix for quantile regression | An alternative to rnorm() proposed by Jack Ballard is using jitter() from the base package. | Cause of singularity in matrix for quantile regression | An alternative to rnorm() proposed by Jack Ballard is using jitter() from the base package. | Cause of singularity in matrix for quantile regression
An alternative to rnorm() proposed by Jack Ballard is using jitter() from the base package. | Cause of singularity in matrix for quantile regression
An alternative to rnorm() proposed by Jack Ballard is using jitter() from the base package. |
36,064 | is Shapiro Wilk test insensitive on the tails? | The situation is complicated, but the results tend to the opposite of this claim: for moderate dataset sizes $n$, the Shapiro-Wilk test is more sensitive in the tails than elsewhere.
Quantifying sensitivity
I take "sensitive" to mean the extent to which the results vary when values in the dataset are perturbed. (Anot... | is Shapiro Wilk test insensitive on the tails? | The situation is complicated, but the results tend to the opposite of this claim: for moderate dataset sizes $n$, the Shapiro-Wilk test is more sensitive in the tails than elsewhere.
Quantifying sens | is Shapiro Wilk test insensitive on the tails?
The situation is complicated, but the results tend to the opposite of this claim: for moderate dataset sizes $n$, the Shapiro-Wilk test is more sensitive in the tails than elsewhere.
Quantifying sensitivity
I take "sensitive" to mean the extent to which the results vary w... | is Shapiro Wilk test insensitive on the tails?
The situation is complicated, but the results tend to the opposite of this claim: for moderate dataset sizes $n$, the Shapiro-Wilk test is more sensitive in the tails than elsewhere.
Quantifying sens |
36,065 | is Shapiro Wilk test insensitive on the tails? | I don't think it's particularly insensitive; I'd say it's more sensitive there than the Lilliefors test, for example, and I'm having trouble thinking of another comparable goodness of fit test in wide use* that I think will be much more sensitive to the tails.
If we look at power comparisons of goodness of fit tests (o... | is Shapiro Wilk test insensitive on the tails? | I don't think it's particularly insensitive; I'd say it's more sensitive there than the Lilliefors test, for example, and I'm having trouble thinking of another comparable goodness of fit test in wide | is Shapiro Wilk test insensitive on the tails?
I don't think it's particularly insensitive; I'd say it's more sensitive there than the Lilliefors test, for example, and I'm having trouble thinking of another comparable goodness of fit test in wide use* that I think will be much more sensitive to the tails.
If we look a... | is Shapiro Wilk test insensitive on the tails?
I don't think it's particularly insensitive; I'd say it's more sensitive there than the Lilliefors test, for example, and I'm having trouble thinking of another comparable goodness of fit test in wide |
36,066 | Why do zero differences not enter computation in the Wilcoxon signed ranked test? | It has to do with the assumptions of the test for which the distribution of the test statistic under the null is derived.
The variables are assumed to be continuous.
The probability of a tie is therefore 0 ... and this makes it possible to compute the permutation distribution of the test statistic under the null for ... | Why do zero differences not enter computation in the Wilcoxon signed ranked test? | It has to do with the assumptions of the test for which the distribution of the test statistic under the null is derived.
The variables are assumed to be continuous.
The probability of a tie is ther | Why do zero differences not enter computation in the Wilcoxon signed ranked test?
It has to do with the assumptions of the test for which the distribution of the test statistic under the null is derived.
The variables are assumed to be continuous.
The probability of a tie is therefore 0 ... and this makes it possible... | Why do zero differences not enter computation in the Wilcoxon signed ranked test?
It has to do with the assumptions of the test for which the distribution of the test statistic under the null is derived.
The variables are assumed to be continuous.
The probability of a tie is ther |
36,067 | Gibbs sampling to produce posterior pdf | I won't belabor the valid points made by @Tomas above so I will just answer with the following: The likelihood for a normal linear model is given by
$$f(y|\beta,\sigma,X)\propto\left(\frac{1}{\sigma^2}\right)^{n/2}\exp\left\{-\frac{1}{2\sigma^2}(y-X\beta)'(y-X\beta)\right\}$$ so now using the standard diffuse prior $$p... | Gibbs sampling to produce posterior pdf | I won't belabor the valid points made by @Tomas above so I will just answer with the following: The likelihood for a normal linear model is given by
$$f(y|\beta,\sigma,X)\propto\left(\frac{1}{\sigma^2 | Gibbs sampling to produce posterior pdf
I won't belabor the valid points made by @Tomas above so I will just answer with the following: The likelihood for a normal linear model is given by
$$f(y|\beta,\sigma,X)\propto\left(\frac{1}{\sigma^2}\right)^{n/2}\exp\left\{-\frac{1}{2\sigma^2}(y-X\beta)'(y-X\beta)\right\}$$ so ... | Gibbs sampling to produce posterior pdf
I won't belabor the valid points made by @Tomas above so I will just answer with the following: The likelihood for a normal linear model is given by
$$f(y|\beta,\sigma,X)\propto\left(\frac{1}{\sigma^2 |
36,068 | Consecutive Log Transformations | I think it helps here to be concrete, not abstract.
Think about the support of such transformations. ln $x$ requires that $x > 0$, ln ln $x$ requires that $x > 1$, ln ln ln $x$ that $x > e = \exp(1)$, and so forth. Can you think of variables that naturally satisfy such limits? Also, if one limit is natural, the others... | Consecutive Log Transformations | I think it helps here to be concrete, not abstract.
Think about the support of such transformations. ln $x$ requires that $x > 0$, ln ln $x$ requires that $x > 1$, ln ln ln $x$ that $x > e = \exp(1)$ | Consecutive Log Transformations
I think it helps here to be concrete, not abstract.
Think about the support of such transformations. ln $x$ requires that $x > 0$, ln ln $x$ requires that $x > 1$, ln ln ln $x$ that $x > e = \exp(1)$, and so forth. Can you think of variables that naturally satisfy such limits? Also, if ... | Consecutive Log Transformations
I think it helps here to be concrete, not abstract.
Think about the support of such transformations. ln $x$ requires that $x > 0$, ln ln $x$ requires that $x > 1$, ln ln ln $x$ that $x > e = \exp(1)$ |
36,069 | Obtaining covariance matrix from correlation matrix | Let $R$ be the correlation matrix and $S$ the vector of standard deviations, so that $S\cdot S$ (where $\cdot$ is the componentwise product) is the vector of variances. Then
$$ \text{diag}(S) R \text{diag}(S) $$ is the covariance matrix. This is fully explained here.
This can be implemented in R as
cor2cov_1 <- functio... | Obtaining covariance matrix from correlation matrix | Let $R$ be the correlation matrix and $S$ the vector of standard deviations, so that $S\cdot S$ (where $\cdot$ is the componentwise product) is the vector of variances. Then
$$ \text{diag}(S) R \text{ | Obtaining covariance matrix from correlation matrix
Let $R$ be the correlation matrix and $S$ the vector of standard deviations, so that $S\cdot S$ (where $\cdot$ is the componentwise product) is the vector of variances. Then
$$ \text{diag}(S) R \text{diag}(S) $$ is the covariance matrix. This is fully explained here.
... | Obtaining covariance matrix from correlation matrix
Let $R$ be the correlation matrix and $S$ the vector of standard deviations, so that $S\cdot S$ (where $\cdot$ is the componentwise product) is the vector of variances. Then
$$ \text{diag}(S) R \text{ |
36,070 | Image reconstruction using compressed sensing | This article helped me to understand this problem by using the Kronecker product. Here is an excerpt of the article:
Creating the $A$ matrix for 2D image data takes a little more ingenuity than it did in the 1D case. In the derivation that follows, we’ll use the Kronecker product $\otimes$ and the fact that the 2D dis... | Image reconstruction using compressed sensing | This article helped me to understand this problem by using the Kronecker product. Here is an excerpt of the article:
Creating the $A$ matrix for 2D image data takes a little more ingenuity than it di | Image reconstruction using compressed sensing
This article helped me to understand this problem by using the Kronecker product. Here is an excerpt of the article:
Creating the $A$ matrix for 2D image data takes a little more ingenuity than it did in the 1D case. In the derivation that follows, we’ll use the Kronecker ... | Image reconstruction using compressed sensing
This article helped me to understand this problem by using the Kronecker product. Here is an excerpt of the article:
Creating the $A$ matrix for 2D image data takes a little more ingenuity than it di |
36,071 | Image reconstruction using compressed sensing | I know that this is an old question but I am answering it in case googles this topic and would like to know the answer.
The problem is the compression matrix and the basis you are doing the sparse reconstruction in are coherent since they are both constructed from the DCT matrix. Do the sparse reconstruction in the DCT... | Image reconstruction using compressed sensing | I know that this is an old question but I am answering it in case googles this topic and would like to know the answer.
The problem is the compression matrix and the basis you are doing the sparse rec | Image reconstruction using compressed sensing
I know that this is an old question but I am answering it in case googles this topic and would like to know the answer.
The problem is the compression matrix and the basis you are doing the sparse reconstruction in are coherent since they are both constructed from the DCT m... | Image reconstruction using compressed sensing
I know that this is an old question but I am answering it in case googles this topic and would like to know the answer.
The problem is the compression matrix and the basis you are doing the sparse rec |
36,072 | What does "principled" mean, as in "principled Bayesian analysis"? | Too long for a comment:
Zhang starts the Bayesian analysis section with the phrase
More principled inferences come from Bayesian analysis.
and later says
There are several advantages of the principled Bayesian analysis.
I don't think "principled Bayesian analysis" is a thing. The word principled is just being used ... | What does "principled" mean, as in "principled Bayesian analysis"? | Too long for a comment:
Zhang starts the Bayesian analysis section with the phrase
More principled inferences come from Bayesian analysis.
and later says
There are several advantages of the princip | What does "principled" mean, as in "principled Bayesian analysis"?
Too long for a comment:
Zhang starts the Bayesian analysis section with the phrase
More principled inferences come from Bayesian analysis.
and later says
There are several advantages of the principled Bayesian analysis.
I don't think "principled Bay... | What does "principled" mean, as in "principled Bayesian analysis"?
Too long for a comment:
Zhang starts the Bayesian analysis section with the phrase
More principled inferences come from Bayesian analysis.
and later says
There are several advantages of the princip |
36,073 | How to incorporate costs (into logit model) of false positive, false negative, true positive, true negative if they are different costs? | This is best thought of, in my opinion, not of a change to the likelihood function, but as a way to translate estimated risk into an optimum decision. We maximize the (standard or standard penalized) likelihood for a reason - to get optimal models. Then optimal decisions are made one individual at a time based on tha... | How to incorporate costs (into logit model) of false positive, false negative, true positive, true n | This is best thought of, in my opinion, not of a change to the likelihood function, but as a way to translate estimated risk into an optimum decision. We maximize the (standard or standard penalized) | How to incorporate costs (into logit model) of false positive, false negative, true positive, true negative if they are different costs?
This is best thought of, in my opinion, not of a change to the likelihood function, but as a way to translate estimated risk into an optimum decision. We maximize the (standard or st... | How to incorporate costs (into logit model) of false positive, false negative, true positive, true n
This is best thought of, in my opinion, not of a change to the likelihood function, but as a way to translate estimated risk into an optimum decision. We maximize the (standard or standard penalized) |
36,074 | How to incorporate costs (into logit model) of false positive, false negative, true positive, true negative if they are different costs? | There are a few approaches that might get you moving in the right direction. First you could train your logistic regression via iterative learning and this would keep the solution confined to employing the likelihood function to estimate the regression parameters. First, estimate the logistic regression and look at the... | How to incorporate costs (into logit model) of false positive, false negative, true positive, true n | There are a few approaches that might get you moving in the right direction. First you could train your logistic regression via iterative learning and this would keep the solution confined to employin | How to incorporate costs (into logit model) of false positive, false negative, true positive, true negative if they are different costs?
There are a few approaches that might get you moving in the right direction. First you could train your logistic regression via iterative learning and this would keep the solution con... | How to incorporate costs (into logit model) of false positive, false negative, true positive, true n
There are a few approaches that might get you moving in the right direction. First you could train your logistic regression via iterative learning and this would keep the solution confined to employin |
36,075 | Is the p-value still uniformly distributed when the null hypothesis is composite? | The answer seems to be 'No' but sometimes 'Yes, asymptotically, depending on the construction of p'. Robins, van der Vaart, and Ventura (2000) go through the details.
The reasoning is basically what @whuber states telegraphically in the comment. The state of nature matters to the nuisance parameters. | Is the p-value still uniformly distributed when the null hypothesis is composite? | The answer seems to be 'No' but sometimes 'Yes, asymptotically, depending on the construction of p'. Robins, van der Vaart, and Ventura (2000) go through the details.
The reasoning is basically what @ | Is the p-value still uniformly distributed when the null hypothesis is composite?
The answer seems to be 'No' but sometimes 'Yes, asymptotically, depending on the construction of p'. Robins, van der Vaart, and Ventura (2000) go through the details.
The reasoning is basically what @whuber states telegraphically in the c... | Is the p-value still uniformly distributed when the null hypothesis is composite?
The answer seems to be 'No' but sometimes 'Yes, asymptotically, depending on the construction of p'. Robins, van der Vaart, and Ventura (2000) go through the details.
The reasoning is basically what @ |
36,076 | Is the p-value still uniformly distributed when the null hypothesis is composite? | First of all let's deal with the simple point hypothesis. It is often claimed (as it is currently in Wikipedia) that the p-value is uniform over [0,1].
This is obviously not the case for discrete outcomes. For example if a coin is tossed 5 times and the test statistic is the number of heads obtained there are only 3 po... | Is the p-value still uniformly distributed when the null hypothesis is composite? | First of all let's deal with the simple point hypothesis. It is often claimed (as it is currently in Wikipedia) that the p-value is uniform over [0,1].
This is obviously not the case for discrete outc | Is the p-value still uniformly distributed when the null hypothesis is composite?
First of all let's deal with the simple point hypothesis. It is often claimed (as it is currently in Wikipedia) that the p-value is uniform over [0,1].
This is obviously not the case for discrete outcomes. For example if a coin is tossed ... | Is the p-value still uniformly distributed when the null hypothesis is composite?
First of all let's deal with the simple point hypothesis. It is often claimed (as it is currently in Wikipedia) that the p-value is uniform over [0,1].
This is obviously not the case for discrete outc |
36,077 | Is it ok to determine early stopping using the validation set in 10-fold cross-validation? | I am not completely clear of what the question is asking, but I think the answer is no. The thing you need to think hard about with cross-validation is that no part of your algorithm can have any access to the test set. If it does, then your cross-validation results will be tainted and not be an accurate measure of the... | Is it ok to determine early stopping using the validation set in 10-fold cross-validation? | I am not completely clear of what the question is asking, but I think the answer is no. The thing you need to think hard about with cross-validation is that no part of your algorithm can have any acce | Is it ok to determine early stopping using the validation set in 10-fold cross-validation?
I am not completely clear of what the question is asking, but I think the answer is no. The thing you need to think hard about with cross-validation is that no part of your algorithm can have any access to the test set. If it doe... | Is it ok to determine early stopping using the validation set in 10-fold cross-validation?
I am not completely clear of what the question is asking, but I think the answer is no. The thing you need to think hard about with cross-validation is that no part of your algorithm can have any acce |
36,078 | Is it ok to determine early stopping using the validation set in 10-fold cross-validation? | The answer is yes as long as you reserve a test set for scoring in your cross validation. This is typically done by a three way partitioning versus a two way: one for train, one for validation (stop), and one for score (test). The validation set is being used to estimate the error on the test set. Thus the idea is t... | Is it ok to determine early stopping using the validation set in 10-fold cross-validation? | The answer is yes as long as you reserve a test set for scoring in your cross validation. This is typically done by a three way partitioning versus a two way: one for train, one for validation (stop) | Is it ok to determine early stopping using the validation set in 10-fold cross-validation?
The answer is yes as long as you reserve a test set for scoring in your cross validation. This is typically done by a three way partitioning versus a two way: one for train, one for validation (stop), and one for score (test). ... | Is it ok to determine early stopping using the validation set in 10-fold cross-validation?
The answer is yes as long as you reserve a test set for scoring in your cross validation. This is typically done by a three way partitioning versus a two way: one for train, one for validation (stop) |
36,079 | Extending the Hellinger Distance to multivariate distributions | It's definitely valid. In fact, Hellinger distance between two measure $P$ and $Q$, which are dominated by the same (sigma-finite) measure $\lambda$, is defined as
$$
H^2(P,Q) = \frac{1}{2}\int\left( \sqrt{\frac{dP}{d\lambda}} - \sqrt{\frac{dQ}{d\lambda}} \right)^2 \, d\lambda \, .
$$
Therefore, you're considering th... | Extending the Hellinger Distance to multivariate distributions | It's definitely valid. In fact, Hellinger distance between two measure $P$ and $Q$, which are dominated by the same (sigma-finite) measure $\lambda$, is defined as
$$
H^2(P,Q) = \frac{1}{2}\int\left | Extending the Hellinger Distance to multivariate distributions
It's definitely valid. In fact, Hellinger distance between two measure $P$ and $Q$, which are dominated by the same (sigma-finite) measure $\lambda$, is defined as
$$
H^2(P,Q) = \frac{1}{2}\int\left( \sqrt{\frac{dP}{d\lambda}} - \sqrt{\frac{dQ}{d\lambda}}... | Extending the Hellinger Distance to multivariate distributions
It's definitely valid. In fact, Hellinger distance between two measure $P$ and $Q$, which are dominated by the same (sigma-finite) measure $\lambda$, is defined as
$$
H^2(P,Q) = \frac{1}{2}\int\left |
36,080 | pivotal statistic versus distribution free statistic | In the first one, the distribution of the quantity involves an unknown parameter or parameters and DOES depend on the distribution of the data. What it doesn't depend on is that parameter or parameters.
So for $X\sim N(\theta,1)$, if we take $Q(\underline{x};\theta) = \bar{x}-\theta$, the distribution of $Q$ is $N(0,1/... | pivotal statistic versus distribution free statistic | In the first one, the distribution of the quantity involves an unknown parameter or parameters and DOES depend on the distribution of the data. What it doesn't depend on is that parameter or parameter | pivotal statistic versus distribution free statistic
In the first one, the distribution of the quantity involves an unknown parameter or parameters and DOES depend on the distribution of the data. What it doesn't depend on is that parameter or parameters.
So for $X\sim N(\theta,1)$, if we take $Q(\underline{x};\theta) ... | pivotal statistic versus distribution free statistic
In the first one, the distribution of the quantity involves an unknown parameter or parameters and DOES depend on the distribution of the data. What it doesn't depend on is that parameter or parameter |
36,081 | Obtaining marginal distributions from the bivariate normal | Following up on whuber's comment,
$$\begin{align}
\left.\left.\frac{1}{2(1-\rho^2)}\right(x^2+y^2-2\rho xy\right)
&=\left.\left.\frac{1}{2(1-\rho^2)}\right(x^2-\rho^2x^2+(y^2-2\rho xy + \rho^2x^2)\right)\\
&= \frac{x^2}{2} + \frac{1}{2}\left(\frac{y-\rho x}{\sqrt{1-\rho^2}}\right)^2
\end{align}$$
and so
$$\int_{-\infty... | Obtaining marginal distributions from the bivariate normal | Following up on whuber's comment,
$$\begin{align}
\left.\left.\frac{1}{2(1-\rho^2)}\right(x^2+y^2-2\rho xy\right)
&=\left.\left.\frac{1}{2(1-\rho^2)}\right(x^2-\rho^2x^2+(y^2-2\rho xy + \rho^2x^2)\rig | Obtaining marginal distributions from the bivariate normal
Following up on whuber's comment,
$$\begin{align}
\left.\left.\frac{1}{2(1-\rho^2)}\right(x^2+y^2-2\rho xy\right)
&=\left.\left.\frac{1}{2(1-\rho^2)}\right(x^2-\rho^2x^2+(y^2-2\rho xy + \rho^2x^2)\right)\\
&= \frac{x^2}{2} + \frac{1}{2}\left(\frac{y-\rho x}{\sq... | Obtaining marginal distributions from the bivariate normal
Following up on whuber's comment,
$$\begin{align}
\left.\left.\frac{1}{2(1-\rho^2)}\right(x^2+y^2-2\rho xy\right)
&=\left.\left.\frac{1}{2(1-\rho^2)}\right(x^2-\rho^2x^2+(y^2-2\rho xy + \rho^2x^2)\rig |
36,082 | Diagnosing why MICE is crashing R when attempting to impute multilevel data | I occasionally have problems with the 2l methods for large data, but have never seen R itself crash on it. My guess would be that they are related to sparse data (very small clusters). How many predictors do you have relative to cluster size?
Some suggestions:
In your data, you have several covariates that have incompl... | Diagnosing why MICE is crashing R when attempting to impute multilevel data | I occasionally have problems with the 2l methods for large data, but have never seen R itself crash on it. My guess would be that they are related to sparse data (very small clusters). How many predic | Diagnosing why MICE is crashing R when attempting to impute multilevel data
I occasionally have problems with the 2l methods for large data, but have never seen R itself crash on it. My guess would be that they are related to sparse data (very small clusters). How many predictors do you have relative to cluster size?
S... | Diagnosing why MICE is crashing R when attempting to impute multilevel data
I occasionally have problems with the 2l methods for large data, but have never seen R itself crash on it. My guess would be that they are related to sparse data (very small clusters). How many predic |
36,083 | Diagnosing why MICE is crashing R when attempting to impute multilevel data | I found what is causing the crash - there was one missing value in grp (which was not being imputed). Still, it does not seem quite right that it crashes R ! After running
dt.fail <- dt.fail[!is.na(dt.fail$grp),]
it no longer crashes, but instead generates the following error:
Error in order(dfr$group) : argument 1 i... | Diagnosing why MICE is crashing R when attempting to impute multilevel data | I found what is causing the crash - there was one missing value in grp (which was not being imputed). Still, it does not seem quite right that it crashes R ! After running
dt.fail <- dt.fail[!is.na(d | Diagnosing why MICE is crashing R when attempting to impute multilevel data
I found what is causing the crash - there was one missing value in grp (which was not being imputed). Still, it does not seem quite right that it crashes R ! After running
dt.fail <- dt.fail[!is.na(dt.fail$grp),]
it no longer crashes, but ins... | Diagnosing why MICE is crashing R when attempting to impute multilevel data
I found what is causing the crash - there was one missing value in grp (which was not being imputed). Still, it does not seem quite right that it crashes R ! After running
dt.fail <- dt.fail[!is.na(d |
36,084 | Smoothing 2D data | You need a to specify a model that separates the signal from the noise.
There is the component of noise at the measurement level that you assume gaussian.
The other components, dependent across measurements:
"This noise, for a fixed frequency, can probably be modelled as random with gaussian distribution". Needs cla... | Smoothing 2D data | You need a to specify a model that separates the signal from the noise.
There is the component of noise at the measurement level that you assume gaussian.
The other components, dependent across meas | Smoothing 2D data
You need a to specify a model that separates the signal from the noise.
There is the component of noise at the measurement level that you assume gaussian.
The other components, dependent across measurements:
"This noise, for a fixed frequency, can probably be modelled as random with gaussian distri... | Smoothing 2D data
You need a to specify a model that separates the signal from the noise.
There is the component of noise at the measurement level that you assume gaussian.
The other components, dependent across meas |
36,085 | Smoothing 2D data | A time series of spectra suggests to me a kinetics experiment, and there is a well-established amount of chemometric literature about this.
What do you know about the spectra? What type of spectra are they? Can you reasonably expect that you have only two species, educt and product?
Can you reasonably assume bilineari... | Smoothing 2D data | A time series of spectra suggests to me a kinetics experiment, and there is a well-established amount of chemometric literature about this.
What do you know about the spectra? What type of spectra ar | Smoothing 2D data
A time series of spectra suggests to me a kinetics experiment, and there is a well-established amount of chemometric literature about this.
What do you know about the spectra? What type of spectra are they? Can you reasonably expect that you have only two species, educt and product?
Can you reasonabl... | Smoothing 2D data
A time series of spectra suggests to me a kinetics experiment, and there is a well-established amount of chemometric literature about this.
What do you know about the spectra? What type of spectra ar |
36,086 | Smoothing 2D data | The data consist of optical spectra (light intensity against frequency) recorded at >varying times. The points were acquired on a regular grid in x (time) , y (frequency).
To me, this sounds very much like a case for functional data analysis (FDA), although I have no idea of the physics behind your problem, and I mig... | Smoothing 2D data | The data consist of optical spectra (light intensity against frequency) recorded at >varying times. The points were acquired on a regular grid in x (time) , y (frequency).
To me, this sounds very muc | Smoothing 2D data
The data consist of optical spectra (light intensity against frequency) recorded at >varying times. The points were acquired on a regular grid in x (time) , y (frequency).
To me, this sounds very much like a case for functional data analysis (FDA), although I have no idea of the physics behind your ... | Smoothing 2D data
The data consist of optical spectra (light intensity against frequency) recorded at >varying times. The points were acquired on a regular grid in x (time) , y (frequency).
To me, this sounds very muc |
36,087 | Smoothing 2D data | Being a simple physicist, not a statistics expert, I'd take a simple approach. The two dimensions are of different natures. It would make sense to smooth along time with one algorithm, and smooth along wavelength with another.
The actual algorithms I'd use: for wavelength, Savitzky-Golay with a higher order, 6 may... | Smoothing 2D data | Being a simple physicist, not a statistics expert, I'd take a simple approach. The two dimensions are of different natures. It would make sense to smooth along time with one algorithm, and smooth al | Smoothing 2D data
Being a simple physicist, not a statistics expert, I'd take a simple approach. The two dimensions are of different natures. It would make sense to smooth along time with one algorithm, and smooth along wavelength with another.
The actual algorithms I'd use: for wavelength, Savitzky-Golay with a h... | Smoothing 2D data
Being a simple physicist, not a statistics expert, I'd take a simple approach. The two dimensions are of different natures. It would make sense to smooth along time with one algorithm, and smooth al |
36,088 | Smoothing 2D data | @baptiste: I'm glad you added the plot like I suggested. It does help a lot:
So, if I understand correctly, your practical goal is to evaluate the exponential decay rate for each wavelength; then let's do just that! Define a function you want to minimize for each wavelength separately, and minimize it.
Let's look at a ... | Smoothing 2D data | @baptiste: I'm glad you added the plot like I suggested. It does help a lot:
So, if I understand correctly, your practical goal is to evaluate the exponential decay rate for each wavelength; then let' | Smoothing 2D data
@baptiste: I'm glad you added the plot like I suggested. It does help a lot:
So, if I understand correctly, your practical goal is to evaluate the exponential decay rate for each wavelength; then let's do just that! Define a function you want to minimize for each wavelength separately, and minimize it... | Smoothing 2D data
@baptiste: I'm glad you added the plot like I suggested. It does help a lot:
So, if I understand correctly, your practical goal is to evaluate the exponential decay rate for each wavelength; then let' |
36,089 | Fixed-effects using demeaned data: why different standard errors when using -plm-? | If you look carefully at the output, you'll notice that the degrees of freedom are different. The degrees of freedom is used to compute the standard errors, thus they are wrong for your demeaned lm. When you apply lm to the demeaned data, lm does not know that the means have been subtracted, or equivalently, that you h... | Fixed-effects using demeaned data: why different standard errors when using -plm-? | If you look carefully at the output, you'll notice that the degrees of freedom are different. The degrees of freedom is used to compute the standard errors, thus they are wrong for your demeaned lm. W | Fixed-effects using demeaned data: why different standard errors when using -plm-?
If you look carefully at the output, you'll notice that the degrees of freedom are different. The degrees of freedom is used to compute the standard errors, thus they are wrong for your demeaned lm. When you apply lm to the demeaned data... | Fixed-effects using demeaned data: why different standard errors when using -plm-?
If you look carefully at the output, you'll notice that the degrees of freedom are different. The degrees of freedom is used to compute the standard errors, thus they are wrong for your demeaned lm. W |
36,090 | p-value with multimodal PDF of a test statistic | I think all this is way too much "p-value centered".
You have to remember what tests are really about: rejecting a null hypothesis with a given value for the α risk. The $p$-value is just a tool for this. In the most general situation, you have build a statistic $T$ with known distribution under the null hypothesis ; ... | p-value with multimodal PDF of a test statistic | I think all this is way too much "p-value centered".
You have to remember what tests are really about: rejecting a null hypothesis with a given value for the α risk. The $p$-value is just a tool for | p-value with multimodal PDF of a test statistic
I think all this is way too much "p-value centered".
You have to remember what tests are really about: rejecting a null hypothesis with a given value for the α risk. The $p$-value is just a tool for this. In the most general situation, you have build a statistic $T$ with... | p-value with multimodal PDF of a test statistic
I think all this is way too much "p-value centered".
You have to remember what tests are really about: rejecting a null hypothesis with a given value for the α risk. The $p$-value is just a tool for |
36,091 | p-value with multimodal PDF of a test statistic | Actually both of you definitions work in different cases, it depends on how you define your null hypothesis (which is often affected by the way you state your alternative hypothesis, so it does matter).
If your null hypothesis is strictly that the parameter(s) equal a given value (or set of values, 1 per parameter), e.... | p-value with multimodal PDF of a test statistic | Actually both of you definitions work in different cases, it depends on how you define your null hypothesis (which is often affected by the way you state your alternative hypothesis, so it does matter | p-value with multimodal PDF of a test statistic
Actually both of you definitions work in different cases, it depends on how you define your null hypothesis (which is often affected by the way you state your alternative hypothesis, so it does matter).
If your null hypothesis is strictly that the parameter(s) equal a giv... | p-value with multimodal PDF of a test statistic
Actually both of you definitions work in different cases, it depends on how you define your null hypothesis (which is often affected by the way you state your alternative hypothesis, so it does matter |
36,092 | p-value with multimodal PDF of a test statistic | This is really two questions:
(1) What is the definition of a p-value?
Answer: Definition 2—the probability under the null hypothesis of getting a value of the test statistic greater than or equal to that observed. (As @whuber pointed out, it needs some qualification: in the case of a composite null hypothesis the prob... | p-value with multimodal PDF of a test statistic | This is really two questions:
(1) What is the definition of a p-value?
Answer: Definition 2—the probability under the null hypothesis of getting a value of the test statistic greater than or equal to | p-value with multimodal PDF of a test statistic
This is really two questions:
(1) What is the definition of a p-value?
Answer: Definition 2—the probability under the null hypothesis of getting a value of the test statistic greater than or equal to that observed. (As @whuber pointed out, it needs some qualification: in ... | p-value with multimodal PDF of a test statistic
This is really two questions:
(1) What is the definition of a p-value?
Answer: Definition 2—the probability under the null hypothesis of getting a value of the test statistic greater than or equal to |
36,093 | Can sub-optimality of various hierarchical clustering methods be assessed or ranked? | Only single-linkage is optimal. Complete-linkage fails, so your intuition was wrong there. ;-)
As a simple example, consider the one-dimensional data set 1,2,3,4,5,6.
The (unique) optimum solution for complete linkage with two clusters is (1,2,3) and (4,5,6) (complete linkage height 2). The (unique) optimum solution wi... | Can sub-optimality of various hierarchical clustering methods be assessed or ranked? | Only single-linkage is optimal. Complete-linkage fails, so your intuition was wrong there. ;-)
As a simple example, consider the one-dimensional data set 1,2,3,4,5,6.
The (unique) optimum solution for | Can sub-optimality of various hierarchical clustering methods be assessed or ranked?
Only single-linkage is optimal. Complete-linkage fails, so your intuition was wrong there. ;-)
As a simple example, consider the one-dimensional data set 1,2,3,4,5,6.
The (unique) optimum solution for complete linkage with two clusters... | Can sub-optimality of various hierarchical clustering methods be assessed or ranked?
Only single-linkage is optimal. Complete-linkage fails, so your intuition was wrong there. ;-)
As a simple example, consider the one-dimensional data set 1,2,3,4,5,6.
The (unique) optimum solution for |
36,094 | Can sub-optimality of various hierarchical clustering methods be assessed or ranked? | A partial answer to your question follows. Single linkage clustering is equivalent to the computation of a minimal spanning tree (references are easy to find). If we disregard ties the result is garantueed to be an optimal solution, or one among a set of optimal solutions, in that the total branch length will be minima... | Can sub-optimality of various hierarchical clustering methods be assessed or ranked? | A partial answer to your question follows. Single linkage clustering is equivalent to the computation of a minimal spanning tree (references are easy to find). If we disregard ties the result is garan | Can sub-optimality of various hierarchical clustering methods be assessed or ranked?
A partial answer to your question follows. Single linkage clustering is equivalent to the computation of a minimal spanning tree (references are easy to find). If we disregard ties the result is garantueed to be an optimal solution, or... | Can sub-optimality of various hierarchical clustering methods be assessed or ranked?
A partial answer to your question follows. Single linkage clustering is equivalent to the computation of a minimal spanning tree (references are easy to find). If we disregard ties the result is garan |
36,095 | Number of needed samples for entropy estimation | Entropy estimation is a surprisingly difficult problem. The fundamental issue is that your estimate is heavily biased by "unobserved" events (which nevertheless have nonzero probability).
There are quite a few different entropy estimators designed specifically to address this problem. For instance, see the BUB esimato... | Number of needed samples for entropy estimation | Entropy estimation is a surprisingly difficult problem. The fundamental issue is that your estimate is heavily biased by "unobserved" events (which nevertheless have nonzero probability).
There are q | Number of needed samples for entropy estimation
Entropy estimation is a surprisingly difficult problem. The fundamental issue is that your estimate is heavily biased by "unobserved" events (which nevertheless have nonzero probability).
There are quite a few different entropy estimators designed specifically to address... | Number of needed samples for entropy estimation
Entropy estimation is a surprisingly difficult problem. The fundamental issue is that your estimate is heavily biased by "unobserved" events (which nevertheless have nonzero probability).
There are q |
36,096 | Number of needed samples for entropy estimation | You need to apply standard propagation of uncertainty (in the non-linear case) to Poisson distribution (i.e. assuming that each count is independent).
That is, you need to expand $H(p_1+\Delta p_1, \ldots, p_n + \Delta p_n)$ in Taylor series of $n$ variables $(\Delta p_1,\ldots ,\Delta p_n)$ around $(0,\ldots, 0)$, i.e... | Number of needed samples for entropy estimation | You need to apply standard propagation of uncertainty (in the non-linear case) to Poisson distribution (i.e. assuming that each count is independent).
That is, you need to expand $H(p_1+\Delta p_1, \l | Number of needed samples for entropy estimation
You need to apply standard propagation of uncertainty (in the non-linear case) to Poisson distribution (i.e. assuming that each count is independent).
That is, you need to expand $H(p_1+\Delta p_1, \ldots, p_n + \Delta p_n)$ in Taylor series of $n$ variables $(\Delta p_1,... | Number of needed samples for entropy estimation
You need to apply standard propagation of uncertainty (in the non-linear case) to Poisson distribution (i.e. assuming that each count is independent).
That is, you need to expand $H(p_1+\Delta p_1, \l |
36,097 | Chi-squared and repeated measures | Interesting, the general question of repeated measures in chi-square has been asked quite a few times but usually obtusely so that it doesn't come up in a simple search. Mcnemar test is what you want. mcnemar.test in R. | Chi-squared and repeated measures | Interesting, the general question of repeated measures in chi-square has been asked quite a few times but usually obtusely so that it doesn't come up in a simple search. Mcnemar test is what you want | Chi-squared and repeated measures
Interesting, the general question of repeated measures in chi-square has been asked quite a few times but usually obtusely so that it doesn't come up in a simple search. Mcnemar test is what you want. mcnemar.test in R. | Chi-squared and repeated measures
Interesting, the general question of repeated measures in chi-square has been asked quite a few times but usually obtusely so that it doesn't come up in a simple search. Mcnemar test is what you want |
36,098 | Chi-squared and repeated measures | The pooling of litters for an individual set of parents seems reasonable to me. If the data could be put into a kxk contingency table and the male mice could be naturally paired with female mice a generalization of Mc Nemar's test could be given. This is a generalization of the the McNemar test for K>2. This paper po... | Chi-squared and repeated measures | The pooling of litters for an individual set of parents seems reasonable to me. If the data could be put into a kxk contingency table and the male mice could be naturally paired with female mice a ge | Chi-squared and repeated measures
The pooling of litters for an individual set of parents seems reasonable to me. If the data could be put into a kxk contingency table and the male mice could be naturally paired with female mice a generalization of Mc Nemar's test could be given. This is a generalization of the the M... | Chi-squared and repeated measures
The pooling of litters for an individual set of parents seems reasonable to me. If the data could be put into a kxk contingency table and the male mice could be naturally paired with female mice a ge |
36,099 | When has a Bayesian approach been critical to addressing a theory, hypothesis or problem? | In the study of medical devices for approval to use for specific indications the US Food and Drug Adminstration has for at least a decade encouraged the use of Bayesian methods in phase III clinical trials to allow prior information about the device to be incorporated along with the trial data. | When has a Bayesian approach been critical to addressing a theory, hypothesis or problem? | In the study of medical devices for approval to use for specific indications the US Food and Drug Adminstration has for at least a decade encouraged the use of Bayesian methods in phase III clinical t | When has a Bayesian approach been critical to addressing a theory, hypothesis or problem?
In the study of medical devices for approval to use for specific indications the US Food and Drug Adminstration has for at least a decade encouraged the use of Bayesian methods in phase III clinical trials to allow prior informati... | When has a Bayesian approach been critical to addressing a theory, hypothesis or problem?
In the study of medical devices for approval to use for specific indications the US Food and Drug Adminstration has for at least a decade encouraged the use of Bayesian methods in phase III clinical t |
36,100 | When has a Bayesian approach been critical to addressing a theory, hypothesis or problem? | A number of papers have been written on using Bayesian methods to estimate diagnostic testing parameters (false-positive, false-negative, ...). The Bayesian method is often preferred due to the fact there are often more parameters than observations. Unlike other common situations, it is nearly impossible to increase ... | When has a Bayesian approach been critical to addressing a theory, hypothesis or problem? | A number of papers have been written on using Bayesian methods to estimate diagnostic testing parameters (false-positive, false-negative, ...). The Bayesian method is often preferred due to the fact | When has a Bayesian approach been critical to addressing a theory, hypothesis or problem?
A number of papers have been written on using Bayesian methods to estimate diagnostic testing parameters (false-positive, false-negative, ...). The Bayesian method is often preferred due to the fact there are often more parameter... | When has a Bayesian approach been critical to addressing a theory, hypothesis or problem?
A number of papers have been written on using Bayesian methods to estimate diagnostic testing parameters (false-positive, false-negative, ...). The Bayesian method is often preferred due to the fact |
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