idx int64 1 56k | question stringlengths 15 155 | answer stringlengths 2 29.2k ⌀ | question_cut stringlengths 15 100 | answer_cut stringlengths 2 200 ⌀ | conversation stringlengths 47 29.3k | conversation_cut stringlengths 47 301 |
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47,601 | In feature selection, what is the reason for considering removing low variance features? | Imagine the limiting case in which you have a feature $x$ which is constant (no variance) will it have an effect on the output $y$? If $y$ is changing, then $x$ should be irrelevant in the relationship because it is constant.
This is the reason, why people tend to discard variables with low variance. The problem is tha... | In feature selection, what is the reason for considering removing low variance features? | Imagine the limiting case in which you have a feature $x$ which is constant (no variance) will it have an effect on the output $y$? If $y$ is changing, then $x$ should be irrelevant in the relationshi | In feature selection, what is the reason for considering removing low variance features?
Imagine the limiting case in which you have a feature $x$ which is constant (no variance) will it have an effect on the output $y$? If $y$ is changing, then $x$ should be irrelevant in the relationship because it is constant.
This ... | In feature selection, what is the reason for considering removing low variance features?
Imagine the limiting case in which you have a feature $x$ which is constant (no variance) will it have an effect on the output $y$? If $y$ is changing, then $x$ should be irrelevant in the relationshi |
47,602 | In feature selection, what is the reason for considering removing low variance features? | Your guess is why I do it. If they have low variance, they likely won't improve your model anyway, so it's safe to remove them. For example, in MNIST, pixels that almost always background. Or some questionnaire items that are nearly always false and so on. Of course, 'variance' is not a good measure for any modality, a... | In feature selection, what is the reason for considering removing low variance features? | Your guess is why I do it. If they have low variance, they likely won't improve your model anyway, so it's safe to remove them. For example, in MNIST, pixels that almost always background. Or some que | In feature selection, what is the reason for considering removing low variance features?
Your guess is why I do it. If they have low variance, they likely won't improve your model anyway, so it's safe to remove them. For example, in MNIST, pixels that almost always background. Or some questionnaire items that are nearl... | In feature selection, what is the reason for considering removing low variance features?
Your guess is why I do it. If they have low variance, they likely won't improve your model anyway, so it's safe to remove them. For example, in MNIST, pixels that almost always background. Or some que |
47,603 | Difference between manifest and observed variables | I agree that this is confusing.
Manifest variables and "observed" variables are both observed, in the sense that they are part of the input dataset, and not latent variables.
The distinction made in the semopy package is that manifest variables are part of the measurement model (ie the definition of the latent variable... | Difference between manifest and observed variables | I agree that this is confusing.
Manifest variables and "observed" variables are both observed, in the sense that they are part of the input dataset, and not latent variables.
The distinction made in t | Difference between manifest and observed variables
I agree that this is confusing.
Manifest variables and "observed" variables are both observed, in the sense that they are part of the input dataset, and not latent variables.
The distinction made in the semopy package is that manifest variables are part of the measurem... | Difference between manifest and observed variables
I agree that this is confusing.
Manifest variables and "observed" variables are both observed, in the sense that they are part of the input dataset, and not latent variables.
The distinction made in t |
47,604 | Expectation of sum of absolute values for correlated normal random variables | Expectation operator distributes over the sum, so correlation amongst $y_i$ is not important in the calculation:
$$\mathbb E\left[\sum_{i=1}^N|y_i|\right]=N\mathbb E[|y_1|]$$
$y_1\sim\mathcal N(0, \sigma_y^2)$ where $\sigma_y^2=\sigma_x^2+\gamma^2\sigma_z^2$. You can calculate the expected value using the mean entry o... | Expectation of sum of absolute values for correlated normal random variables | Expectation operator distributes over the sum, so correlation amongst $y_i$ is not important in the calculation:
$$\mathbb E\left[\sum_{i=1}^N|y_i|\right]=N\mathbb E[|y_1|]$$
$y_1\sim\mathcal N(0, \si | Expectation of sum of absolute values for correlated normal random variables
Expectation operator distributes over the sum, so correlation amongst $y_i$ is not important in the calculation:
$$\mathbb E\left[\sum_{i=1}^N|y_i|\right]=N\mathbb E[|y_1|]$$
$y_1\sim\mathcal N(0, \sigma_y^2)$ where $\sigma_y^2=\sigma_x^2+\gam... | Expectation of sum of absolute values for correlated normal random variables
Expectation operator distributes over the sum, so correlation amongst $y_i$ is not important in the calculation:
$$\mathbb E\left[\sum_{i=1}^N|y_i|\right]=N\mathbb E[|y_1|]$$
$y_1\sim\mathcal N(0, \si |
47,605 | Interview question: How to measure performance of linear regression? | The question is rather broad, though I guess that is the intention with an interview question :)
How to measure performance of linear regression?
You question then goes on to talk about training and test sets, and of course this could be part of the answer, however I would back up a bit and suggest that performance s... | Interview question: How to measure performance of linear regression? | The question is rather broad, though I guess that is the intention with an interview question :)
How to measure performance of linear regression?
You question then goes on to talk about training and | Interview question: How to measure performance of linear regression?
The question is rather broad, though I guess that is the intention with an interview question :)
How to measure performance of linear regression?
You question then goes on to talk about training and test sets, and of course this could be part of the... | Interview question: How to measure performance of linear regression?
The question is rather broad, though I guess that is the intention with an interview question :)
How to measure performance of linear regression?
You question then goes on to talk about training and |
47,606 | Looking for book recommendations for numerical optimization | Another two books similar to Nocedal & Wright are
Numerical Optimization, by Bonnans et al.
Optimization Theory and Methods, by Sun & Yuan
But since you're looking for optimization methods applicable in data science and machine learning, keep in mind that the sheer size of models in this field usually requires stocha... | Looking for book recommendations for numerical optimization | Another two books similar to Nocedal & Wright are
Numerical Optimization, by Bonnans et al.
Optimization Theory and Methods, by Sun & Yuan
But since you're looking for optimization methods applicabl | Looking for book recommendations for numerical optimization
Another two books similar to Nocedal & Wright are
Numerical Optimization, by Bonnans et al.
Optimization Theory and Methods, by Sun & Yuan
But since you're looking for optimization methods applicable in data science and machine learning, keep in mind that th... | Looking for book recommendations for numerical optimization
Another two books similar to Nocedal & Wright are
Numerical Optimization, by Bonnans et al.
Optimization Theory and Methods, by Sun & Yuan
But since you're looking for optimization methods applicabl |
47,607 | Looking for book recommendations for numerical optimization | Aside Nocedal & Wright (2006), as books of a similar level, I have found:
"Iterative methods in Optimisation" by Kelley (1999) and
"Optimization" by Lange (2013).
Both books are equally easy to follow too with N&W and cover standard numerical optimisation topics (KKT Theory, Newton's Method, Quasi-Newton, etc.) nicel... | Looking for book recommendations for numerical optimization | Aside Nocedal & Wright (2006), as books of a similar level, I have found:
"Iterative methods in Optimisation" by Kelley (1999) and
"Optimization" by Lange (2013).
Both books are equally easy to foll | Looking for book recommendations for numerical optimization
Aside Nocedal & Wright (2006), as books of a similar level, I have found:
"Iterative methods in Optimisation" by Kelley (1999) and
"Optimization" by Lange (2013).
Both books are equally easy to follow too with N&W and cover standard numerical optimisation to... | Looking for book recommendations for numerical optimization
Aside Nocedal & Wright (2006), as books of a similar level, I have found:
"Iterative methods in Optimisation" by Kelley (1999) and
"Optimization" by Lange (2013).
Both books are equally easy to foll |
47,608 | Looking for book recommendations for numerical optimization | It's great that you shared your books. Thanks a lot for it! I really like Numerical Optimization (Springer Series in Operations Research and Financial Engineering), which you already mentioned, but I would still recommend Numerical Recipes 3rd Edition: The Art of Scientific Computing to study. I also recommend reading ... | Looking for book recommendations for numerical optimization | It's great that you shared your books. Thanks a lot for it! I really like Numerical Optimization (Springer Series in Operations Research and Financial Engineering), which you already mentioned, but I | Looking for book recommendations for numerical optimization
It's great that you shared your books. Thanks a lot for it! I really like Numerical Optimization (Springer Series in Operations Research and Financial Engineering), which you already mentioned, but I would still recommend Numerical Recipes 3rd Edition: The Art... | Looking for book recommendations for numerical optimization
It's great that you shared your books. Thanks a lot for it! I really like Numerical Optimization (Springer Series in Operations Research and Financial Engineering), which you already mentioned, but I |
47,609 | Is the average of n independent Laplace random variables a Gaussian distribution? | TL;DR
You cannot use either the Lyapunov or the Lindeberg CLT to say anything about the convergence in distribution of $\frac{1}{s_n}\sum_{i=1}^n X_i$ (where $s_n^2=\sum_{i=1}^n\sigma_i^2$) without additional conditions on the sequence of variances $(\sigma_i^2)$.
Neither CLT would say anything about $\frac{1}{n}\sum_{... | Is the average of n independent Laplace random variables a Gaussian distribution? | TL;DR
You cannot use either the Lyapunov or the Lindeberg CLT to say anything about the convergence in distribution of $\frac{1}{s_n}\sum_{i=1}^n X_i$ (where $s_n^2=\sum_{i=1}^n\sigma_i^2$) without ad | Is the average of n independent Laplace random variables a Gaussian distribution?
TL;DR
You cannot use either the Lyapunov or the Lindeberg CLT to say anything about the convergence in distribution of $\frac{1}{s_n}\sum_{i=1}^n X_i$ (where $s_n^2=\sum_{i=1}^n\sigma_i^2$) without additional conditions on the sequence of... | Is the average of n independent Laplace random variables a Gaussian distribution?
TL;DR
You cannot use either the Lyapunov or the Lindeberg CLT to say anything about the convergence in distribution of $\frac{1}{s_n}\sum_{i=1}^n X_i$ (where $s_n^2=\sum_{i=1}^n\sigma_i^2$) without ad |
47,610 | Is the average of n independent Laplace random variables a Gaussian distribution? | The other answer by Stephen Kolassa gives you an excellent analysis of the Lyapunov condition in this case. However, I think it is also fruitful to look at this problem using moment generating functions. In your problem you have independent values $X_i \sim \text{Laplace}(0, \sigma_i/\sqrt{2})$, so these random varia... | Is the average of n independent Laplace random variables a Gaussian distribution? | The other answer by Stephen Kolassa gives you an excellent analysis of the Lyapunov condition in this case. However, I think it is also fruitful to look at this problem using moment generating functi | Is the average of n independent Laplace random variables a Gaussian distribution?
The other answer by Stephen Kolassa gives you an excellent analysis of the Lyapunov condition in this case. However, I think it is also fruitful to look at this problem using moment generating functions. In your problem you have indepen... | Is the average of n independent Laplace random variables a Gaussian distribution?
The other answer by Stephen Kolassa gives you an excellent analysis of the Lyapunov condition in this case. However, I think it is also fruitful to look at this problem using moment generating functi |
47,611 | Understanding The Visual Representation Of A Neural Network? | I believe you've misunderstood the role of input variables (or I've misunderstood you). $X_1...X_5$ are your features belonging to a single observation in the data. So, input dimension is $5$, meaning your data is five dimensional. This has nothing to do with the output dimension, which is typically equal to the number... | Understanding The Visual Representation Of A Neural Network? | I believe you've misunderstood the role of input variables (or I've misunderstood you). $X_1...X_5$ are your features belonging to a single observation in the data. So, input dimension is $5$, meaning | Understanding The Visual Representation Of A Neural Network?
I believe you've misunderstood the role of input variables (or I've misunderstood you). $X_1...X_5$ are your features belonging to a single observation in the data. So, input dimension is $5$, meaning your data is five dimensional. This has nothing to do with... | Understanding The Visual Representation Of A Neural Network?
I believe you've misunderstood the role of input variables (or I've misunderstood you). $X_1...X_5$ are your features belonging to a single observation in the data. So, input dimension is $5$, meaning |
47,612 | Understanding The Visual Representation Of A Neural Network? | Just for clarity I will refer to the image of your question. From left to right, this Neural Network (NN) has one input layer of 5 neurons, one hidden layer of 2 neurons and one output layer of 5 neurons.
how does the graphical representation work? Let's say you have a single new predictor value and you feed it into t... | Understanding The Visual Representation Of A Neural Network? | Just for clarity I will refer to the image of your question. From left to right, this Neural Network (NN) has one input layer of 5 neurons, one hidden layer of 2 neurons and one output layer of 5 neur | Understanding The Visual Representation Of A Neural Network?
Just for clarity I will refer to the image of your question. From left to right, this Neural Network (NN) has one input layer of 5 neurons, one hidden layer of 2 neurons and one output layer of 5 neurons.
how does the graphical representation work? Let's say... | Understanding The Visual Representation Of A Neural Network?
Just for clarity I will refer to the image of your question. From left to right, this Neural Network (NN) has one input layer of 5 neurons, one hidden layer of 2 neurons and one output layer of 5 neur |
47,613 | How to get log odds from these results of logistic regression | The question title is:
How to get log odds from these results of logistic regression
The estimates are already on the log-odds scale. All you have to do is read the relevant entry.
What are the odds of a male surviving as compared to a female?
The log-odds of a male surviving compared to a female is -2.5221, holdin... | How to get log odds from these results of logistic regression | The question title is:
How to get log odds from these results of logistic regression
The estimates are already on the log-odds scale. All you have to do is read the relevant entry.
What are the odd | How to get log odds from these results of logistic regression
The question title is:
How to get log odds from these results of logistic regression
The estimates are already on the log-odds scale. All you have to do is read the relevant entry.
What are the odds of a male surviving as compared to a female?
The log-od... | How to get log odds from these results of logistic regression
The question title is:
How to get log odds from these results of logistic regression
The estimates are already on the log-odds scale. All you have to do is read the relevant entry.
What are the odd |
47,614 | Interpretation of binomial GLM (glmer) with interaction and results description | Please try not to be too concerned with p-values. They don't tell you anything about practical significance.
I am wondering if the interpretation is as simply as, for example, there is a significant difference in the maximum depth (max_depths) reached between feeding and non-feeding dives, with maximum depth taking hi... | Interpretation of binomial GLM (glmer) with interaction and results description | Please try not to be too concerned with p-values. They don't tell you anything about practical significance.
I am wondering if the interpretation is as simply as, for example, there is a significant | Interpretation of binomial GLM (glmer) with interaction and results description
Please try not to be too concerned with p-values. They don't tell you anything about practical significance.
I am wondering if the interpretation is as simply as, for example, there is a significant difference in the maximum depth (max_dep... | Interpretation of binomial GLM (glmer) with interaction and results description
Please try not to be too concerned with p-values. They don't tell you anything about practical significance.
I am wondering if the interpretation is as simply as, for example, there is a significant |
47,615 | What's the MSE of $\hat{Y}$ in ordinary least squares using bias-variance decomposition? | More explanation in the edit below
I think the confusion arises because of the two different meanings of the MSE:
A value calculated from a sample of fitted values or predictions; this is usually what we mean when we write $\operatorname{MSE}(\hat{Y})$ in the context of OLS, since $\hat{Y}$ is the vector of fitted val... | What's the MSE of $\hat{Y}$ in ordinary least squares using bias-variance decomposition? | More explanation in the edit below
I think the confusion arises because of the two different meanings of the MSE:
A value calculated from a sample of fitted values or predictions; this is usually wha | What's the MSE of $\hat{Y}$ in ordinary least squares using bias-variance decomposition?
More explanation in the edit below
I think the confusion arises because of the two different meanings of the MSE:
A value calculated from a sample of fitted values or predictions; this is usually what we mean when we write $\opera... | What's the MSE of $\hat{Y}$ in ordinary least squares using bias-variance decomposition?
More explanation in the edit below
I think the confusion arises because of the two different meanings of the MSE:
A value calculated from a sample of fitted values or predictions; this is usually wha |
47,616 | What is the difference between a confounder, collinearity, and interaction term? | Your understanding of confounding and collinearity is correct. Note that in many contexts collinearity really refers to "perfect collinearity" where one variable is a linear combination of one or more other variables, but in some contexts it just refers to "high correlation" between variables.
Of course, in order for c... | What is the difference between a confounder, collinearity, and interaction term? | Your understanding of confounding and collinearity is correct. Note that in many contexts collinearity really refers to "perfect collinearity" where one variable is a linear combination of one or more | What is the difference between a confounder, collinearity, and interaction term?
Your understanding of confounding and collinearity is correct. Note that in many contexts collinearity really refers to "perfect collinearity" where one variable is a linear combination of one or more other variables, but in some contexts ... | What is the difference between a confounder, collinearity, and interaction term?
Your understanding of confounding and collinearity is correct. Note that in many contexts collinearity really refers to "perfect collinearity" where one variable is a linear combination of one or more |
47,617 | How to identify which variables are collinear in a singular regression matrix? [duplicate] | You can use the QR decomposition with column pivoting (see e.g. "The Behavior of the QR-Factorization Algorithm with Column Pivoting" by Engler (1997)). As described in that paper, the pivots give an ordering of the columns by "most linearly independent". Assuming we've computed the rank of the matrix already (which is... | How to identify which variables are collinear in a singular regression matrix? [duplicate] | You can use the QR decomposition with column pivoting (see e.g. "The Behavior of the QR-Factorization Algorithm with Column Pivoting" by Engler (1997)). As described in that paper, the pivots give an | How to identify which variables are collinear in a singular regression matrix? [duplicate]
You can use the QR decomposition with column pivoting (see e.g. "The Behavior of the QR-Factorization Algorithm with Column Pivoting" by Engler (1997)). As described in that paper, the pivots give an ordering of the columns by "m... | How to identify which variables are collinear in a singular regression matrix? [duplicate]
You can use the QR decomposition with column pivoting (see e.g. "The Behavior of the QR-Factorization Algorithm with Column Pivoting" by Engler (1997)). As described in that paper, the pivots give an |
47,618 | How to identify which variables are collinear in a singular regression matrix? [duplicate] | It looks like you have perfect collinearity among one of the pairs of your 3 independent variables. Run a correlation matrix, and check which pair has a correlation of exactly 1. In R,
cor(count_FGT_free)
You could also create a smaller dataframe with just those three variables if count_FGT_free is large. | How to identify which variables are collinear in a singular regression matrix? [duplicate] | It looks like you have perfect collinearity among one of the pairs of your 3 independent variables. Run a correlation matrix, and check which pair has a correlation of exactly 1. In R,
cor(count_FGT_f | How to identify which variables are collinear in a singular regression matrix? [duplicate]
It looks like you have perfect collinearity among one of the pairs of your 3 independent variables. Run a correlation matrix, and check which pair has a correlation of exactly 1. In R,
cor(count_FGT_free)
You could also create a... | How to identify which variables are collinear in a singular regression matrix? [duplicate]
It looks like you have perfect collinearity among one of the pairs of your 3 independent variables. Run a correlation matrix, and check which pair has a correlation of exactly 1. In R,
cor(count_FGT_f |
47,619 | R: Post-hoc test on lmer. emmeans and multcomp packages | In modeling you have to be careful not to include the exact same situation in different ways. For example, you already found that the design with all the period = 0 cases having Treatment C made it impossible to get useful results. In the summary(lm1) output, that led to reporting only 1 coefficient for period when the... | R: Post-hoc test on lmer. emmeans and multcomp packages | In modeling you have to be careful not to include the exact same situation in different ways. For example, you already found that the design with all the period = 0 cases having Treatment C made it im | R: Post-hoc test on lmer. emmeans and multcomp packages
In modeling you have to be careful not to include the exact same situation in different ways. For example, you already found that the design with all the period = 0 cases having Treatment C made it impossible to get useful results. In the summary(lm1) output, that... | R: Post-hoc test on lmer. emmeans and multcomp packages
In modeling you have to be careful not to include the exact same situation in different ways. For example, you already found that the design with all the period = 0 cases having Treatment C made it im |
47,620 | R: Post-hoc test on lmer. emmeans and multcomp packages | I will attempt to answer (2).
First, the code given does not produce the results shown. In order to obtain those results, I needed the following manipulations of the data before fitting the model:
DF$Treatment = relevel(factor(DF$Treatment), ref = "C")
DF$age = as.numeric(DF$age)
DF$period = factor(DF$period)
In futur... | R: Post-hoc test on lmer. emmeans and multcomp packages | I will attempt to answer (2).
First, the code given does not produce the results shown. In order to obtain those results, I needed the following manipulations of the data before fitting the model:
DF$ | R: Post-hoc test on lmer. emmeans and multcomp packages
I will attempt to answer (2).
First, the code given does not produce the results shown. In order to obtain those results, I needed the following manipulations of the data before fitting the model:
DF$Treatment = relevel(factor(DF$Treatment), ref = "C")
DF$age = as... | R: Post-hoc test on lmer. emmeans and multcomp packages
I will attempt to answer (2).
First, the code given does not produce the results shown. In order to obtain those results, I needed the following manipulations of the data before fitting the model:
DF$ |
47,621 | R: Post-hoc test on lmer. emmeans and multcomp packages | Following the current advice of removing sequence, I suggest also including period as nested within ID and removing it from fixed effects i.e. lmer(lipid~Treatment + sex + age + (1|id/period), data = DF, REML = F)
I have found this guide to be quite helpful:
https://bbolker.github.io/mixedmodels-misc/glmmFAQ.html#mode... | R: Post-hoc test on lmer. emmeans and multcomp packages | Following the current advice of removing sequence, I suggest also including period as nested within ID and removing it from fixed effects i.e. lmer(lipid~Treatment + sex + age + (1|id/period), data = | R: Post-hoc test on lmer. emmeans and multcomp packages
Following the current advice of removing sequence, I suggest also including period as nested within ID and removing it from fixed effects i.e. lmer(lipid~Treatment + sex + age + (1|id/period), data = DF, REML = F)
I have found this guide to be quite helpful:
http... | R: Post-hoc test on lmer. emmeans and multcomp packages
Following the current advice of removing sequence, I suggest also including period as nested within ID and removing it from fixed effects i.e. lmer(lipid~Treatment + sex + age + (1|id/period), data = |
47,622 | Covariance matrix of the residuals in the linear regression model | After some investigation, I think I found a small (but crucial!) imprecision in what your post.
The first formula you wrote : $var(\varepsilon) = \sigma^2 (I - H)$ is actually not totally exact. The formula should be $var(\hat \varepsilon) = \sigma ^2 (I - H)$ where $\hat\varepsilon = Y - \hat\beta X$ considering the O... | Covariance matrix of the residuals in the linear regression model | After some investigation, I think I found a small (but crucial!) imprecision in what your post.
The first formula you wrote : $var(\varepsilon) = \sigma^2 (I - H)$ is actually not totally exact. The f | Covariance matrix of the residuals in the linear regression model
After some investigation, I think I found a small (but crucial!) imprecision in what your post.
The first formula you wrote : $var(\varepsilon) = \sigma^2 (I - H)$ is actually not totally exact. The formula should be $var(\hat \varepsilon) = \sigma ^2 (I... | Covariance matrix of the residuals in the linear regression model
After some investigation, I think I found a small (but crucial!) imprecision in what your post.
The first formula you wrote : $var(\varepsilon) = \sigma^2 (I - H)$ is actually not totally exact. The f |
47,623 | Covariance matrix of the residuals in the linear regression model | In basic OLS you don't estimate the covariance matrix of residuals. You assume that errors (not residuals) are spherical, meaning that they're not correlated with each other. Residuals will come out of OLS uncorrelated.
What you described as a second method is a different assumption. When applying basic OLS to time ser... | Covariance matrix of the residuals in the linear regression model | In basic OLS you don't estimate the covariance matrix of residuals. You assume that errors (not residuals) are spherical, meaning that they're not correlated with each other. Residuals will come out o | Covariance matrix of the residuals in the linear regression model
In basic OLS you don't estimate the covariance matrix of residuals. You assume that errors (not residuals) are spherical, meaning that they're not correlated with each other. Residuals will come out of OLS uncorrelated.
What you described as a second met... | Covariance matrix of the residuals in the linear regression model
In basic OLS you don't estimate the covariance matrix of residuals. You assume that errors (not residuals) are spherical, meaning that they're not correlated with each other. Residuals will come out o |
47,624 | Tukey depth intuition | Bagplot
A bagplot is a method in robust statistics for visualizing two- or three-dimensional statistical data, analogous to the one-dimensional box plot.
Construction of a Bagplot
The bagplot consists of three nested polygons, called the "bag", the "fence", and the "loop".
The inner polygon, called the bag, is cons... | Tukey depth intuition | Bagplot
A bagplot is a method in robust statistics for visualizing two- or three-dimensional statistical data, analogous to the one-dimensional box plot.
Construction of a Bagplot
The bagplot consis | Tukey depth intuition
Bagplot
A bagplot is a method in robust statistics for visualizing two- or three-dimensional statistical data, analogous to the one-dimensional box plot.
Construction of a Bagplot
The bagplot consists of three nested polygons, called the "bag", the "fence", and the "loop".
The inner polygon, c... | Tukey depth intuition
Bagplot
A bagplot is a method in robust statistics for visualizing two- or three-dimensional statistical data, analogous to the one-dimensional box plot.
Construction of a Bagplot
The bagplot consis |
47,625 | Are inconsistent estimators ever preferable? A twist | In the previous question, the example by whuber was actually a cost function that was minimized when the estimate $t$ equals the true parameter value $t=\mu$, Namely it was zero for $\mu \leq t \leq \mu+1$, and thus at the minimum value for $t=\mu$.
Edit: The question has changed, but that example by whuber will still ... | Are inconsistent estimators ever preferable? A twist | In the previous question, the example by whuber was actually a cost function that was minimized when the estimate $t$ equals the true parameter value $t=\mu$, Namely it was zero for $\mu \leq t \leq \ | Are inconsistent estimators ever preferable? A twist
In the previous question, the example by whuber was actually a cost function that was minimized when the estimate $t$ equals the true parameter value $t=\mu$, Namely it was zero for $\mu \leq t \leq \mu+1$, and thus at the minimum value for $t=\mu$.
Edit: The questio... | Are inconsistent estimators ever preferable? A twist
In the previous question, the example by whuber was actually a cost function that was minimized when the estimate $t$ equals the true parameter value $t=\mu$, Namely it was zero for $\mu \leq t \leq \ |
47,626 | Are inconsistent estimators ever preferable? A twist | I think the correct question here is not whether an inconsistent estimator can be better than one specific consistent estimator. With this question, you can create very lousy consistent estimators that can be beaten by lousy inconsistent estimators.
The correct question here seems to be if there aren't any consistent e... | Are inconsistent estimators ever preferable? A twist | I think the correct question here is not whether an inconsistent estimator can be better than one specific consistent estimator. With this question, you can create very lousy consistent estimators tha | Are inconsistent estimators ever preferable? A twist
I think the correct question here is not whether an inconsistent estimator can be better than one specific consistent estimator. With this question, you can create very lousy consistent estimators that can be beaten by lousy inconsistent estimators.
The correct quest... | Are inconsistent estimators ever preferable? A twist
I think the correct question here is not whether an inconsistent estimator can be better than one specific consistent estimator. With this question, you can create very lousy consistent estimators tha |
47,627 | Why McFadden's pseudo-R^2? | McFadden's pseudo-$R^2$ is consistent with the log-likelihood model we optimise in logistic regression. The ordinary $R^2$ is consistent with the log-likelihood model for the linear regression.
In linear regression, we maximise the log-likelihood:
$$
- \sum_i (y_i - \beta x_i)^2
$$
Compare this with the definition of $... | Why McFadden's pseudo-R^2? | McFadden's pseudo-$R^2$ is consistent with the log-likelihood model we optimise in logistic regression. The ordinary $R^2$ is consistent with the log-likelihood model for the linear regression.
In lin | Why McFadden's pseudo-R^2?
McFadden's pseudo-$R^2$ is consistent with the log-likelihood model we optimise in logistic regression. The ordinary $R^2$ is consistent with the log-likelihood model for the linear regression.
In linear regression, we maximise the log-likelihood:
$$
- \sum_i (y_i - \beta x_i)^2
$$
Compare th... | Why McFadden's pseudo-R^2?
McFadden's pseudo-$R^2$ is consistent with the log-likelihood model we optimise in logistic regression. The ordinary $R^2$ is consistent with the log-likelihood model for the linear regression.
In lin |
47,628 | regarding profile function in the context of linear mixed effects models | Let's start by clarifying what the .sig01 (etc) and .sigma represent in the output from confint(). (I figure that you understand, but other readers might not have studied so diligently.) The .sigma is for the standard deviation of the residual error. The others of the form .sig0n are for the standard deviation estimate... | regarding profile function in the context of linear mixed effects models | Let's start by clarifying what the .sig01 (etc) and .sigma represent in the output from confint(). (I figure that you understand, but other readers might not have studied so diligently.) The .sigma is | regarding profile function in the context of linear mixed effects models
Let's start by clarifying what the .sig01 (etc) and .sigma represent in the output from confint(). (I figure that you understand, but other readers might not have studied so diligently.) The .sigma is for the standard deviation of the residual err... | regarding profile function in the context of linear mixed effects models
Let's start by clarifying what the .sig01 (etc) and .sigma represent in the output from confint(). (I figure that you understand, but other readers might not have studied so diligently.) The .sigma is |
47,629 | What is the $dF(X)$ in some integrals concerning probability densities? | This notation refers to the Lebesgue-Stieltjes integral and $F$ is the cumulative distribution function of the random variable under consideration. This integral form is a useful way to write expectations of functions of random variables in cases where you want to include both continuous and discrete cases (and mixed ... | What is the $dF(X)$ in some integrals concerning probability densities? | This notation refers to the Lebesgue-Stieltjes integral and $F$ is the cumulative distribution function of the random variable under consideration. This integral form is a useful way to write expecta | What is the $dF(X)$ in some integrals concerning probability densities?
This notation refers to the Lebesgue-Stieltjes integral and $F$ is the cumulative distribution function of the random variable under consideration. This integral form is a useful way to write expectations of functions of random variables in cases ... | What is the $dF(X)$ in some integrals concerning probability densities?
This notation refers to the Lebesgue-Stieltjes integral and $F$ is the cumulative distribution function of the random variable under consideration. This integral form is a useful way to write expecta |
47,630 | How can I find the asymptotic variance of the MLE of $\beta$ for $f_y(y|\beta,\mathbf{x})=\frac{\beta x}{1+\beta x}(\frac{1}{1+\beta x})^{y-1}$? | Your present working appears to be taking all the $x_i$ values to be the same, which is not sufficient generality to properly describe your problem. In your initial setup for the problem there is no stipulation that these values must be the same. Taking the values $\mathbf{x} = (x_1,...,x_n)$ to be fixed explanatory ... | How can I find the asymptotic variance of the MLE of $\beta$ for $f_y(y|\beta,\mathbf{x})=\frac{\bet | Your present working appears to be taking all the $x_i$ values to be the same, which is not sufficient generality to properly describe your problem. In your initial setup for the problem there is no | How can I find the asymptotic variance of the MLE of $\beta$ for $f_y(y|\beta,\mathbf{x})=\frac{\beta x}{1+\beta x}(\frac{1}{1+\beta x})^{y-1}$?
Your present working appears to be taking all the $x_i$ values to be the same, which is not sufficient generality to properly describe your problem. In your initial setup for... | How can I find the asymptotic variance of the MLE of $\beta$ for $f_y(y|\beta,\mathbf{x})=\frac{\bet
Your present working appears to be taking all the $x_i$ values to be the same, which is not sufficient generality to properly describe your problem. In your initial setup for the problem there is no |
47,631 | What are continuous distributions that are additive and have finite support | A minimal example is obtained by taking literally any distribution with compact support on the nonnegative reals. Letting $F$ be its cumulative distribution function, this means there exist $0\le a\le b$ for which $F(a)=0$ and $F(b)=1.$ Repeated convolution produces the sequence of distribution functions $F_n,$ $n=1,... | What are continuous distributions that are additive and have finite support | A minimal example is obtained by taking literally any distribution with compact support on the nonnegative reals. Letting $F$ be its cumulative distribution function, this means there exist $0\le a\l | What are continuous distributions that are additive and have finite support
A minimal example is obtained by taking literally any distribution with compact support on the nonnegative reals. Letting $F$ be its cumulative distribution function, this means there exist $0\le a\le b$ for which $F(a)=0$ and $F(b)=1.$ Repea... | What are continuous distributions that are additive and have finite support
A minimal example is obtained by taking literally any distribution with compact support on the nonnegative reals. Letting $F$ be its cumulative distribution function, this means there exist $0\le a\l |
47,632 | What are continuous distributions that are additive and have finite support | Let $X$ and $Y$ are from same continues distribution with finite support $(a,b)$.
so $a<X<b$ and $a<Y<b$ , in-hence $2a<X+Y<2b$. Since the support of $X+Y$ equal to $(2a,2b)$ so I think it can not be happen. at least one of $a$ , $b$ $\rightarrow$ $\infty$ and other should be zero. like Chi-square distribution. | What are continuous distributions that are additive and have finite support | Let $X$ and $Y$ are from same continues distribution with finite support $(a,b)$.
so $a<X<b$ and $a<Y<b$ , in-hence $2a<X+Y<2b$. Since the support of $X+Y$ equal to $(2a,2b)$ so I think it can not b | What are continuous distributions that are additive and have finite support
Let $X$ and $Y$ are from same continues distribution with finite support $(a,b)$.
so $a<X<b$ and $a<Y<b$ , in-hence $2a<X+Y<2b$. Since the support of $X+Y$ equal to $(2a,2b)$ so I think it can not be happen. at least one of $a$ , $b$ $\righta... | What are continuous distributions that are additive and have finite support
Let $X$ and $Y$ are from same continues distribution with finite support $(a,b)$.
so $a<X<b$ and $a<Y<b$ , in-hence $2a<X+Y<2b$. Since the support of $X+Y$ equal to $(2a,2b)$ so I think it can not b |
47,633 | Sufficient Statistics - Relating the Intuition with the Mathematical Definition | I think a common way to motivate the mathematical definition is the following.
Say you have the sufficient statistic $T(X)$, and I just have the data/random sample $X$.
By the mathematical definition of sufficiency,
$$ p(X|T(X), \theta) = P(X|T(X)).$$
The r.h.s. is a probability distribution you, again per definition... | Sufficient Statistics - Relating the Intuition with the Mathematical Definition | I think a common way to motivate the mathematical definition is the following.
Say you have the sufficient statistic $T(X)$, and I just have the data/random sample $X$.
By the mathematical definition | Sufficient Statistics - Relating the Intuition with the Mathematical Definition
I think a common way to motivate the mathematical definition is the following.
Say you have the sufficient statistic $T(X)$, and I just have the data/random sample $X$.
By the mathematical definition of sufficiency,
$$ p(X|T(X), \theta) =... | Sufficient Statistics - Relating the Intuition with the Mathematical Definition
I think a common way to motivate the mathematical definition is the following.
Say you have the sufficient statistic $T(X)$, and I just have the data/random sample $X$.
By the mathematical definition |
47,634 | Sufficient Statistics - Relating the Intuition with the Mathematical Definition | "A statistic t=T(X) is sufficient for underlying parameter θ precisely if the conditional probability distribution of the data X, given the statistic t = T(X), does not depend on the parameter θ."
If the sampling distribution for some data $X$ does not depend on $\theta$ then how can that data say anything about $\the... | Sufficient Statistics - Relating the Intuition with the Mathematical Definition | "A statistic t=T(X) is sufficient for underlying parameter θ precisely if the conditional probability distribution of the data X, given the statistic t = T(X), does not depend on the parameter θ."
If | Sufficient Statistics - Relating the Intuition with the Mathematical Definition
"A statistic t=T(X) is sufficient for underlying parameter θ precisely if the conditional probability distribution of the data X, given the statistic t = T(X), does not depend on the parameter θ."
If the sampling distribution for some data... | Sufficient Statistics - Relating the Intuition with the Mathematical Definition
"A statistic t=T(X) is sufficient for underlying parameter θ precisely if the conditional probability distribution of the data X, given the statistic t = T(X), does not depend on the parameter θ."
If |
47,635 | Sufficient Statistics - Relating the Intuition with the Mathematical Definition | Here is a very simple example that might make things clear. For a normal model $X\sim N(\theta,1)$ with a sample size of $n=1$, $X$ is sufficient for $\theta$. Without conditioning on $T(X)=X$, then $P(X\le x)=\Phi(x-\theta)$ depends on $\theta$. If I condition on $T(X)=X=c$ then
$$
P(X\le x|X=c)=\left\{\begin{array... | Sufficient Statistics - Relating the Intuition with the Mathematical Definition | Here is a very simple example that might make things clear. For a normal model $X\sim N(\theta,1)$ with a sample size of $n=1$, $X$ is sufficient for $\theta$. Without conditioning on $T(X)=X$, then | Sufficient Statistics - Relating the Intuition with the Mathematical Definition
Here is a very simple example that might make things clear. For a normal model $X\sim N(\theta,1)$ with a sample size of $n=1$, $X$ is sufficient for $\theta$. Without conditioning on $T(X)=X$, then $P(X\le x)=\Phi(x-\theta)$ depends on $... | Sufficient Statistics - Relating the Intuition with the Mathematical Definition
Here is a very simple example that might make things clear. For a normal model $X\sim N(\theta,1)$ with a sample size of $n=1$, $X$ is sufficient for $\theta$. Without conditioning on $T(X)=X$, then |
47,636 | Was Amazon's AI tool, more than human recruiters, biased against women? | This is not a full answer. In the question I mentioned one way how I can imagine a small bias being amplified. In this question I write it down in more detail. I consider this way of amplification a bit trivial and wonder whether there are more reasons why Amazon's recruitment tool was considered biased, especially why... | Was Amazon's AI tool, more than human recruiters, biased against women? | This is not a full answer. In the question I mentioned one way how I can imagine a small bias being amplified. In this question I write it down in more detail. I consider this way of amplification a b | Was Amazon's AI tool, more than human recruiters, biased against women?
This is not a full answer. In the question I mentioned one way how I can imagine a small bias being amplified. In this question I write it down in more detail. I consider this way of amplification a bit trivial and wonder whether there are more rea... | Was Amazon's AI tool, more than human recruiters, biased against women?
This is not a full answer. In the question I mentioned one way how I can imagine a small bias being amplified. In this question I write it down in more detail. I consider this way of amplification a b |
47,637 | Was Amazon's AI tool, more than human recruiters, biased against women? | Sample selection bias is introduced by the selection of individuals, groups, or data for analysis in such a way that the samples are not representative of the population intended to be analyzed.9 In particular, sample selection bias occurs during data analysis as a result of conditioning on some variables in the datase... | Was Amazon's AI tool, more than human recruiters, biased against women? | Sample selection bias is introduced by the selection of individuals, groups, or data for analysis in such a way that the samples are not representative of the population intended to be analyzed.9 In p | Was Amazon's AI tool, more than human recruiters, biased against women?
Sample selection bias is introduced by the selection of individuals, groups, or data for analysis in such a way that the samples are not representative of the population intended to be analyzed.9 In particular, sample selection bias occurs during d... | Was Amazon's AI tool, more than human recruiters, biased against women?
Sample selection bias is introduced by the selection of individuals, groups, or data for analysis in such a way that the samples are not representative of the population intended to be analyzed.9 In p |
47,638 | Was Amazon's AI tool, more than human recruiters, biased against women? | One additional thought, not fully explored: Maybe we should think whether overfitting can amplify existing bias.
In a linear model (where we understand better what happens), we observe overfitting with coefficents being of too large absolute size.
Increased bias against women then may be expressed as the coefficient fo... | Was Amazon's AI tool, more than human recruiters, biased against women? | One additional thought, not fully explored: Maybe we should think whether overfitting can amplify existing bias.
In a linear model (where we understand better what happens), we observe overfitting wit | Was Amazon's AI tool, more than human recruiters, biased against women?
One additional thought, not fully explored: Maybe we should think whether overfitting can amplify existing bias.
In a linear model (where we understand better what happens), we observe overfitting with coefficents being of too large absolute size.
... | Was Amazon's AI tool, more than human recruiters, biased against women?
One additional thought, not fully explored: Maybe we should think whether overfitting can amplify existing bias.
In a linear model (where we understand better what happens), we observe overfitting wit |
47,639 | Was Amazon's AI tool, more than human recruiters, biased against women? | Also, the AI was focusing on patterns that negatively biased women, e.g. "women’s chess club captain" doing worse than "chess club captain".
In effect, Amazon’s system taught itself that male candidates were preferable. It penalized resumes that included the word “women’s,” as in “women’s chess club captain.” And it d... | Was Amazon's AI tool, more than human recruiters, biased against women? | Also, the AI was focusing on patterns that negatively biased women, e.g. "women’s chess club captain" doing worse than "chess club captain".
In effect, Amazon’s system taught itself that male candida | Was Amazon's AI tool, more than human recruiters, biased against women?
Also, the AI was focusing on patterns that negatively biased women, e.g. "women’s chess club captain" doing worse than "chess club captain".
In effect, Amazon’s system taught itself that male candidates were preferable. It penalized resumes that i... | Was Amazon's AI tool, more than human recruiters, biased against women?
Also, the AI was focusing on patterns that negatively biased women, e.g. "women’s chess club captain" doing worse than "chess club captain".
In effect, Amazon’s system taught itself that male candida |
47,640 | Is a singular fit with no correlations near +/- 1 or variances of zero, a false positive in lme4 | Does this mean the warning is a "false positive" and can safely be ignored ?
No.
A singular fit is quite specifically defined, at least in lme4, which I assume is what you are using.
The warning in lme4 comes from a principal components analysis of the variance-covariance matrix of estimated random effects. If this... | Is a singular fit with no correlations near +/- 1 or variances of zero, a false positive in lme4 | Does this mean the warning is a "false positive" and can safely be ignored ?
No.
A singular fit is quite specifically defined, at least in lme4, which I assume is what you are using.
The warning i | Is a singular fit with no correlations near +/- 1 or variances of zero, a false positive in lme4
Does this mean the warning is a "false positive" and can safely be ignored ?
No.
A singular fit is quite specifically defined, at least in lme4, which I assume is what you are using.
The warning in lme4 comes from a pri... | Is a singular fit with no correlations near +/- 1 or variances of zero, a false positive in lme4
Does this mean the warning is a "false positive" and can safely be ignored ?
No.
A singular fit is quite specifically defined, at least in lme4, which I assume is what you are using.
The warning i |
47,641 | Extract confidence intervals confint() for random estimates of lmer models | Try confint(linear.mod.n, oldNames=FALSE) for more useful labels; .sig02 represents the intercept-slope correlation (which is completely undetermined — the confidence intervals span the entire possible range from -1 to 1 ...) | Extract confidence intervals confint() for random estimates of lmer models | Try confint(linear.mod.n, oldNames=FALSE) for more useful labels; .sig02 represents the intercept-slope correlation (which is completely undetermined — the confidence intervals span the entire possibl | Extract confidence intervals confint() for random estimates of lmer models
Try confint(linear.mod.n, oldNames=FALSE) for more useful labels; .sig02 represents the intercept-slope correlation (which is completely undetermined — the confidence intervals span the entire possible range from -1 to 1 ...) | Extract confidence intervals confint() for random estimates of lmer models
Try confint(linear.mod.n, oldNames=FALSE) for more useful labels; .sig02 represents the intercept-slope correlation (which is completely undetermined — the confidence intervals span the entire possibl |
47,642 | Extract confidence intervals confint() for random estimates of lmer models | Welcome to the site, nguyenllp!
With random effects (varying parameters) in mixed models, looking at statistical significance of estimates do not make the same sense that they do with fixed effects (non-varying parameters). Instead, we use likelihood ratio testing of competing models to determine whether the added com... | Extract confidence intervals confint() for random estimates of lmer models | Welcome to the site, nguyenllp!
With random effects (varying parameters) in mixed models, looking at statistical significance of estimates do not make the same sense that they do with fixed effects ( | Extract confidence intervals confint() for random estimates of lmer models
Welcome to the site, nguyenllp!
With random effects (varying parameters) in mixed models, looking at statistical significance of estimates do not make the same sense that they do with fixed effects (non-varying parameters). Instead, we use like... | Extract confidence intervals confint() for random estimates of lmer models
Welcome to the site, nguyenllp!
With random effects (varying parameters) in mixed models, looking at statistical significance of estimates do not make the same sense that they do with fixed effects ( |
47,643 | Putting prior on a function of parameters | Another perspective on this: Yes, of course you can do that, the only question in practice is how you do it.
There's several options:
You can work out the changes in variables etc. and explicitly define the implied priors on the untransformed variables. This is often impractical / requires a lot of work.
If you can d... | Putting prior on a function of parameters | Another perspective on this: Yes, of course you can do that, the only question in practice is how you do it.
There's several options:
You can work out the changes in variables etc. and explicitly de | Putting prior on a function of parameters
Another perspective on this: Yes, of course you can do that, the only question in practice is how you do it.
There's several options:
You can work out the changes in variables etc. and explicitly define the implied priors on the untransformed variables. This is often impracti... | Putting prior on a function of parameters
Another perspective on this: Yes, of course you can do that, the only question in practice is how you do it.
There's several options:
You can work out the changes in variables etc. and explicitly de |
47,644 | Putting prior on a function of parameters | As I understand your question, I don't know weither this approach has a name ; expect maybe those of change-of-variable.
Indeed, by defining a prior on $g(\theta)$, you are simply defining a prior on $\theta$ (assuming $g$ is monotonic, or bijective in multidimensional setting).
More formally, using change of variable ... | Putting prior on a function of parameters | As I understand your question, I don't know weither this approach has a name ; expect maybe those of change-of-variable.
Indeed, by defining a prior on $g(\theta)$, you are simply defining a prior on | Putting prior on a function of parameters
As I understand your question, I don't know weither this approach has a name ; expect maybe those of change-of-variable.
Indeed, by defining a prior on $g(\theta)$, you are simply defining a prior on $\theta$ (assuming $g$ is monotonic, or bijective in multidimensional setting)... | Putting prior on a function of parameters
As I understand your question, I don't know weither this approach has a name ; expect maybe those of change-of-variable.
Indeed, by defining a prior on $g(\theta)$, you are simply defining a prior on |
47,645 | Putting prior on a function of parameters | When you can not compute a posterior for $\mu$ because of missing information in the likelihood
Below is a counterexample for a case where the likelihood function $p(y\vert \mu)$ is not uniquely defined by $\mu$, but depends in a more complex way on the vector $\theta$.
Say you have the likelihoodfunction:
$$Y \vert \... | Putting prior on a function of parameters | When you can not compute a posterior for $\mu$ because of missing information in the likelihood
Below is a counterexample for a case where the likelihood function $p(y\vert \mu)$ is not uniquely defin | Putting prior on a function of parameters
When you can not compute a posterior for $\mu$ because of missing information in the likelihood
Below is a counterexample for a case where the likelihood function $p(y\vert \mu)$ is not uniquely defined by $\mu$, but depends in a more complex way on the vector $\theta$.
Say yo... | Putting prior on a function of parameters
When you can not compute a posterior for $\mu$ because of missing information in the likelihood
Below is a counterexample for a case where the likelihood function $p(y\vert \mu)$ is not uniquely defin |
47,646 | The lines on my scatterplot for ANCOVA results doesn't look right, personal error or model error? | You appear to be misunderstanding the output from your model.
In your code, the line:
abline(fit.mice$coefficients[1:2], col="skyblue3")
plots a line with the correct intercept, but the wrong slope. fit.mice$coefficients[1] is the intercept, but fit.mice$coefficients[2] is the estimate for treat in the Mice added grou... | The lines on my scatterplot for ANCOVA results doesn't look right, personal error or model error? | You appear to be misunderstanding the output from your model.
In your code, the line:
abline(fit.mice$coefficients[1:2], col="skyblue3")
plots a line with the correct intercept, but the wrong slope. | The lines on my scatterplot for ANCOVA results doesn't look right, personal error or model error?
You appear to be misunderstanding the output from your model.
In your code, the line:
abline(fit.mice$coefficients[1:2], col="skyblue3")
plots a line with the correct intercept, but the wrong slope. fit.mice$coefficients[... | The lines on my scatterplot for ANCOVA results doesn't look right, personal error or model error?
You appear to be misunderstanding the output from your model.
In your code, the line:
abline(fit.mice$coefficients[1:2], col="skyblue3")
plots a line with the correct intercept, but the wrong slope. |
47,647 | Fitting a Regression Model to log-log distributed data | Two points:
Your data are log-log scaled. So why don't you take the logs of them?
Since you expect a sigmoid function behind the data, why not trying fitting it to the data?
Below, I model your log-transformed data as a (scaled) difference of two softplus functions, $y = log(1+e^x)$, plus a constant term:
$$
y = log(... | Fitting a Regression Model to log-log distributed data | Two points:
Your data are log-log scaled. So why don't you take the logs of them?
Since you expect a sigmoid function behind the data, why not trying fitting it to the data?
Below, I model your log- | Fitting a Regression Model to log-log distributed data
Two points:
Your data are log-log scaled. So why don't you take the logs of them?
Since you expect a sigmoid function behind the data, why not trying fitting it to the data?
Below, I model your log-transformed data as a (scaled) difference of two softplus functio... | Fitting a Regression Model to log-log distributed data
Two points:
Your data are log-log scaled. So why don't you take the logs of them?
Since you expect a sigmoid function behind the data, why not trying fitting it to the data?
Below, I model your log- |
47,648 | What is the computational complexity of a 1D convolutional layer? | I realized what may be missing is the number of filters in the layer.
Even though they don't have a letter for it in the table, the authors might be assuming implicitly that the order of magnitude of the number of filters is the same as that of the number of depth dimensions. Or even more simply, that the number of fi... | What is the computational complexity of a 1D convolutional layer? | I realized what may be missing is the number of filters in the layer.
Even though they don't have a letter for it in the table, the authors might be assuming implicitly that the order of magnitude of | What is the computational complexity of a 1D convolutional layer?
I realized what may be missing is the number of filters in the layer.
Even though they don't have a letter for it in the table, the authors might be assuming implicitly that the order of magnitude of the number of filters is the same as that of the numb... | What is the computational complexity of a 1D convolutional layer?
I realized what may be missing is the number of filters in the layer.
Even though they don't have a letter for it in the table, the authors might be assuming implicitly that the order of magnitude of |
47,649 | Non-tautological explanation for why do low-probability events happen rarely? | Probabilities are units used to quantify statements like "I don't need umbrella today, because it's unlikely to rain". They measure what they measure because this is how we defined them. What you mention are different possible interpretations of probability. There are different possible interpretations, because "probab... | Non-tautological explanation for why do low-probability events happen rarely? | Probabilities are units used to quantify statements like "I don't need umbrella today, because it's unlikely to rain". They measure what they measure because this is how we defined them. What you ment | Non-tautological explanation for why do low-probability events happen rarely?
Probabilities are units used to quantify statements like "I don't need umbrella today, because it's unlikely to rain". They measure what they measure because this is how we defined them. What you mention are different possible interpretations... | Non-tautological explanation for why do low-probability events happen rarely?
Probabilities are units used to quantify statements like "I don't need umbrella today, because it's unlikely to rain". They measure what they measure because this is how we defined them. What you ment |
47,650 | Non-tautological explanation for why do low-probability events happen rarely? | By definition (or measurement), low probability events rarely happen.
But your example of your choice to take an umbrella suggests your underlying inquiry really has more to do with decision-making under uncertainty.
You might find Daniel Kahneman's book "Thinking, fast and slow" to be a good guide to understanding suc... | Non-tautological explanation for why do low-probability events happen rarely? | By definition (or measurement), low probability events rarely happen.
But your example of your choice to take an umbrella suggests your underlying inquiry really has more to do with decision-making un | Non-tautological explanation for why do low-probability events happen rarely?
By definition (or measurement), low probability events rarely happen.
But your example of your choice to take an umbrella suggests your underlying inquiry really has more to do with decision-making under uncertainty.
You might find Daniel Kah... | Non-tautological explanation for why do low-probability events happen rarely?
By definition (or measurement), low probability events rarely happen.
But your example of your choice to take an umbrella suggests your underlying inquiry really has more to do with decision-making un |
47,651 | Overfitting the validation set | One thing that is not widely appreciated is that over-fitting the model selection criteria (e.g. validation set performance) can result in a model that over-fits the training data or it can result in a model that underfits the training data.
This example is from my paper (with Mrs Marsupial)
Gavin C. Cawley, Nicola L. ... | Overfitting the validation set | One thing that is not widely appreciated is that over-fitting the model selection criteria (e.g. validation set performance) can result in a model that over-fits the training data or it can result in | Overfitting the validation set
One thing that is not widely appreciated is that over-fitting the model selection criteria (e.g. validation set performance) can result in a model that over-fits the training data or it can result in a model that underfits the training data.
This example is from my paper (with Mrs Marsupi... | Overfitting the validation set
One thing that is not widely appreciated is that over-fitting the model selection criteria (e.g. validation set performance) can result in a model that over-fits the training data or it can result in |
47,652 | Overfitting the validation set | Choosing the best model is nothing but like hyper parameter optimization. We’re using training set to learn the parameters and validation set to learn the hyper parameters. In HPO, we typically evaluate the model on the candidate configurations and choose the best. In training, we use fancier stuff like gradient descen... | Overfitting the validation set | Choosing the best model is nothing but like hyper parameter optimization. We’re using training set to learn the parameters and validation set to learn the hyper parameters. In HPO, we typically evalua | Overfitting the validation set
Choosing the best model is nothing but like hyper parameter optimization. We’re using training set to learn the parameters and validation set to learn the hyper parameters. In HPO, we typically evaluate the model on the candidate configurations and choose the best. In training, we use fan... | Overfitting the validation set
Choosing the best model is nothing but like hyper parameter optimization. We’re using training set to learn the parameters and validation set to learn the hyper parameters. In HPO, we typically evalua |
47,653 | exact form for the marginal posterior | Answer:
Posterior of $\sigma^2|Y_1,..., Y_n$ is an instance of inverse gamma distribution with the probability density
$$ p(\sigma^2|Y_1,...,Y_n) = \frac{\beta^\alpha}{\Gamma(\alpha)} (\sigma^2)^{-\alpha+1}\exp(-\frac{\beta}{\sigma^2}), $$
where
\begin{align}
\alpha:=\frac{\nu_0+n}{2}, \quad& \beta:=\frac{\nu_0\sigma... | exact form for the marginal posterior | Answer:
Posterior of $\sigma^2|Y_1,..., Y_n$ is an instance of inverse gamma distribution with the probability density
$$ p(\sigma^2|Y_1,...,Y_n) = \frac{\beta^\alpha}{\Gamma(\alpha)} (\sigma^2)^{-\a | exact form for the marginal posterior
Answer:
Posterior of $\sigma^2|Y_1,..., Y_n$ is an instance of inverse gamma distribution with the probability density
$$ p(\sigma^2|Y_1,...,Y_n) = \frac{\beta^\alpha}{\Gamma(\alpha)} (\sigma^2)^{-\alpha+1}\exp(-\frac{\beta}{\sigma^2}), $$
where
\begin{align}
\alpha:=\frac{\nu_0+... | exact form for the marginal posterior
Answer:
Posterior of $\sigma^2|Y_1,..., Y_n$ is an instance of inverse gamma distribution with the probability density
$$ p(\sigma^2|Y_1,...,Y_n) = \frac{\beta^\alpha}{\Gamma(\alpha)} (\sigma^2)^{-\a |
47,654 | exact form for the marginal posterior | For this type of analysis, it is often possible to decompose the posterior density into a part representing the marginal posterior of one of the parameters, and another part representing the conditional posterior of the other parameter. It turns out to be possible to do this in the present case.
To facilitate our an... | exact form for the marginal posterior | For this type of analysis, it is often possible to decompose the posterior density into a part representing the marginal posterior of one of the parameters, and another part representing the condition | exact form for the marginal posterior
For this type of analysis, it is often possible to decompose the posterior density into a part representing the marginal posterior of one of the parameters, and another part representing the conditional posterior of the other parameter. It turns out to be possible to do this in th... | exact form for the marginal posterior
For this type of analysis, it is often possible to decompose the posterior density into a part representing the marginal posterior of one of the parameters, and another part representing the condition |
47,655 | Interpreting the intercept of a Linear Mixed Model Results in Python - Statsmodel Package | The intercept estimate of 15.724 is the global intercept, around which the (72) random intercepts vary. The random intercepts are estimated as samples from a normal distribution with a variance of 40.384 and mean of zero - hence the need for a global (fixed) intercept. | Interpreting the intercept of a Linear Mixed Model Results in Python - Statsmodel Package | The intercept estimate of 15.724 is the global intercept, around which the (72) random intercepts vary. The random intercepts are estimated as samples from a normal distribution with a variance of 40. | Interpreting the intercept of a Linear Mixed Model Results in Python - Statsmodel Package
The intercept estimate of 15.724 is the global intercept, around which the (72) random intercepts vary. The random intercepts are estimated as samples from a normal distribution with a variance of 40.384 and mean of zero - hence t... | Interpreting the intercept of a Linear Mixed Model Results in Python - Statsmodel Package
The intercept estimate of 15.724 is the global intercept, around which the (72) random intercepts vary. The random intercepts are estimated as samples from a normal distribution with a variance of 40. |
47,656 | How to optimise waterfall questions of purchase value | Short answer:
Indeed, when the same customer may be approached at most $n$ times, it is optimal to start with offer $y_1=\frac{n-1}{n}x$ and decrease the price by $\frac{x}{n}$ with every refusal.
The above result only holds for the uniform distribution of the customer's valuation $v$. Under the normal distribution, c... | How to optimise waterfall questions of purchase value | Short answer:
Indeed, when the same customer may be approached at most $n$ times, it is optimal to start with offer $y_1=\frac{n-1}{n}x$ and decrease the price by $\frac{x}{n}$ with every refusal.
Th | How to optimise waterfall questions of purchase value
Short answer:
Indeed, when the same customer may be approached at most $n$ times, it is optimal to start with offer $y_1=\frac{n-1}{n}x$ and decrease the price by $\frac{x}{n}$ with every refusal.
The above result only holds for the uniform distribution of the cust... | How to optimise waterfall questions of purchase value
Short answer:
Indeed, when the same customer may be approached at most $n$ times, it is optimal to start with offer $y_1=\frac{n-1}{n}x$ and decrease the price by $\frac{x}{n}$ with every refusal.
Th |
47,657 | How to optimise waterfall questions of purchase value | This kind of problem is an optimisation problem that can either be solved directly from the profit function, or in two-steps using backward induction. To show you how to uses either of these methods, I will first write the optimisation problem out in a helpful mathematical form. I will show the solution by both metho... | How to optimise waterfall questions of purchase value | This kind of problem is an optimisation problem that can either be solved directly from the profit function, or in two-steps using backward induction. To show you how to uses either of these methods, | How to optimise waterfall questions of purchase value
This kind of problem is an optimisation problem that can either be solved directly from the profit function, or in two-steps using backward induction. To show you how to uses either of these methods, I will first write the optimisation problem out in a helpful math... | How to optimise waterfall questions of purchase value
This kind of problem is an optimisation problem that can either be solved directly from the profit function, or in two-steps using backward induction. To show you how to uses either of these methods, |
47,658 | Multinomial distribution: probability that one outcome is greater than another | There is a closed form for this probability, but it is not particularly concise. To obtain the formula, start with the probability of the event of interest, conditional on the event $X_1+X_2=r$. It can easily be shown that:
$$X_1 | X_1 + X_2 = r, n, \mathbf{p} \sim \text{Bin} \Big( r, \frac{p_1}{p_1+p_2} \Big).$$
Und... | Multinomial distribution: probability that one outcome is greater than another | There is a closed form for this probability, but it is not particularly concise. To obtain the formula, start with the probability of the event of interest, conditional on the event $X_1+X_2=r$. It | Multinomial distribution: probability that one outcome is greater than another
There is a closed form for this probability, but it is not particularly concise. To obtain the formula, start with the probability of the event of interest, conditional on the event $X_1+X_2=r$. It can easily be shown that:
$$X_1 | X_1 + X... | Multinomial distribution: probability that one outcome is greater than another
There is a closed form for this probability, but it is not particularly concise. To obtain the formula, start with the probability of the event of interest, conditional on the event $X_1+X_2=r$. It |
47,659 | Multinomial distribution: probability that one outcome is greater than another | Let $Z_i$ be independent draws from a categorical variable take takes values 1,2 and 3 with probability $p_1,p_2$ and $1-p_1-p_2$. Then, $X_k = \sum_{i=1}^n 1\{Z_i = k\}$ has the desired multinomial distribution. Let $Y_i = \{Z_i = 1\} - 1\{Z_i = 2\}$ and let $W_n = \sum_{i=1}^n Y_i$. The desired probability is $P(W_n ... | Multinomial distribution: probability that one outcome is greater than another | Let $Z_i$ be independent draws from a categorical variable take takes values 1,2 and 3 with probability $p_1,p_2$ and $1-p_1-p_2$. Then, $X_k = \sum_{i=1}^n 1\{Z_i = k\}$ has the desired multinomial d | Multinomial distribution: probability that one outcome is greater than another
Let $Z_i$ be independent draws from a categorical variable take takes values 1,2 and 3 with probability $p_1,p_2$ and $1-p_1-p_2$. Then, $X_k = \sum_{i=1}^n 1\{Z_i = k\}$ has the desired multinomial distribution. Let $Y_i = \{Z_i = 1\} - 1\{... | Multinomial distribution: probability that one outcome is greater than another
Let $Z_i$ be independent draws from a categorical variable take takes values 1,2 and 3 with probability $p_1,p_2$ and $1-p_1-p_2$. Then, $X_k = \sum_{i=1}^n 1\{Z_i = k\}$ has the desired multinomial d |
47,660 | What test can I use to compare intercepts from two or more regression models when slopes might differ? | I will answer the technical question, then try to talk you out of doing this.
The intercept is the predicted value when the abscissa is equal to zero. Hence, the intercepts in the example are obtained via:
> mod = lm(Sepal.Length ~ Petal.Width*Species, data = iris)
> library("emmeans")
> (emm = emmeans(mod, "Species",... | What test can I use to compare intercepts from two or more regression models when slopes might diffe | I will answer the technical question, then try to talk you out of doing this.
The intercept is the predicted value when the abscissa is equal to zero. Hence, the intercepts in the example are obtained | What test can I use to compare intercepts from two or more regression models when slopes might differ?
I will answer the technical question, then try to talk you out of doing this.
The intercept is the predicted value when the abscissa is equal to zero. Hence, the intercepts in the example are obtained via:
> mod = lm(... | What test can I use to compare intercepts from two or more regression models when slopes might diffe
I will answer the technical question, then try to talk you out of doing this.
The intercept is the predicted value when the abscissa is equal to zero. Hence, the intercepts in the example are obtained |
47,661 | What test can I use to compare intercepts from two or more regression models when slopes might differ? | In principle, once you have the linear regression object generated by lm(), you can test for significant differences between any desired linear combinations of predictor values that you wish by applying the formula for the variance of a sum to the covariance matrix for the linear regression, the matrix provided provide... | What test can I use to compare intercepts from two or more regression models when slopes might diffe | In principle, once you have the linear regression object generated by lm(), you can test for significant differences between any desired linear combinations of predictor values that you wish by applyi | What test can I use to compare intercepts from two or more regression models when slopes might differ?
In principle, once you have the linear regression object generated by lm(), you can test for significant differences between any desired linear combinations of predictor values that you wish by applying the formula fo... | What test can I use to compare intercepts from two or more regression models when slopes might diffe
In principle, once you have the linear regression object generated by lm(), you can test for significant differences between any desired linear combinations of predictor values that you wish by applyi |
47,662 | How i add uniformly distributed noisy attributes to data set? | One way would be to train a model that learns the distribution of each feature separately; it could be a KDE for each feature.
Then you could use this model to generate outliers for the data. I'd suggest producing the outliers by generating values at 4 std from the mean for a few of the features and generate realistic ... | How i add uniformly distributed noisy attributes to data set? | One way would be to train a model that learns the distribution of each feature separately; it could be a KDE for each feature.
Then you could use this model to generate outliers for the data. I'd sugg | How i add uniformly distributed noisy attributes to data set?
One way would be to train a model that learns the distribution of each feature separately; it could be a KDE for each feature.
Then you could use this model to generate outliers for the data. I'd suggest producing the outliers by generating values at 4 std f... | How i add uniformly distributed noisy attributes to data set?
One way would be to train a model that learns the distribution of each feature separately; it could be a KDE for each feature.
Then you could use this model to generate outliers for the data. I'd sugg |
47,663 | ARIMAX vs. Regression With ARIMA Errors | Assuming you are fitting the regression with ARIMA error model using arima(), Arima() or auto.arima(), the estimation is done in one step, not two as you describe. That is, the regression coefficients are estimated simultaneously with the ARMA coefficients.
If you are studying the effect of the exogenous variables, you... | ARIMAX vs. Regression With ARIMA Errors | Assuming you are fitting the regression with ARIMA error model using arima(), Arima() or auto.arima(), the estimation is done in one step, not two as you describe. That is, the regression coefficients | ARIMAX vs. Regression With ARIMA Errors
Assuming you are fitting the regression with ARIMA error model using arima(), Arima() or auto.arima(), the estimation is done in one step, not two as you describe. That is, the regression coefficients are estimated simultaneously with the ARMA coefficients.
If you are studying th... | ARIMAX vs. Regression With ARIMA Errors
Assuming you are fitting the regression with ARIMA error model using arima(), Arima() or auto.arima(), the estimation is done in one step, not two as you describe. That is, the regression coefficients |
47,664 | Combining regression estimates by summing | Based on your clarification in the comments, and your amended notation, you want to use a Gaussian linear model where the parameters and error terms in each of the initial regressions are different. You therefore have the model:
$$\begin{matrix}
Y_{it}^{(1)} = \alpha_i^{(1)} + \gamma_t^{(1)} + X_{it}\beta^{(1)} + \eps... | Combining regression estimates by summing | Based on your clarification in the comments, and your amended notation, you want to use a Gaussian linear model where the parameters and error terms in each of the initial regressions are different. | Combining regression estimates by summing
Based on your clarification in the comments, and your amended notation, you want to use a Gaussian linear model where the parameters and error terms in each of the initial regressions are different. You therefore have the model:
$$\begin{matrix}
Y_{it}^{(1)} = \alpha_i^{(1)} +... | Combining regression estimates by summing
Based on your clarification in the comments, and your amended notation, you want to use a Gaussian linear model where the parameters and error terms in each of the initial regressions are different. |
47,665 | Combining regression estimates by summing | $Y_1 \sim \mathcal{N}(X\beta_1,\sigma_1^2)$ ==> $Y_1=X\beta_1+\epsilon_1$ and $\epsilon_1\sim \mathcal{N}(0,\sigma_1^2) $
$Y_2 \sim \mathcal{N}(X\beta_2,\sigma_2^2)$ ==> $Y_2=X\beta_2+\epsilon_2$ and $\epsilon_2\sim \mathcal{N}(0,\sigma_2^2) $
Assume $\epsilon_1$ and $\epsilon_2$ are independent, then
$Y_1 + Y_2 \si... | Combining regression estimates by summing | $Y_1 \sim \mathcal{N}(X\beta_1,\sigma_1^2)$ ==> $Y_1=X\beta_1+\epsilon_1$ and $\epsilon_1\sim \mathcal{N}(0,\sigma_1^2) $
$Y_2 \sim \mathcal{N}(X\beta_2,\sigma_2^2)$ ==> $Y_2=X\beta_2+\epsilon_2$ an | Combining regression estimates by summing
$Y_1 \sim \mathcal{N}(X\beta_1,\sigma_1^2)$ ==> $Y_1=X\beta_1+\epsilon_1$ and $\epsilon_1\sim \mathcal{N}(0,\sigma_1^2) $
$Y_2 \sim \mathcal{N}(X\beta_2,\sigma_2^2)$ ==> $Y_2=X\beta_2+\epsilon_2$ and $\epsilon_2\sim \mathcal{N}(0,\sigma_2^2) $
Assume $\epsilon_1$ and $\epsilo... | Combining regression estimates by summing
$Y_1 \sim \mathcal{N}(X\beta_1,\sigma_1^2)$ ==> $Y_1=X\beta_1+\epsilon_1$ and $\epsilon_1\sim \mathcal{N}(0,\sigma_1^2) $
$Y_2 \sim \mathcal{N}(X\beta_2,\sigma_2^2)$ ==> $Y_2=X\beta_2+\epsilon_2$ an |
47,666 | Combining regression estimates by summing | Short answer:
In the described theoretical setting, you are right to expect $\beta_3 = \beta_1+\beta_2$ in the linear setting. The time- and individual- FE does not change it.
In the linear setting, $\beta_3$ can differ from $\beta_1+\beta_2$ for instance due to data limitations. (please look at the bottom of the post... | Combining regression estimates by summing | Short answer:
In the described theoretical setting, you are right to expect $\beta_3 = \beta_1+\beta_2$ in the linear setting. The time- and individual- FE does not change it.
In the linear setting, | Combining regression estimates by summing
Short answer:
In the described theoretical setting, you are right to expect $\beta_3 = \beta_1+\beta_2$ in the linear setting. The time- and individual- FE does not change it.
In the linear setting, $\beta_3$ can differ from $\beta_1+\beta_2$ for instance due to data limitatio... | Combining regression estimates by summing
Short answer:
In the described theoretical setting, you are right to expect $\beta_3 = \beta_1+\beta_2$ in the linear setting. The time- and individual- FE does not change it.
In the linear setting, |
47,667 | Combining regression estimates by summing | **** Edits to the question made this answer obsolete ****
I'm no expert, so interpret with caution. Isn't the model that you fit for the sum supposed to be
$$
Y^{sum} = 2 \alpha_i + 2\gamma_t + \beta_3 X + 2\epsilon_{it},
$$
thus changing what you should expect. This assumes that your parameters $\alpha_i$ and $\gamma_... | Combining regression estimates by summing | **** Edits to the question made this answer obsolete ****
I'm no expert, so interpret with caution. Isn't the model that you fit for the sum supposed to be
$$
Y^{sum} = 2 \alpha_i + 2\gamma_t + \beta_ | Combining regression estimates by summing
**** Edits to the question made this answer obsolete ****
I'm no expert, so interpret with caution. Isn't the model that you fit for the sum supposed to be
$$
Y^{sum} = 2 \alpha_i + 2\gamma_t + \beta_3 X + 2\epsilon_{it},
$$
thus changing what you should expect. This assumes th... | Combining regression estimates by summing
**** Edits to the question made this answer obsolete ****
I'm no expert, so interpret with caution. Isn't the model that you fit for the sum supposed to be
$$
Y^{sum} = 2 \alpha_i + 2\gamma_t + \beta_ |
47,668 | Non-uniform distribution of p-values | As whuber has commented: the Kolmogorov-Smirnov test is only valid as a comparison against a fully specified distribution. You cannot use it to compare an observed distribution against a distribution whose parameters have been estimated based on your observed sample. If you do so, your p-values will not be uniformly di... | Non-uniform distribution of p-values | As whuber has commented: the Kolmogorov-Smirnov test is only valid as a comparison against a fully specified distribution. You cannot use it to compare an observed distribution against a distribution | Non-uniform distribution of p-values
As whuber has commented: the Kolmogorov-Smirnov test is only valid as a comparison against a fully specified distribution. You cannot use it to compare an observed distribution against a distribution whose parameters have been estimated based on your observed sample. If you do so, y... | Non-uniform distribution of p-values
As whuber has commented: the Kolmogorov-Smirnov test is only valid as a comparison against a fully specified distribution. You cannot use it to compare an observed distribution against a distribution |
47,669 | Why is bagging stable classifiers not a good idea? | Summary: bagging is a bias-variance tradeoff for the model, accepting some bias to reduce variance.
If there's nothing to gain by reducing variance, there can still be losses due to bias compared to training on $\mathcal L$.
We can check whether variance reduction leads to substantial improvements (also in situations ... | Why is bagging stable classifiers not a good idea? | Summary: bagging is a bias-variance tradeoff for the model, accepting some bias to reduce variance.
If there's nothing to gain by reducing variance, there can still be losses due to bias compared to | Why is bagging stable classifiers not a good idea?
Summary: bagging is a bias-variance tradeoff for the model, accepting some bias to reduce variance.
If there's nothing to gain by reducing variance, there can still be losses due to bias compared to training on $\mathcal L$.
We can check whether variance reduction lea... | Why is bagging stable classifiers not a good idea?
Summary: bagging is a bias-variance tradeoff for the model, accepting some bias to reduce variance.
If there's nothing to gain by reducing variance, there can still be losses due to bias compared to |
47,670 | What is the correct definition of the root mean square percentage error (RMSPE)? | There are several alternative sources (Swanson et al., Fomby, Shcherbakov et al.), which agree that the RMSPE is defined as:
\begin{equation}
\text{RMSPE} = \sqrt{\frac{1}{n} \cdot \sum_{i=1}^n \Delta X^2_{\text{rel},i}} \cdot 100\%
\end{equation} | What is the correct definition of the root mean square percentage error (RMSPE)? | There are several alternative sources (Swanson et al., Fomby, Shcherbakov et al.), which agree that the RMSPE is defined as:
\begin{equation}
\text{RMSPE} = \sqrt{\frac{1}{n} \cdot \sum_{i=1}^n \Delta | What is the correct definition of the root mean square percentage error (RMSPE)?
There are several alternative sources (Swanson et al., Fomby, Shcherbakov et al.), which agree that the RMSPE is defined as:
\begin{equation}
\text{RMSPE} = \sqrt{\frac{1}{n} \cdot \sum_{i=1}^n \Delta X^2_{\text{rel},i}} \cdot 100\%
\end{e... | What is the correct definition of the root mean square percentage error (RMSPE)?
There are several alternative sources (Swanson et al., Fomby, Shcherbakov et al.), which agree that the RMSPE is defined as:
\begin{equation}
\text{RMSPE} = \sqrt{\frac{1}{n} \cdot \sum_{i=1}^n \Delta |
47,671 | Camera trapping and the Poisson distribution | It is almost never a good idea to use a Poisson distribution (or any other single parameter distribution) for modelling --- this distribution fixes the variance in relation to the mean, which means that the model does not allow the estimated variability to conform to the data. For this type of data, you should use a n... | Camera trapping and the Poisson distribution | It is almost never a good idea to use a Poisson distribution (or any other single parameter distribution) for modelling --- this distribution fixes the variance in relation to the mean, which means th | Camera trapping and the Poisson distribution
It is almost never a good idea to use a Poisson distribution (or any other single parameter distribution) for modelling --- this distribution fixes the variance in relation to the mean, which means that the model does not allow the estimated variability to conform to the dat... | Camera trapping and the Poisson distribution
It is almost never a good idea to use a Poisson distribution (or any other single parameter distribution) for modelling --- this distribution fixes the variance in relation to the mean, which means th |
47,672 | Camera trapping and the Poisson distribution | Consider $n$ counts having the same covariate pattern (replicates). Suppose the $i$th count $X_i$ were to follow a Poisson distribution with its own mean $\mu_i$; the joint mass function of $n$ independent counts is then
$$\begin{align}
f_{\vec{X}}(\vec{x};\mu_1,\ldots,\mu_n) &= \prod_{i=1}^n\frac{\mu_i^{x_i}\exp(-\mu_... | Camera trapping and the Poisson distribution | Consider $n$ counts having the same covariate pattern (replicates). Suppose the $i$th count $X_i$ were to follow a Poisson distribution with its own mean $\mu_i$; the joint mass function of $n$ indepe | Camera trapping and the Poisson distribution
Consider $n$ counts having the same covariate pattern (replicates). Suppose the $i$th count $X_i$ were to follow a Poisson distribution with its own mean $\mu_i$; the joint mass function of $n$ independent counts is then
$$\begin{align}
f_{\vec{X}}(\vec{x};\mu_1,\ldots,\mu_n... | Camera trapping and the Poisson distribution
Consider $n$ counts having the same covariate pattern (replicates). Suppose the $i$th count $X_i$ were to follow a Poisson distribution with its own mean $\mu_i$; the joint mass function of $n$ indepe |
47,673 | How would someone use curves as an input to a supervised learning model? | The response was idiotic, my condolences. What you suggested is not unreasonable. It will probably not work, but how would you know in advance? Both your options were good starting points.
Although the simple polynomial approach is probably not a good idea in a literal sense, but in principle, it's not much different f... | How would someone use curves as an input to a supervised learning model? | The response was idiotic, my condolences. What you suggested is not unreasonable. It will probably not work, but how would you know in advance? Both your options were good starting points.
Although th | How would someone use curves as an input to a supervised learning model?
The response was idiotic, my condolences. What you suggested is not unreasonable. It will probably not work, but how would you know in advance? Both your options were good starting points.
Although the simple polynomial approach is probably not a ... | How would someone use curves as an input to a supervised learning model?
The response was idiotic, my condolences. What you suggested is not unreasonable. It will probably not work, but how would you know in advance? Both your options were good starting points.
Although th |
47,674 | What is the difference between BLUE and MVUE? | BLUE means an estimator is Best among the class of Linear and Unbiased Estimators. By best we mean that it is the most efficient estimator in the class of the estimators that are Unbiased plus Linear.
MVUE is the Minimum Variance estimator in the class of Unbiased Estimators. They need not be linear. But yes if any Lin... | What is the difference between BLUE and MVUE? | BLUE means an estimator is Best among the class of Linear and Unbiased Estimators. By best we mean that it is the most efficient estimator in the class of the estimators that are Unbiased plus Linear. | What is the difference between BLUE and MVUE?
BLUE means an estimator is Best among the class of Linear and Unbiased Estimators. By best we mean that it is the most efficient estimator in the class of the estimators that are Unbiased plus Linear.
MVUE is the Minimum Variance estimator in the class of Unbiased Estimator... | What is the difference between BLUE and MVUE?
BLUE means an estimator is Best among the class of Linear and Unbiased Estimators. By best we mean that it is the most efficient estimator in the class of the estimators that are Unbiased plus Linear. |
47,675 | Why does discrete data distribution has differential entropy of negative infinity? | The differential entropy is defined as:
$$h=-\int_{-\infty}^\infty f(x)\ln(f(x))dx$$
vwhere $f(x)$ is the PDf of the function. For the discrete distribution, there is not PDF, but there is a probability mass function. However, we could represent the PDF with Dirac delta function $\delta(x)$:
$$f(x)=\sum_ip_i\delta(x-x_... | Why does discrete data distribution has differential entropy of negative infinity? | The differential entropy is defined as:
$$h=-\int_{-\infty}^\infty f(x)\ln(f(x))dx$$
vwhere $f(x)$ is the PDf of the function. For the discrete distribution, there is not PDF, but there is a probabili | Why does discrete data distribution has differential entropy of negative infinity?
The differential entropy is defined as:
$$h=-\int_{-\infty}^\infty f(x)\ln(f(x))dx$$
vwhere $f(x)$ is the PDf of the function. For the discrete distribution, there is not PDF, but there is a probability mass function. However, we could r... | Why does discrete data distribution has differential entropy of negative infinity?
The differential entropy is defined as:
$$h=-\int_{-\infty}^\infty f(x)\ln(f(x))dx$$
vwhere $f(x)$ is the PDf of the function. For the discrete distribution, there is not PDF, but there is a probabili |
47,676 | Why does discrete data distribution has differential entropy of negative infinity? | The next sentence in that paper has a citation that clears it up:
To avoid this case, it is becoming best practice to add real-valued noise
to the integer pixel values to dequantize the data (e.g., Uria et al., 2013; van den Oord & Schrauwen, 2014; Theis & Bethge, 2015))
The Uria et al. 2013 paper on RNADE explains i... | Why does discrete data distribution has differential entropy of negative infinity? | The next sentence in that paper has a citation that clears it up:
To avoid this case, it is becoming best practice to add real-valued noise
to the integer pixel values to dequantize the data (e.g., U | Why does discrete data distribution has differential entropy of negative infinity?
The next sentence in that paper has a citation that clears it up:
To avoid this case, it is becoming best practice to add real-valued noise
to the integer pixel values to dequantize the data (e.g., Uria et al., 2013; van den Oord & Schr... | Why does discrete data distribution has differential entropy of negative infinity?
The next sentence in that paper has a citation that clears it up:
To avoid this case, it is becoming best practice to add real-valued noise
to the integer pixel values to dequantize the data (e.g., U |
47,677 | Uniform(0,$\theta$) ratio UMVUE? | Your working looks entirely correct to me. We can also confirm this result by an alternative method. Let us posit that the UMVUE is likely to be some scaled version of the ratio statistic:
$$R_n \equiv \frac{X_{(n)}}{Y_{(n)}}.$$
For all $r > 0$ we have:
$$\begin{equation} \begin{aligned}
F_{R_n}(r) \equiv \mathbb{P}(... | Uniform(0,$\theta$) ratio UMVUE? | Your working looks entirely correct to me. We can also confirm this result by an alternative method. Let us posit that the UMVUE is likely to be some scaled version of the ratio statistic:
$$R_n \eq | Uniform(0,$\theta$) ratio UMVUE?
Your working looks entirely correct to me. We can also confirm this result by an alternative method. Let us posit that the UMVUE is likely to be some scaled version of the ratio statistic:
$$R_n \equiv \frac{X_{(n)}}{Y_{(n)}}.$$
For all $r > 0$ we have:
$$\begin{equation} \begin{align... | Uniform(0,$\theta$) ratio UMVUE?
Your working looks entirely correct to me. We can also confirm this result by an alternative method. Let us posit that the UMVUE is likely to be some scaled version of the ratio statistic:
$$R_n \eq |
47,678 | What are disadvantages of "Sequential analysis" | From a frequentist perspective, there are some clear disadvantages of a sequential analyses. That is, if we are concerned with preserving type I errors, we need to recognize that we are doing multiple comparisons: if I do 3 analyses of the data, then I have three non-independent chances to make a type I error and need ... | What are disadvantages of "Sequential analysis" | From a frequentist perspective, there are some clear disadvantages of a sequential analyses. That is, if we are concerned with preserving type I errors, we need to recognize that we are doing multiple | What are disadvantages of "Sequential analysis"
From a frequentist perspective, there are some clear disadvantages of a sequential analyses. That is, if we are concerned with preserving type I errors, we need to recognize that we are doing multiple comparisons: if I do 3 analyses of the data, then I have three non-inde... | What are disadvantages of "Sequential analysis"
From a frequentist perspective, there are some clear disadvantages of a sequential analyses. That is, if we are concerned with preserving type I errors, we need to recognize that we are doing multiple |
47,679 | "Appropriate conditions" for method of moments estimator to exist, be consistent, and asymptotically normal? | Almost all arguments to asymptotic normality of a sequence of statistics hinge on arguments using Taylor series, and thus, the "appropriate conditions" are generally smoothness conditions required to write the Taylor series, eliminate some of the terms, and then infer vanishing of the higher-order terms. Thus, the "ap... | "Appropriate conditions" for method of moments estimator to exist, be consistent, and asymptotically | Almost all arguments to asymptotic normality of a sequence of statistics hinge on arguments using Taylor series, and thus, the "appropriate conditions" are generally smoothness conditions required to | "Appropriate conditions" for method of moments estimator to exist, be consistent, and asymptotically normal?
Almost all arguments to asymptotic normality of a sequence of statistics hinge on arguments using Taylor series, and thus, the "appropriate conditions" are generally smoothness conditions required to write the T... | "Appropriate conditions" for method of moments estimator to exist, be consistent, and asymptotically
Almost all arguments to asymptotic normality of a sequence of statistics hinge on arguments using Taylor series, and thus, the "appropriate conditions" are generally smoothness conditions required to |
47,680 | Correlation: If $Z^2$s are correlated, it doesnt imply that $Z$s are correlated? | Let
$X$ be a standard normal random variable with distribution $\mathcal N(0,1)$,
$Y$ be independently another standard normal random variable and
$Z=\text{sign}(Y) \, |X|$, also a standard normal random variable
Then $X^2=Z^2$, so with correlation of $1$ between them, but $X$ and $Z$ are uncorrelated with correla... | Correlation: If $Z^2$s are correlated, it doesnt imply that $Z$s are correlated? | Let
$X$ be a standard normal random variable with distribution $\mathcal N(0,1)$,
$Y$ be independently another standard normal random variable and
$Z=\text{sign}(Y) \, |X|$, also a standard normal | Correlation: If $Z^2$s are correlated, it doesnt imply that $Z$s are correlated?
Let
$X$ be a standard normal random variable with distribution $\mathcal N(0,1)$,
$Y$ be independently another standard normal random variable and
$Z=\text{sign}(Y) \, |X|$, also a standard normal random variable
Then $X^2=Z^2$, so wi... | Correlation: If $Z^2$s are correlated, it doesnt imply that $Z$s are correlated?
Let
$X$ be a standard normal random variable with distribution $\mathcal N(0,1)$,
$Y$ be independently another standard normal random variable and
$Z=\text{sign}(Y) \, |X|$, also a standard normal |
47,681 | 10% rule for sample sizes | In statistical models that use parameters for the underlying distributions, these parameters correspond to aspects of the empirical distribution of an infinite population (called a "superpopulation"). Thus, for statistical tests and confidence intervals that deal with model parameters, we are implicitly making inferen... | 10% rule for sample sizes | In statistical models that use parameters for the underlying distributions, these parameters correspond to aspects of the empirical distribution of an infinite population (called a "superpopulation"). | 10% rule for sample sizes
In statistical models that use parameters for the underlying distributions, these parameters correspond to aspects of the empirical distribution of an infinite population (called a "superpopulation"). Thus, for statistical tests and confidence intervals that deal with model parameters, we are... | 10% rule for sample sizes
In statistical models that use parameters for the underlying distributions, these parameters correspond to aspects of the empirical distribution of an infinite population (called a "superpopulation"). |
47,682 | 10% rule for sample sizes | If you're sampling a finite population without replacement, you're not sampling independently; your new observations in the sample avoid previously sampled cases.
This is generally a good thing!
However if you're using calculations based on assuming independence you will overestimate variances (instead of the formulas ... | 10% rule for sample sizes | If you're sampling a finite population without replacement, you're not sampling independently; your new observations in the sample avoid previously sampled cases.
This is generally a good thing!
Howev | 10% rule for sample sizes
If you're sampling a finite population without replacement, you're not sampling independently; your new observations in the sample avoid previously sampled cases.
This is generally a good thing!
However if you're using calculations based on assuming independence you will overestimate variances... | 10% rule for sample sizes
If you're sampling a finite population without replacement, you're not sampling independently; your new observations in the sample avoid previously sampled cases.
This is generally a good thing!
Howev |
47,683 | How to derive the formula of the t-test of the correlation coefficient | A t-test is a test on a statistic that has a t-distribution under the null hypothesis. A variable $Z$ has a t-distribution if it is obtained by dividing a Normally-distributed variable $X$ by a $\chi^2$-distributed variable $Y$. For the familiar t-test, $X$ is the sample mean of some IID data, which by the central limi... | How to derive the formula of the t-test of the correlation coefficient | A t-test is a test on a statistic that has a t-distribution under the null hypothesis. A variable $Z$ has a t-distribution if it is obtained by dividing a Normally-distributed variable $X$ by a $\chi^ | How to derive the formula of the t-test of the correlation coefficient
A t-test is a test on a statistic that has a t-distribution under the null hypothesis. A variable $Z$ has a t-distribution if it is obtained by dividing a Normally-distributed variable $X$ by a $\chi^2$-distributed variable $Y$. For the familiar t-t... | How to derive the formula of the t-test of the correlation coefficient
A t-test is a test on a statistic that has a t-distribution under the null hypothesis. A variable $Z$ has a t-distribution if it is obtained by dividing a Normally-distributed variable $X$ by a $\chi^ |
47,684 | Why are Generative Adversarial Networks classed as unsupervised | There are many different flavors of GANs, so in this answer, I will refer to the original GAN. It's regarded as unsupervised because you don't assume that you have a target variable in your dataset -- and if you have one, you don't use it. All you need is some features (e.g., images) -- you don't need class label infor... | Why are Generative Adversarial Networks classed as unsupervised | There are many different flavors of GANs, so in this answer, I will refer to the original GAN. It's regarded as unsupervised because you don't assume that you have a target variable in your dataset -- | Why are Generative Adversarial Networks classed as unsupervised
There are many different flavors of GANs, so in this answer, I will refer to the original GAN. It's regarded as unsupervised because you don't assume that you have a target variable in your dataset -- and if you have one, you don't use it. All you need is ... | Why are Generative Adversarial Networks classed as unsupervised
There are many different flavors of GANs, so in this answer, I will refer to the original GAN. It's regarded as unsupervised because you don't assume that you have a target variable in your dataset -- |
47,685 | Why are Generative Adversarial Networks classed as unsupervised | I think the following perspective might further clarify the confusion.
Generative Adversarial Networks attempt to solve an unsupervised learning problem by jointly solving
a supervised learning problems,
an optimization problem.
Suppose we have training data that takes the form x1,...,xN without labels. Since there... | Why are Generative Adversarial Networks classed as unsupervised | I think the following perspective might further clarify the confusion.
Generative Adversarial Networks attempt to solve an unsupervised learning problem by jointly solving
a supervised learning pro | Why are Generative Adversarial Networks classed as unsupervised
I think the following perspective might further clarify the confusion.
Generative Adversarial Networks attempt to solve an unsupervised learning problem by jointly solving
a supervised learning problems,
an optimization problem.
Suppose we have trainin... | Why are Generative Adversarial Networks classed as unsupervised
I think the following perspective might further clarify the confusion.
Generative Adversarial Networks attempt to solve an unsupervised learning problem by jointly solving
a supervised learning pro |
47,686 | Why do you set 1 as intercept in linear regression model in python? | I don't know the python function/method you are referring to. But you may be confusing that the 1 you add is to your variables/feature such that it is multiplied by the intercept parameter in your parameter vector. In other words, 1 is rather added to your features and is NOT the value of your intercept. | Why do you set 1 as intercept in linear regression model in python? | I don't know the python function/method you are referring to. But you may be confusing that the 1 you add is to your variables/feature such that it is multiplied by the intercept parameter in your par | Why do you set 1 as intercept in linear regression model in python?
I don't know the python function/method you are referring to. But you may be confusing that the 1 you add is to your variables/feature such that it is multiplied by the intercept parameter in your parameter vector. In other words, 1 is rather added to ... | Why do you set 1 as intercept in linear regression model in python?
I don't know the python function/method you are referring to. But you may be confusing that the 1 you add is to your variables/feature such that it is multiplied by the intercept parameter in your par |
47,687 | Why do you set 1 as intercept in linear regression model in python? | I do not know Python, but as you can readily illustrate in R, setting the value of the intercept to 1 is really just a convention (a useful one, though, of course, allowing us to interpret the intercept as the expected effect when $x=0$).
n <- 10
y <- rnorm(n) # some random data
x <- rnorm(n)
intercept <- r... | Why do you set 1 as intercept in linear regression model in python? | I do not know Python, but as you can readily illustrate in R, setting the value of the intercept to 1 is really just a convention (a useful one, though, of course, allowing us to interpret the interce | Why do you set 1 as intercept in linear regression model in python?
I do not know Python, but as you can readily illustrate in R, setting the value of the intercept to 1 is really just a convention (a useful one, though, of course, allowing us to interpret the intercept as the expected effect when $x=0$).
n <- 10
y <- ... | Why do you set 1 as intercept in linear regression model in python?
I do not know Python, but as you can readily illustrate in R, setting the value of the intercept to 1 is really just a convention (a useful one, though, of course, allowing us to interpret the interce |
47,688 | Least Squares Estimator Vs Ordinary Least Squares Estimator | Dropping out the Estimator keyword, Least Squares and Ordinary Least Squares, referred as LS and OLS respectively, are not the same. LS is much more general. It consist of linear and non-linear LS. And, linear LS consist of OLS, and some other types (e.g. GLS: Generalized LS, WLS: Weighted LS). The nonlinear part is it... | Least Squares Estimator Vs Ordinary Least Squares Estimator | Dropping out the Estimator keyword, Least Squares and Ordinary Least Squares, referred as LS and OLS respectively, are not the same. LS is much more general. It consist of linear and non-linear LS. An | Least Squares Estimator Vs Ordinary Least Squares Estimator
Dropping out the Estimator keyword, Least Squares and Ordinary Least Squares, referred as LS and OLS respectively, are not the same. LS is much more general. It consist of linear and non-linear LS. And, linear LS consist of OLS, and some other types (e.g. GLS:... | Least Squares Estimator Vs Ordinary Least Squares Estimator
Dropping out the Estimator keyword, Least Squares and Ordinary Least Squares, referred as LS and OLS respectively, are not the same. LS is much more general. It consist of linear and non-linear LS. An |
47,689 | Gaussian-to-gaussian transformations | The thread at Normal Distribution Existence Non-affine Invariant Transformation? exhibits many non-affine transformations that map normally distributed variables into normally distributed variables, so the answer is in the negative.
(For the record, an affine transformation $f:\mathbb R\to \mathbb R$ is one of the form... | Gaussian-to-gaussian transformations | The thread at Normal Distribution Existence Non-affine Invariant Transformation? exhibits many non-affine transformations that map normally distributed variables into normally distributed variables, s | Gaussian-to-gaussian transformations
The thread at Normal Distribution Existence Non-affine Invariant Transformation? exhibits many non-affine transformations that map normally distributed variables into normally distributed variables, so the answer is in the negative.
(For the record, an affine transformation $f:\math... | Gaussian-to-gaussian transformations
The thread at Normal Distribution Existence Non-affine Invariant Transformation? exhibits many non-affine transformations that map normally distributed variables into normally distributed variables, s |
47,690 | Gaussian-to-gaussian transformations | If $y=f(x), x,y\in\mathbb{R}^m$, then the condition that $x$ and $y$ are normally distributed is that the Jacobian of the transformation $f$ exists and is constant everywhere, with thanks to @henry for improvements.
Please see the comment by @whuber in the OP’s question, viz., Normal Distribution Existence Non-affine ... | Gaussian-to-gaussian transformations | If $y=f(x), x,y\in\mathbb{R}^m$, then the condition that $x$ and $y$ are normally distributed is that the Jacobian of the transformation $f$ exists and is constant everywhere, with thanks to @henry fo | Gaussian-to-gaussian transformations
If $y=f(x), x,y\in\mathbb{R}^m$, then the condition that $x$ and $y$ are normally distributed is that the Jacobian of the transformation $f$ exists and is constant everywhere, with thanks to @henry for improvements.
Please see the comment by @whuber in the OP’s question, viz., Norm... | Gaussian-to-gaussian transformations
If $y=f(x), x,y\in\mathbb{R}^m$, then the condition that $x$ and $y$ are normally distributed is that the Jacobian of the transformation $f$ exists and is constant everywhere, with thanks to @henry fo |
47,691 | Interpretation of fixed effect coefficients from GLMs and GLMMs | Indeed in GLMs and because you have no random effects, the inverse-link transformed regression coefficients have an interpretation for the for the mean of the outcome.
However, in GLMMs and because there you do have random effects, the inverse-link transformed regression coefficients have an interpretation for the for ... | Interpretation of fixed effect coefficients from GLMs and GLMMs | Indeed in GLMs and because you have no random effects, the inverse-link transformed regression coefficients have an interpretation for the for the mean of the outcome.
However, in GLMMs and because th | Interpretation of fixed effect coefficients from GLMs and GLMMs
Indeed in GLMs and because you have no random effects, the inverse-link transformed regression coefficients have an interpretation for the for the mean of the outcome.
However, in GLMMs and because there you do have random effects, the inverse-link transfo... | Interpretation of fixed effect coefficients from GLMs and GLMMs
Indeed in GLMs and because you have no random effects, the inverse-link transformed regression coefficients have an interpretation for the for the mean of the outcome.
However, in GLMMs and because th |
47,692 | Non-monotone hazard functions | What you search for is called a U-formed hazard function or bathtub function (and references in those links). One specific case is the Gompertz-Makeham law from demography. An example is the hazard function of humans, high but falling hazard first few years of life, a minimum around 9-10 years of life, then slowly incr... | Non-monotone hazard functions | What you search for is called a U-formed hazard function or bathtub function (and references in those links). One specific case is the Gompertz-Makeham law from demography. An example is the hazard fu | Non-monotone hazard functions
What you search for is called a U-formed hazard function or bathtub function (and references in those links). One specific case is the Gompertz-Makeham law from demography. An example is the hazard function of humans, high but falling hazard first few years of life, a minimum around 9-10 y... | Non-monotone hazard functions
What you search for is called a U-formed hazard function or bathtub function (and references in those links). One specific case is the Gompertz-Makeham law from demography. An example is the hazard fu |
47,693 | Are all symmetric matrices with diagonal elements 1 and other values between -1 and 1 correlation matrices? | I thought this must be asked & answered before, but cannot find it, so here it goes ... Let $S$ be a covariance matrix (for the algebra that follows it does not matter if it is theoretical or empirical). Let $D$ be a diagonal matrix with the diagonal of $S$. Then the correlation matrix $R$ is given by
$$
R= D^{-1/... | Are all symmetric matrices with diagonal elements 1 and other values between -1 and 1 correlation ma | I thought this must be asked & answered before, but cannot find it, so here it goes ... Let $S$ be a covariance matrix (for the algebra that follows it does not matter if it is theoretical or empiric | Are all symmetric matrices with diagonal elements 1 and other values between -1 and 1 correlation matrices?
I thought this must be asked & answered before, but cannot find it, so here it goes ... Let $S$ be a covariance matrix (for the algebra that follows it does not matter if it is theoretical or empirical). Let $D$... | Are all symmetric matrices with diagonal elements 1 and other values between -1 and 1 correlation ma
I thought this must be asked & answered before, but cannot find it, so here it goes ... Let $S$ be a covariance matrix (for the algebra that follows it does not matter if it is theoretical or empiric |
47,694 | Interpreting Regression Diagnostic Plots | As mentioned above there are a fair few answers to assessing these kind of plots but it can't hurt to have all the answers in one place. I have created some data and code in R to illustrate my answer:
#Data creation
df <- data.frame(y = c(rep(1:100, 10)))
df$x <- df$y + rnorm(1000, sd = 5)
To begin with it is always g... | Interpreting Regression Diagnostic Plots | As mentioned above there are a fair few answers to assessing these kind of plots but it can't hurt to have all the answers in one place. I have created some data and code in R to illustrate my answer: | Interpreting Regression Diagnostic Plots
As mentioned above there are a fair few answers to assessing these kind of plots but it can't hurt to have all the answers in one place. I have created some data and code in R to illustrate my answer:
#Data creation
df <- data.frame(y = c(rep(1:100, 10)))
df$x <- df$y + rnorm(10... | Interpreting Regression Diagnostic Plots
As mentioned above there are a fair few answers to assessing these kind of plots but it can't hurt to have all the answers in one place. I have created some data and code in R to illustrate my answer: |
47,695 | What, if anything, is wrong with the SE welcome wagon blog post's statistical analysis? | This is a great question, and it is nice to see the analysis conducted by StackExchange subjected to the rigour of its own contributing experts! Nevertheless, it is a bit difficult to assess a blog post "from an academic perspective" since the level of rigour in blog posts differs substantially from those of published... | What, if anything, is wrong with the SE welcome wagon blog post's statistical analysis? | This is a great question, and it is nice to see the analysis conducted by StackExchange subjected to the rigour of its own contributing experts! Nevertheless, it is a bit difficult to assess a blog p | What, if anything, is wrong with the SE welcome wagon blog post's statistical analysis?
This is a great question, and it is nice to see the analysis conducted by StackExchange subjected to the rigour of its own contributing experts! Nevertheless, it is a bit difficult to assess a blog post "from an academic perspectiv... | What, if anything, is wrong with the SE welcome wagon blog post's statistical analysis?
This is a great question, and it is nice to see the analysis conducted by StackExchange subjected to the rigour of its own contributing experts! Nevertheless, it is a bit difficult to assess a blog p |
47,696 | Why does dropout increase the training time per epoch in a neural network? | but I thought that the training time per epoch would decrease by
dropping out units.
That's not the case. I understand your rationale though. You thought that zeroing out components would make for less computation. That would be the case for sparse matrices, but not for dense matrices.
TensorFlow, and any deep learn... | Why does dropout increase the training time per epoch in a neural network? | but I thought that the training time per epoch would decrease by
dropping out units.
That's not the case. I understand your rationale though. You thought that zeroing out components would make for | Why does dropout increase the training time per epoch in a neural network?
but I thought that the training time per epoch would decrease by
dropping out units.
That's not the case. I understand your rationale though. You thought that zeroing out components would make for less computation. That would be the case for ... | Why does dropout increase the training time per epoch in a neural network?
but I thought that the training time per epoch would decrease by
dropping out units.
That's not the case. I understand your rationale though. You thought that zeroing out components would make for |
47,697 | The meaning of Bayesian update | Posteriors and priors are all distributions on the parameter space, so they can be compared as such, even if they are not of the same shape. If you are interested in performing multiple updates, i.e. to go from a posterior p(theta|Y1) to a second posterior p(theta|Y1,Y2), etc, then you can absolutely use p(theta|Y1) as... | The meaning of Bayesian update | Posteriors and priors are all distributions on the parameter space, so they can be compared as such, even if they are not of the same shape. If you are interested in performing multiple updates, i.e. | The meaning of Bayesian update
Posteriors and priors are all distributions on the parameter space, so they can be compared as such, even if they are not of the same shape. If you are interested in performing multiple updates, i.e. to go from a posterior p(theta|Y1) to a second posterior p(theta|Y1,Y2), etc, then you ca... | The meaning of Bayesian update
Posteriors and priors are all distributions on the parameter space, so they can be compared as such, even if they are not of the same shape. If you are interested in performing multiple updates, i.e. |
47,698 | The meaning of Bayesian update | Pierrot's answer is correct, but as this seems to be a question about intuition, I wanted to give what might be a more intuitive approach to thinking about the question.
I (+1)'d this question because it is in a way insightful; you are taking seriously that you need to understand what a method really means. However, wh... | The meaning of Bayesian update | Pierrot's answer is correct, but as this seems to be a question about intuition, I wanted to give what might be a more intuitive approach to thinking about the question.
I (+1)'d this question because | The meaning of Bayesian update
Pierrot's answer is correct, but as this seems to be a question about intuition, I wanted to give what might be a more intuitive approach to thinking about the question.
I (+1)'d this question because it is in a way insightful; you are taking seriously that you need to understand what a m... | The meaning of Bayesian update
Pierrot's answer is correct, but as this seems to be a question about intuition, I wanted to give what might be a more intuitive approach to thinking about the question.
I (+1)'d this question because |
47,699 | Principled understanding of why AlphaZero's algorithm works? | First a small note: AlphaGo Zero actually does only use a single network, it no longer has separate value and policy networks like the original AlphaGo did. That single network does still have separate value and policy heads though (two separate outputs)... so I suppose you can intuitively still view it as having two n... | Principled understanding of why AlphaZero's algorithm works? | First a small note: AlphaGo Zero actually does only use a single network, it no longer has separate value and policy networks like the original AlphaGo did. That single network does still have separat | Principled understanding of why AlphaZero's algorithm works?
First a small note: AlphaGo Zero actually does only use a single network, it no longer has separate value and policy networks like the original AlphaGo did. That single network does still have separate value and policy heads though (two separate outputs)... s... | Principled understanding of why AlphaZero's algorithm works?
First a small note: AlphaGo Zero actually does only use a single network, it no longer has separate value and policy networks like the original AlphaGo did. That single network does still have separat |
47,700 | Principled understanding of why AlphaZero's algorithm works? | Using a policy network and a value network seems related to the trick that dueling DQNs use. The simplest dueling DQN is a single network that "branches" near the final layers to compute advantage values $A(s,a)$ for each action, as well as value $V(s)$ for the current state. Explicitly separating the advantage for eac... | Principled understanding of why AlphaZero's algorithm works? | Using a policy network and a value network seems related to the trick that dueling DQNs use. The simplest dueling DQN is a single network that "branches" near the final layers to compute advantage val | Principled understanding of why AlphaZero's algorithm works?
Using a policy network and a value network seems related to the trick that dueling DQNs use. The simplest dueling DQN is a single network that "branches" near the final layers to compute advantage values $A(s,a)$ for each action, as well as value $V(s)$ for t... | Principled understanding of why AlphaZero's algorithm works?
Using a policy network and a value network seems related to the trick that dueling DQNs use. The simplest dueling DQN is a single network that "branches" near the final layers to compute advantage val |
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