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11,501 | Coefficient of Determination ($r^2$): I have never fully grasped the interpretation | A mathematical demonstration of the relationship between the two is here: Pearson's correlation and least squares regression analysis.
I am not sure if there is a geometric or any other intuition that can be offered apart from the math but if I can think of one I will update this answer.
Update: Geometric Intuition
Her... | Coefficient of Determination ($r^2$): I have never fully grasped the interpretation | A mathematical demonstration of the relationship between the two is here: Pearson's correlation and least squares regression analysis.
I am not sure if there is a geometric or any other intuition that | Coefficient of Determination ($r^2$): I have never fully grasped the interpretation
A mathematical demonstration of the relationship between the two is here: Pearson's correlation and least squares regression analysis.
I am not sure if there is a geometric or any other intuition that can be offered apart from the math ... | Coefficient of Determination ($r^2$): I have never fully grasped the interpretation
A mathematical demonstration of the relationship between the two is here: Pearson's correlation and least squares regression analysis.
I am not sure if there is a geometric or any other intuition that |
11,502 | Coefficient of Determination ($r^2$): I have never fully grasped the interpretation | The Regression By Eye applet could be of use if you're trying to develop some intuition.
It lets you generate data then guess a value for R, which you can then compare with the actual value. | Coefficient of Determination ($r^2$): I have never fully grasped the interpretation | The Regression By Eye applet could be of use if you're trying to develop some intuition.
It lets you generate data then guess a value for R, which you can then compare with the actual value. | Coefficient of Determination ($r^2$): I have never fully grasped the interpretation
The Regression By Eye applet could be of use if you're trying to develop some intuition.
It lets you generate data then guess a value for R, which you can then compare with the actual value. | Coefficient of Determination ($r^2$): I have never fully grasped the interpretation
The Regression By Eye applet could be of use if you're trying to develop some intuition.
It lets you generate data then guess a value for R, which you can then compare with the actual value. |
11,503 | The magic money tree problem | This is a well-known problem. It is called a Kelly bet. The answer, by the way, is 1/3rd. It is equivalent to maximizing the log utility of wealth.
Kelly began with taking time to infinity and then solving backward. Since you can always express returns in terms of continuous compounding, then you can also reverse t... | The magic money tree problem | This is a well-known problem. It is called a Kelly bet. The answer, by the way, is 1/3rd. It is equivalent to maximizing the log utility of wealth.
Kelly began with taking time to infinity and then | The magic money tree problem
This is a well-known problem. It is called a Kelly bet. The answer, by the way, is 1/3rd. It is equivalent to maximizing the log utility of wealth.
Kelly began with taking time to infinity and then solving backward. Since you can always express returns in terms of continuous compounding... | The magic money tree problem
This is a well-known problem. It is called a Kelly bet. The answer, by the way, is 1/3rd. It is equivalent to maximizing the log utility of wealth.
Kelly began with taking time to infinity and then |
11,504 | The magic money tree problem | I don't think this is much different from the Martingale. In your case, there are no doubling bets, but the winning payout is 3x.
I coded a "living replica" of your tree. I run 10 simulations. In each simulation (trace), you start with 200 coins and try with the tree, 1 coin each time for 20,000 times.
The only conditi... | The magic money tree problem | I don't think this is much different from the Martingale. In your case, there are no doubling bets, but the winning payout is 3x.
I coded a "living replica" of your tree. I run 10 simulations. In each | The magic money tree problem
I don't think this is much different from the Martingale. In your case, there are no doubling bets, but the winning payout is 3x.
I coded a "living replica" of your tree. I run 10 simulations. In each simulation (trace), you start with 200 coins and try with the tree, 1 coin each time for 2... | The magic money tree problem
I don't think this is much different from the Martingale. In your case, there are no doubling bets, but the winning payout is 3x.
I coded a "living replica" of your tree. I run 10 simulations. In each |
11,505 | The magic money tree problem | I liked the answer given by Dave harris. just though I would come at the problem from a "low risk" perspective, rather than profit maximising
The random walk you are doing, assuming your fraction bet is $q$ and probability of winning $p=0.5$ has is given as
$$Y_t|Y_{t-1}=(1-q+3qX_t)Y_{t-1}$$
where $X_t\sim Bernoulli(p)... | The magic money tree problem | I liked the answer given by Dave harris. just though I would come at the problem from a "low risk" perspective, rather than profit maximising
The random walk you are doing, assuming your fraction bet | The magic money tree problem
I liked the answer given by Dave harris. just though I would come at the problem from a "low risk" perspective, rather than profit maximising
The random walk you are doing, assuming your fraction bet is $q$ and probability of winning $p=0.5$ has is given as
$$Y_t|Y_{t-1}=(1-q+3qX_t)Y_{t-1}$... | The magic money tree problem
I liked the answer given by Dave harris. just though I would come at the problem from a "low risk" perspective, rather than profit maximising
The random walk you are doing, assuming your fraction bet |
11,506 | The magic money tree problem | Problem statement
$\mathbf{M_t}$: the amount of money $M_t$ the gambler has at time $t$
$\mathbf{Y_t}$: Let $Y_t = \log_{10}(M_t)$ be the logarithm of $M_t$.
$\mathbf{Y_0}$: Let $Y_0 = 1$ be the amount of money that the gambler starts with (ten dollars).
$\mathbf{Y_L}$: Let $Y_L=-2$ be the amount of money where the ... | The magic money tree problem | Problem statement
$\mathbf{M_t}$: the amount of money $M_t$ the gambler has at time $t$
$\mathbf{Y_t}$: Let $Y_t = \log_{10}(M_t)$ be the logarithm of $M_t$.
$\mathbf{Y_0}$: Let $Y_0 = 1$ be the amo | The magic money tree problem
Problem statement
$\mathbf{M_t}$: the amount of money $M_t$ the gambler has at time $t$
$\mathbf{Y_t}$: Let $Y_t = \log_{10}(M_t)$ be the logarithm of $M_t$.
$\mathbf{Y_0}$: Let $Y_0 = 1$ be the amount of money that the gambler starts with (ten dollars).
$\mathbf{Y_L}$: Let $Y_L=-2$ be t... | The magic money tree problem
Problem statement
$\mathbf{M_t}$: the amount of money $M_t$ the gambler has at time $t$
$\mathbf{Y_t}$: Let $Y_t = \log_{10}(M_t)$ be the logarithm of $M_t$.
$\mathbf{Y_0}$: Let $Y_0 = 1$ be the amo |
11,507 | How to split r-squared between predictor variables in multiple regression? | You can just get the two separate correlations and square them or run two separate models and get the R^2. They will only sum up if the predictors are orthogonal. | How to split r-squared between predictor variables in multiple regression? | You can just get the two separate correlations and square them or run two separate models and get the R^2. They will only sum up if the predictors are orthogonal. | How to split r-squared between predictor variables in multiple regression?
You can just get the two separate correlations and square them or run two separate models and get the R^2. They will only sum up if the predictors are orthogonal. | How to split r-squared between predictor variables in multiple regression?
You can just get the two separate correlations and square them or run two separate models and get the R^2. They will only sum up if the predictors are orthogonal. |
11,508 | How to split r-squared between predictor variables in multiple regression? | In addition to John's answer, you may wish to obtain the squared semi-partial correlations for each predictor.
Uncorrelated predictors: If the predictors are orthogonal (i.e., uncorrelated), then the squared semi-partial correlations will be the same as the squared zero-order correlations.
Correlated predictors: If ... | How to split r-squared between predictor variables in multiple regression? | In addition to John's answer, you may wish to obtain the squared semi-partial correlations for each predictor.
Uncorrelated predictors: If the predictors are orthogonal (i.e., uncorrelated), then th | How to split r-squared between predictor variables in multiple regression?
In addition to John's answer, you may wish to obtain the squared semi-partial correlations for each predictor.
Uncorrelated predictors: If the predictors are orthogonal (i.e., uncorrelated), then the squared semi-partial correlations will be t... | How to split r-squared between predictor variables in multiple regression?
In addition to John's answer, you may wish to obtain the squared semi-partial correlations for each predictor.
Uncorrelated predictors: If the predictors are orthogonal (i.e., uncorrelated), then th |
11,509 | How to split r-squared between predictor variables in multiple regression? | I added the variance-decomposition tag to your question. Here is part of its tag wiki:
One common method is to add regressors to the model one by one and record the increase in $R^2$ as each regressor is added. Since this value depends on the regressors already in the model, one needs to do this for every possible ord... | How to split r-squared between predictor variables in multiple regression? | I added the variance-decomposition tag to your question. Here is part of its tag wiki:
One common method is to add regressors to the model one by one and record the increase in $R^2$ as each regresso | How to split r-squared between predictor variables in multiple regression?
I added the variance-decomposition tag to your question. Here is part of its tag wiki:
One common method is to add regressors to the model one by one and record the increase in $R^2$ as each regressor is added. Since this value depends on the r... | How to split r-squared between predictor variables in multiple regression?
I added the variance-decomposition tag to your question. Here is part of its tag wiki:
One common method is to add regressors to the model one by one and record the increase in $R^2$ as each regresso |
11,510 | How to calculate a confidence interval for Spearman's rank correlation? | In a nutshell, a 95% confidence interval is given by
$$\tanh(\operatorname{atanh}r\pm1.96/\sqrt{n-3}),$$
where $r$ is the estimate of the correlation and $n$ is the sample size.
Explanation: The Fisher transformation is atanh. On the transformed scale, the sampling distribution of the estimate is approximately normal, ... | How to calculate a confidence interval for Spearman's rank correlation? | In a nutshell, a 95% confidence interval is given by
$$\tanh(\operatorname{atanh}r\pm1.96/\sqrt{n-3}),$$
where $r$ is the estimate of the correlation and $n$ is the sample size.
Explanation: The Fishe | How to calculate a confidence interval for Spearman's rank correlation?
In a nutshell, a 95% confidence interval is given by
$$\tanh(\operatorname{atanh}r\pm1.96/\sqrt{n-3}),$$
where $r$ is the estimate of the correlation and $n$ is the sample size.
Explanation: The Fisher transformation is atanh. On the transformed sc... | How to calculate a confidence interval for Spearman's rank correlation?
In a nutshell, a 95% confidence interval is given by
$$\tanh(\operatorname{atanh}r\pm1.96/\sqrt{n-3}),$$
where $r$ is the estimate of the correlation and $n$ is the sample size.
Explanation: The Fishe |
11,511 | How to calculate a confidence interval for Spearman's rank correlation? | Maybe some additional remarks about the comment of @chl
The Spearman correlation can be seen as a Pearson correlation of the ranks. Ranks clearly do not follow a normal distribution, with the consequence that the variance of the Fisher transformation ($\zeta$) is not well approximated by $(n-3)^{-1}$ especially at larg... | How to calculate a confidence interval for Spearman's rank correlation? | Maybe some additional remarks about the comment of @chl
The Spearman correlation can be seen as a Pearson correlation of the ranks. Ranks clearly do not follow a normal distribution, with the conseque | How to calculate a confidence interval for Spearman's rank correlation?
Maybe some additional remarks about the comment of @chl
The Spearman correlation can be seen as a Pearson correlation of the ranks. Ranks clearly do not follow a normal distribution, with the consequence that the variance of the Fisher transformati... | How to calculate a confidence interval for Spearman's rank correlation?
Maybe some additional remarks about the comment of @chl
The Spearman correlation can be seen as a Pearson correlation of the ranks. Ranks clearly do not follow a normal distribution, with the conseque |
11,512 | Probability of defeating a dragon in one turn rolling a 20 sided die | Your suggestion to solve a general version of the problem is spot on. Let's set this up.
The die has two special outcomes: "death," which terminates the process, and 0, which has no effect. We might as well remove the 0, creating a "truncated die" of 19 sides. Let the probability that the die shows up a numeric valu... | Probability of defeating a dragon in one turn rolling a 20 sided die | Your suggestion to solve a general version of the problem is spot on. Let's set this up.
The die has two special outcomes: "death," which terminates the process, and 0, which has no effect. We might | Probability of defeating a dragon in one turn rolling a 20 sided die
Your suggestion to solve a general version of the problem is spot on. Let's set this up.
The die has two special outcomes: "death," which terminates the process, and 0, which has no effect. We might as well remove the 0, creating a "truncated die" o... | Probability of defeating a dragon in one turn rolling a 20 sided die
Your suggestion to solve a general version of the problem is spot on. Let's set this up.
The die has two special outcomes: "death," which terminates the process, and 0, which has no effect. We might |
11,513 | Probability of defeating a dragon in one turn rolling a 20 sided die | I think the most understandable method to compute probabilities like these is to define a Markov chain that represents all of the possible states that the game can be in, with absorbing states that represent the death of either the player or the dragon.
A Markov chain is a set of states together with an associated prob... | Probability of defeating a dragon in one turn rolling a 20 sided die | I think the most understandable method to compute probabilities like these is to define a Markov chain that represents all of the possible states that the game can be in, with absorbing states that re | Probability of defeating a dragon in one turn rolling a 20 sided die
I think the most understandable method to compute probabilities like these is to define a Markov chain that represents all of the possible states that the game can be in, with absorbing states that represent the death of either the player or the drago... | Probability of defeating a dragon in one turn rolling a 20 sided die
I think the most understandable method to compute probabilities like these is to define a Markov chain that represents all of the possible states that the game can be in, with absorbing states that re |
11,514 | Probability of defeating a dragon in one turn rolling a 20 sided die | Here's an approach that uses ideas from Markov chains & generating functions.
Plan: We'll construct the recursion relation for the probabilities in question, and then apply techniques from linear algebra to solve it. (The nice feature of this approach is that its computational complexity is independent of how many heal... | Probability of defeating a dragon in one turn rolling a 20 sided die | Here's an approach that uses ideas from Markov chains & generating functions.
Plan: We'll construct the recursion relation for the probabilities in question, and then apply techniques from linear alge | Probability of defeating a dragon in one turn rolling a 20 sided die
Here's an approach that uses ideas from Markov chains & generating functions.
Plan: We'll construct the recursion relation for the probabilities in question, and then apply techniques from linear algebra to solve it. (The nice feature of this approach... | Probability of defeating a dragon in one turn rolling a 20 sided die
Here's an approach that uses ideas from Markov chains & generating functions.
Plan: We'll construct the recursion relation for the probabilities in question, and then apply techniques from linear alge |
11,515 | What's the formula for the Benjamini-Hochberg adjusted p-value? | The famous seminal Benjamini & Hochberg (1995) paper described the procedure for accepting/rejecting hypotheses based on adjusting the alpha levels. This procedure has a straightforward equivalent reformulation in terms of adjusted $p$-values, but it was not discussed in the original paper. According to Gordon Smyth, h... | What's the formula for the Benjamini-Hochberg adjusted p-value? | The famous seminal Benjamini & Hochberg (1995) paper described the procedure for accepting/rejecting hypotheses based on adjusting the alpha levels. This procedure has a straightforward equivalent ref | What's the formula for the Benjamini-Hochberg adjusted p-value?
The famous seminal Benjamini & Hochberg (1995) paper described the procedure for accepting/rejecting hypotheses based on adjusting the alpha levels. This procedure has a straightforward equivalent reformulation in terms of adjusted $p$-values, but it was n... | What's the formula for the Benjamini-Hochberg adjusted p-value?
The famous seminal Benjamini & Hochberg (1995) paper described the procedure for accepting/rejecting hypotheses based on adjusting the alpha levels. This procedure has a straightforward equivalent ref |
11,516 | What's the formula for the Benjamini-Hochberg adjusted p-value? | First a to the point answer. Consider that $p_0$ is the (single test) $p$ value associated with value $z_0$ of the test statistic. The Benjamini-Hochberg FDR is computed in two steps ($N_0$ = # pvalues $\le$ $p_0$, $N$ = # pvalues):
$\text{FDR }(p_0) = \frac{\quad p_0 \quad }{\frac{N_0}{N}}$
$\text{FDR }(p_i) = \min ... | What's the formula for the Benjamini-Hochberg adjusted p-value? | First a to the point answer. Consider that $p_0$ is the (single test) $p$ value associated with value $z_0$ of the test statistic. The Benjamini-Hochberg FDR is computed in two steps ($N_0$ = # pvalue | What's the formula for the Benjamini-Hochberg adjusted p-value?
First a to the point answer. Consider that $p_0$ is the (single test) $p$ value associated with value $z_0$ of the test statistic. The Benjamini-Hochberg FDR is computed in two steps ($N_0$ = # pvalues $\le$ $p_0$, $N$ = # pvalues):
$\text{FDR }(p_0) = \... | What's the formula for the Benjamini-Hochberg adjusted p-value?
First a to the point answer. Consider that $p_0$ is the (single test) $p$ value associated with value $z_0$ of the test statistic. The Benjamini-Hochberg FDR is computed in two steps ($N_0$ = # pvalue |
11,517 | Jackknife vs. LOOCV | In cross-validation you compute a statistic on the left-out sample(s). Most often, you predict the left-out sample(s) by a model built on the kept samples. In jackknifing, you compute a statistic from the kept samples only. | Jackknife vs. LOOCV | In cross-validation you compute a statistic on the left-out sample(s). Most often, you predict the left-out sample(s) by a model built on the kept samples. In jackknifing, you compute a statistic from | Jackknife vs. LOOCV
In cross-validation you compute a statistic on the left-out sample(s). Most often, you predict the left-out sample(s) by a model built on the kept samples. In jackknifing, you compute a statistic from the kept samples only. | Jackknife vs. LOOCV
In cross-validation you compute a statistic on the left-out sample(s). Most often, you predict the left-out sample(s) by a model built on the kept samples. In jackknifing, you compute a statistic from |
11,518 | Jackknife vs. LOOCV | Jackknife often refers to 2 related but different processes, both of which rely on a leave-one-out approach -- leading to this very confusion.
In one context, jackknife can be used to estimate population parameters and their standards errors. For example, to use a jackknife approach to estimate the slope and intercept... | Jackknife vs. LOOCV | Jackknife often refers to 2 related but different processes, both of which rely on a leave-one-out approach -- leading to this very confusion.
In one context, jackknife can be used to estimate populat | Jackknife vs. LOOCV
Jackknife often refers to 2 related but different processes, both of which rely on a leave-one-out approach -- leading to this very confusion.
In one context, jackknife can be used to estimate population parameters and their standards errors. For example, to use a jackknife approach to estimate the... | Jackknife vs. LOOCV
Jackknife often refers to 2 related but different processes, both of which rely on a leave-one-out approach -- leading to this very confusion.
In one context, jackknife can be used to estimate populat |
11,519 | How does neural network recognise images? | A major insight into how a neural network can learn to classify something as complex as image data given just examples and correct answers came to me while studying the work of Professor Kunihiko Fukushima on the neocognitrion in the 1980's. Instead of just showing his network a bunch of images, and using back-propaga... | How does neural network recognise images? | A major insight into how a neural network can learn to classify something as complex as image data given just examples and correct answers came to me while studying the work of Professor Kunihiko Fuku | How does neural network recognise images?
A major insight into how a neural network can learn to classify something as complex as image data given just examples and correct answers came to me while studying the work of Professor Kunihiko Fukushima on the neocognitrion in the 1980's. Instead of just showing his network... | How does neural network recognise images?
A major insight into how a neural network can learn to classify something as complex as image data given just examples and correct answers came to me while studying the work of Professor Kunihiko Fuku |
11,520 | How does neural network recognise images? | You may have heard it said that neural networks are "universal function approximators". In essence, the Cybenko theorem says that for any function mapping reals to reals, you can approximate it with a neural network with sigmoid activation functions. In fact, it turns out that neural networks allow you to compute any f... | How does neural network recognise images? | You may have heard it said that neural networks are "universal function approximators". In essence, the Cybenko theorem says that for any function mapping reals to reals, you can approximate it with a | How does neural network recognise images?
You may have heard it said that neural networks are "universal function approximators". In essence, the Cybenko theorem says that for any function mapping reals to reals, you can approximate it with a neural network with sigmoid activation functions. In fact, it turns out that ... | How does neural network recognise images?
You may have heard it said that neural networks are "universal function approximators". In essence, the Cybenko theorem says that for any function mapping reals to reals, you can approximate it with a |
11,521 | How does neural network recognise images? | That what confused you is
how it learns about what's in an image.
What is in an image is digitally represented by the values in the image's pixels. If you take an example of color in the image. The pixel may have three values, each for the three main colors - Red, Green and Blue (RGB). A pixel with (10,50,100) means... | How does neural network recognise images? | That what confused you is
how it learns about what's in an image.
What is in an image is digitally represented by the values in the image's pixels. If you take an example of color in the image. The | How does neural network recognise images?
That what confused you is
how it learns about what's in an image.
What is in an image is digitally represented by the values in the image's pixels. If you take an example of color in the image. The pixel may have three values, each for the three main colors - Red, Green and ... | How does neural network recognise images?
That what confused you is
how it learns about what's in an image.
What is in an image is digitally represented by the values in the image's pixels. If you take an example of color in the image. The |
11,522 | How does neural network recognise images? | All the machine learning problems are same. You have some train data, learn a model that represent this data and have ability to generalize this knowledge in that way you cluster,classify, learn with different algorithms.
In Image recognition you have again a set of images you want to to learn about.
These images fir... | How does neural network recognise images? | All the machine learning problems are same. You have some train data, learn a model that represent this data and have ability to generalize this knowledge in that way you cluster,classify, learn with | How does neural network recognise images?
All the machine learning problems are same. You have some train data, learn a model that represent this data and have ability to generalize this knowledge in that way you cluster,classify, learn with different algorithms.
In Image recognition you have again a set of images you ... | How does neural network recognise images?
All the machine learning problems are same. You have some train data, learn a model that represent this data and have ability to generalize this knowledge in that way you cluster,classify, learn with |
11,523 | How does neural network recognise images? | I would also like to mention very popular for image recognition convolutional neural networks.
Here is a link to simplified explanation of a CNN.
Briefly, in CNN image is first split into features, like edges, shapes, collections of shapes. Then these features are 'fed' into a 'regular' fully-connected multi-layer neur... | How does neural network recognise images? | I would also like to mention very popular for image recognition convolutional neural networks.
Here is a link to simplified explanation of a CNN.
Briefly, in CNN image is first split into features, li | How does neural network recognise images?
I would also like to mention very popular for image recognition convolutional neural networks.
Here is a link to simplified explanation of a CNN.
Briefly, in CNN image is first split into features, like edges, shapes, collections of shapes. Then these features are 'fed' into a ... | How does neural network recognise images?
I would also like to mention very popular for image recognition convolutional neural networks.
Here is a link to simplified explanation of a CNN.
Briefly, in CNN image is first split into features, li |
11,524 | How does neural network recognise images? | It's good to know ANN can create any function f(x) or f(x,y,z,..) or any multifunction for that matter. But it's also important to know that functions have limits in how they can classify data...there are more complex relations subsets of powersets of objects, which are important in classification and these are not de... | How does neural network recognise images? | It's good to know ANN can create any function f(x) or f(x,y,z,..) or any multifunction for that matter. But it's also important to know that functions have limits in how they can classify data...ther | How does neural network recognise images?
It's good to know ANN can create any function f(x) or f(x,y,z,..) or any multifunction for that matter. But it's also important to know that functions have limits in how they can classify data...there are more complex relations subsets of powersets of objects, which are import... | How does neural network recognise images?
It's good to know ANN can create any function f(x) or f(x,y,z,..) or any multifunction for that matter. But it's also important to know that functions have limits in how they can classify data...ther |
11,525 | How can I estimate coefficient standard errors when using ridge regression? | I think boostrap would the best option to obtain robust SEs. This was done in some applied work using shrinkage methods, e.g. Analysis of North American Rheumatoid Arthritis Consortium data using a penalized logistic regression approach (BMC Proceedings 2009).
There is also a nice paper from Casella on SE computation w... | How can I estimate coefficient standard errors when using ridge regression? | I think boostrap would the best option to obtain robust SEs. This was done in some applied work using shrinkage methods, e.g. Analysis of North American Rheumatoid Arthritis Consortium data using a pe | How can I estimate coefficient standard errors when using ridge regression?
I think boostrap would the best option to obtain robust SEs. This was done in some applied work using shrinkage methods, e.g. Analysis of North American Rheumatoid Arthritis Consortium data using a penalized logistic regression approach (BMC Pr... | How can I estimate coefficient standard errors when using ridge regression?
I think boostrap would the best option to obtain robust SEs. This was done in some applied work using shrinkage methods, e.g. Analysis of North American Rheumatoid Arthritis Consortium data using a pe |
11,526 | How can I estimate coefficient standard errors when using ridge regression? | Assuming that the data generating process follows the standard assumptions behind OLS the standard errors for ridge regression is given by:
$ \sigma^2 (A^T A + \Gamma^T \Gamma)^{-1} A^T A (A^T A + \Gamma^T \Gamma)^{-1}$
The notation above follows the wiki notation for ridge regression. Specifically,
$A$ is the covrai... | How can I estimate coefficient standard errors when using ridge regression? | Assuming that the data generating process follows the standard assumptions behind OLS the standard errors for ridge regression is given by:
$ \sigma^2 (A^T A + \Gamma^T \Gamma)^{-1} A^T A (A^T A + \Ga | How can I estimate coefficient standard errors when using ridge regression?
Assuming that the data generating process follows the standard assumptions behind OLS the standard errors for ridge regression is given by:
$ \sigma^2 (A^T A + \Gamma^T \Gamma)^{-1} A^T A (A^T A + \Gamma^T \Gamma)^{-1}$
The notation above fol... | How can I estimate coefficient standard errors when using ridge regression?
Assuming that the data generating process follows the standard assumptions behind OLS the standard errors for ridge regression is given by:
$ \sigma^2 (A^T A + \Gamma^T \Gamma)^{-1} A^T A (A^T A + \Ga |
11,527 | How can I estimate coefficient standard errors when using ridge regression? | Ridge regression is a subset of Tikhonov regularization (Tk) that normalizes the smoothing factors. The more general regularizing term $\Gamma ^T\Gamma$ is replaced in ridge regression by $\text{$\lambda $I}$, where $\text{I}$ is the identity matrix, and $\lambda $ is a Lagrange (i.e., constraint) multiplier, also com... | How can I estimate coefficient standard errors when using ridge regression? | Ridge regression is a subset of Tikhonov regularization (Tk) that normalizes the smoothing factors. The more general regularizing term $\Gamma ^T\Gamma$ is replaced in ridge regression by $\text{$\lam | How can I estimate coefficient standard errors when using ridge regression?
Ridge regression is a subset of Tikhonov regularization (Tk) that normalizes the smoothing factors. The more general regularizing term $\Gamma ^T\Gamma$ is replaced in ridge regression by $\text{$\lambda $I}$, where $\text{I}$ is the identity m... | How can I estimate coefficient standard errors when using ridge regression?
Ridge regression is a subset of Tikhonov regularization (Tk) that normalizes the smoothing factors. The more general regularizing term $\Gamma ^T\Gamma$ is replaced in ridge regression by $\text{$\lam |
11,528 | Should feature selection be performed only on training data (or all data)? | The procedure you are using will result in optimistically biased performance estimates, because you use the data from the test set used in steps 2 and 3 to decide which features used in step 1. Repeating the exercise reduces the variance of the performance estimate, not the bias, so the bias will not average out. To ... | Should feature selection be performed only on training data (or all data)? | The procedure you are using will result in optimistically biased performance estimates, because you use the data from the test set used in steps 2 and 3 to decide which features used in step 1. Repea | Should feature selection be performed only on training data (or all data)?
The procedure you are using will result in optimistically biased performance estimates, because you use the data from the test set used in steps 2 and 3 to decide which features used in step 1. Repeating the exercise reduces the variance of the... | Should feature selection be performed only on training data (or all data)?
The procedure you are using will result in optimistically biased performance estimates, because you use the data from the test set used in steps 2 and 3 to decide which features used in step 1. Repea |
11,529 | Should feature selection be performed only on training data (or all data)? | Just as an addendum to the answers here, I've got two links that really helped me understand why this isn't a good procedure:
http://nbviewer.jupyter.org/github/cs109/content/blob/master/lec_10_cross_val.ipynb
https://www.youtube.com/watch?v=S06JpVoNaA0
Edit: as requested, a brief explanation of the contents of the ... | Should feature selection be performed only on training data (or all data)? | Just as an addendum to the answers here, I've got two links that really helped me understand why this isn't a good procedure:
http://nbviewer.jupyter.org/github/cs109/content/blob/master/lec_10_cross | Should feature selection be performed only on training data (or all data)?
Just as an addendum to the answers here, I've got two links that really helped me understand why this isn't a good procedure:
http://nbviewer.jupyter.org/github/cs109/content/blob/master/lec_10_cross_val.ipynb
https://www.youtube.com/watch?v=S... | Should feature selection be performed only on training data (or all data)?
Just as an addendum to the answers here, I've got two links that really helped me understand why this isn't a good procedure:
http://nbviewer.jupyter.org/github/cs109/content/blob/master/lec_10_cross |
11,530 | Should feature selection be performed only on training data (or all data)? | The Efron-Gong "optimism" bootstrap is very good for this. The idea is to use all available data for developing the predictive model, and using all data for estimating the likely future performance of that same model. And your sample size is too small by a factor of 100 for any split-sample approaches to work.
To use... | Should feature selection be performed only on training data (or all data)? | The Efron-Gong "optimism" bootstrap is very good for this. The idea is to use all available data for developing the predictive model, and using all data for estimating the likely future performance o | Should feature selection be performed only on training data (or all data)?
The Efron-Gong "optimism" bootstrap is very good for this. The idea is to use all available data for developing the predictive model, and using all data for estimating the likely future performance of that same model. And your sample size is t... | Should feature selection be performed only on training data (or all data)?
The Efron-Gong "optimism" bootstrap is very good for this. The idea is to use all available data for developing the predictive model, and using all data for estimating the likely future performance o |
11,531 | How to get started with applying item response theory and what software to use? | As a good starter to IRT, I always recommend reading A visual guide to item response theory.
A survey of available software can be found on www.rasch.org.
From my experience, I found the Raschtest (and associated) Stata command(s) very handy in most cases where one is interested in fitting one-parameter model. For more... | How to get started with applying item response theory and what software to use? | As a good starter to IRT, I always recommend reading A visual guide to item response theory.
A survey of available software can be found on www.rasch.org.
From my experience, I found the Raschtest (an | How to get started with applying item response theory and what software to use?
As a good starter to IRT, I always recommend reading A visual guide to item response theory.
A survey of available software can be found on www.rasch.org.
From my experience, I found the Raschtest (and associated) Stata command(s) very hand... | How to get started with applying item response theory and what software to use?
As a good starter to IRT, I always recommend reading A visual guide to item response theory.
A survey of available software can be found on www.rasch.org.
From my experience, I found the Raschtest (an |
11,532 | How to get started with applying item response theory and what software to use? | To the first question, I don't have any information about jMetrick.
In applying IRT, (as with any other statistical procedure) the first step is to use it with as many different kinds of data as possible. There is a learning curve, but I believe that it is worth it.
One important feature of IRT is the differentiation b... | How to get started with applying item response theory and what software to use? | To the first question, I don't have any information about jMetrick.
In applying IRT, (as with any other statistical procedure) the first step is to use it with as many different kinds of data as possi | How to get started with applying item response theory and what software to use?
To the first question, I don't have any information about jMetrick.
In applying IRT, (as with any other statistical procedure) the first step is to use it with as many different kinds of data as possible. There is a learning curve, but I be... | How to get started with applying item response theory and what software to use?
To the first question, I don't have any information about jMetrick.
In applying IRT, (as with any other statistical procedure) the first step is to use it with as many different kinds of data as possi |
11,533 | How to get started with applying item response theory and what software to use? | jMetrik is more powerful than you may think. It is designed for operational work where researchers need multiple procedures in a single unified framework. Currently you can estimate IRT parameters for the Rasch, partial credit and rating scale models. It also allows for IRT scale linking via the Stocking-Lord, Haebara ... | How to get started with applying item response theory and what software to use? | jMetrik is more powerful than you may think. It is designed for operational work where researchers need multiple procedures in a single unified framework. Currently you can estimate IRT parameters for | How to get started with applying item response theory and what software to use?
jMetrik is more powerful than you may think. It is designed for operational work where researchers need multiple procedures in a single unified framework. Currently you can estimate IRT parameters for the Rasch, partial credit and rating sc... | How to get started with applying item response theory and what software to use?
jMetrik is more powerful than you may think. It is designed for operational work where researchers need multiple procedures in a single unified framework. Currently you can estimate IRT parameters for |
11,534 | How to get started with applying item response theory and what software to use? | You have quite a broad list of questions here, but quite relevant for many researchers!
I highly recommend you go forward in IRT, but only if your situation meets the requirements. For example, it fits well with the types of tests you use, and probably most importantly that you have the necessary sample sizes. For di... | How to get started with applying item response theory and what software to use? | You have quite a broad list of questions here, but quite relevant for many researchers!
I highly recommend you go forward in IRT, but only if your situation meets the requirements. For example, it fi | How to get started with applying item response theory and what software to use?
You have quite a broad list of questions here, but quite relevant for many researchers!
I highly recommend you go forward in IRT, but only if your situation meets the requirements. For example, it fits well with the types of tests you use,... | How to get started with applying item response theory and what software to use?
You have quite a broad list of questions here, but quite relevant for many researchers!
I highly recommend you go forward in IRT, but only if your situation meets the requirements. For example, it fi |
11,535 | How to get started with applying item response theory and what software to use? | In the mean time there has published a new book by Frank Baker, Baker Frank B. , Seock-Ho Kim. The Basics of Item Response Theory Using R. Springer International Publishing (2017). It does not make use of R packages but offers snippets.
A (crowded) list of R packages for IRT with succinct description is available on CR... | How to get started with applying item response theory and what software to use? | In the mean time there has published a new book by Frank Baker, Baker Frank B. , Seock-Ho Kim. The Basics of Item Response Theory Using R. Springer International Publishing (2017). It does not make us | How to get started with applying item response theory and what software to use?
In the mean time there has published a new book by Frank Baker, Baker Frank B. , Seock-Ho Kim. The Basics of Item Response Theory Using R. Springer International Publishing (2017). It does not make use of R packages but offers snippets.
A (... | How to get started with applying item response theory and what software to use?
In the mean time there has published a new book by Frank Baker, Baker Frank B. , Seock-Ho Kim. The Basics of Item Response Theory Using R. Springer International Publishing (2017). It does not make us |
11,536 | What could be the reason for using square root transformation on data? | In general, parametric regression / GLM assume that the relationship between the $Y$ variable and each $X$ variable is linear, that the residuals once you've fitted the model follow a normal distribution and that the size of the residuals stays about the same all the way along your fitted line(s). When your data don't... | What could be the reason for using square root transformation on data? | In general, parametric regression / GLM assume that the relationship between the $Y$ variable and each $X$ variable is linear, that the residuals once you've fitted the model follow a normal distribut | What could be the reason for using square root transformation on data?
In general, parametric regression / GLM assume that the relationship between the $Y$ variable and each $X$ variable is linear, that the residuals once you've fitted the model follow a normal distribution and that the size of the residuals stays abou... | What could be the reason for using square root transformation on data?
In general, parametric regression / GLM assume that the relationship between the $Y$ variable and each $X$ variable is linear, that the residuals once you've fitted the model follow a normal distribut |
11,537 | What could be the reason for using square root transformation on data? | The square-root transformation is just a special case of Box-Cox power transformation (a nice overview by Pengfi Li, could be useful reading and is found here), with $\lambda = 0.5$ and omitting some centering.
The aim of the Box-Cox transformations is to ensure the usual
assumptions for Linear Model hold. That is,... | What could be the reason for using square root transformation on data? | The square-root transformation is just a special case of Box-Cox power transformation (a nice overview by Pengfi Li, could be useful reading and is found here), with $\lambda = 0.5$ and omitting some | What could be the reason for using square root transformation on data?
The square-root transformation is just a special case of Box-Cox power transformation (a nice overview by Pengfi Li, could be useful reading and is found here), with $\lambda = 0.5$ and omitting some centering.
The aim of the Box-Cox transformatio... | What could be the reason for using square root transformation on data?
The square-root transformation is just a special case of Box-Cox power transformation (a nice overview by Pengfi Li, could be useful reading and is found here), with $\lambda = 0.5$ and omitting some |
11,538 | What could be the reason for using square root transformation on data? | When the variable follows a Poisson distribution, the results of the square root transform will be much closer to Gaussian. | What could be the reason for using square root transformation on data? | When the variable follows a Poisson distribution, the results of the square root transform will be much closer to Gaussian. | What could be the reason for using square root transformation on data?
When the variable follows a Poisson distribution, the results of the square root transform will be much closer to Gaussian. | What could be the reason for using square root transformation on data?
When the variable follows a Poisson distribution, the results of the square root transform will be much closer to Gaussian. |
11,539 | What could be the reason for using square root transformation on data? | Taking the square root is sometimes advocated to make a non-normal variable appear like a normal variable in regression problems. The logarithm is another common possible transformation. | What could be the reason for using square root transformation on data? | Taking the square root is sometimes advocated to make a non-normal variable appear like a normal variable in regression problems. The logarithm is another common possible transformation. | What could be the reason for using square root transformation on data?
Taking the square root is sometimes advocated to make a non-normal variable appear like a normal variable in regression problems. The logarithm is another common possible transformation. | What could be the reason for using square root transformation on data?
Taking the square root is sometimes advocated to make a non-normal variable appear like a normal variable in regression problems. The logarithm is another common possible transformation. |
11,540 | What could be the reason for using square root transformation on data? | Distance matrix calculated with Bray-Curtis are usually not metric for some data, giving rise to negative eigenvalues. One of the solutions to overcome this problem is to transform (logarithmic, Square root or double Square root) it. | What could be the reason for using square root transformation on data? | Distance matrix calculated with Bray-Curtis are usually not metric for some data, giving rise to negative eigenvalues. One of the solutions to overcome this problem is to transform (logarithmic, Squar | What could be the reason for using square root transformation on data?
Distance matrix calculated with Bray-Curtis are usually not metric for some data, giving rise to negative eigenvalues. One of the solutions to overcome this problem is to transform (logarithmic, Square root or double Square root) it. | What could be the reason for using square root transformation on data?
Distance matrix calculated with Bray-Curtis are usually not metric for some data, giving rise to negative eigenvalues. One of the solutions to overcome this problem is to transform (logarithmic, Squar |
11,541 | difference between conditional probability and bayes rule | OK, now that you have updated your question to include the two formulas:
$$P(A\mid B) = \frac{P(A\cap B)}{P(B)} ~~ \text{provided that }
P(B) > 0, \tag{1}$$
is the definition of the conditional probability of $A$ given that
$B$ occurred. Similarly,
$$P(B\mid A) = \frac{P(B\cap A)}{P(A)} = \frac{P(A\cap B)}{P(A)} ~~ ... | difference between conditional probability and bayes rule | OK, now that you have updated your question to include the two formulas:
$$P(A\mid B) = \frac{P(A\cap B)}{P(B)} ~~ \text{provided that }
P(B) > 0, \tag{1}$$
is the definition of the conditional proba | difference between conditional probability and bayes rule
OK, now that you have updated your question to include the two formulas:
$$P(A\mid B) = \frac{P(A\cap B)}{P(B)} ~~ \text{provided that }
P(B) > 0, \tag{1}$$
is the definition of the conditional probability of $A$ given that
$B$ occurred. Similarly,
$$P(B\mid A... | difference between conditional probability and bayes rule
OK, now that you have updated your question to include the two formulas:
$$P(A\mid B) = \frac{P(A\cap B)}{P(B)} ~~ \text{provided that }
P(B) > 0, \tag{1}$$
is the definition of the conditional proba |
11,542 | difference between conditional probability and bayes rule | One way to intuitively think of Bayes' theorem is that when any one of these is easy to calculate
$$P(A∣B) ~~ \text{or } P(B∣A)$$
we can calculate the other one even though the other one seems to be bit hard at first
Consider an example,
Here $$P(A∣B)$$ is say I have a curtain and I told you there is an animal behind ... | difference between conditional probability and bayes rule | One way to intuitively think of Bayes' theorem is that when any one of these is easy to calculate
$$P(A∣B) ~~ \text{or } P(B∣A)$$
we can calculate the other one even though the other one seems to be b | difference between conditional probability and bayes rule
One way to intuitively think of Bayes' theorem is that when any one of these is easy to calculate
$$P(A∣B) ~~ \text{or } P(B∣A)$$
we can calculate the other one even though the other one seems to be bit hard at first
Consider an example,
Here $$P(A∣B)$$ is say ... | difference between conditional probability and bayes rule
One way to intuitively think of Bayes' theorem is that when any one of these is easy to calculate
$$P(A∣B) ~~ \text{or } P(B∣A)$$
we can calculate the other one even though the other one seems to be b |
11,543 | difference between conditional probability and bayes rule | While converting P(A|B) to P(B|A) might be helpful in probability problems, we should take care not to imply causality. A large number of people with umbrellas (A) might indicate a high probability of rain (B), and rain (B) may equally indicate a high probability of umbrellas (A). We might be able to argue that the ra... | difference between conditional probability and bayes rule | While converting P(A|B) to P(B|A) might be helpful in probability problems, we should take care not to imply causality. A large number of people with umbrellas (A) might indicate a high probability of | difference between conditional probability and bayes rule
While converting P(A|B) to P(B|A) might be helpful in probability problems, we should take care not to imply causality. A large number of people with umbrellas (A) might indicate a high probability of rain (B), and rain (B) may equally indicate a high probabilit... | difference between conditional probability and bayes rule
While converting P(A|B) to P(B|A) might be helpful in probability problems, we should take care not to imply causality. A large number of people with umbrellas (A) might indicate a high probability of |
11,544 | How does `predict.randomForest` estimate class probabilities? | It's just the proportion of votes of the trees in the ensemble.
library(randomForest)
rf = randomForest(Species~., data = iris, norm.votes = TRUE, proximity = TRUE)
p1 = predict(rf, iris, type = "prob")
p2 = predict(rf, iris, type = "vote", norm.votes = TRUE)
identical(p1,p2)
#[1] TRUE
Alternatively, if you multipl... | How does `predict.randomForest` estimate class probabilities? | It's just the proportion of votes of the trees in the ensemble.
library(randomForest)
rf = randomForest(Species~., data = iris, norm.votes = TRUE, proximity = TRUE)
p1 = predict(rf, iris, type = "pro | How does `predict.randomForest` estimate class probabilities?
It's just the proportion of votes of the trees in the ensemble.
library(randomForest)
rf = randomForest(Species~., data = iris, norm.votes = TRUE, proximity = TRUE)
p1 = predict(rf, iris, type = "prob")
p2 = predict(rf, iris, type = "vote", norm.votes = TRU... | How does `predict.randomForest` estimate class probabilities?
It's just the proportion of votes of the trees in the ensemble.
library(randomForest)
rf = randomForest(Species~., data = iris, norm.votes = TRUE, proximity = TRUE)
p1 = predict(rf, iris, type = "pro |
11,545 | How does `predict.randomForest` estimate class probabilities? | The Malley (2012) is available here: http://dx.doi.org/10.3414%2FME00-01-0052. A full reference is in the references part in the ranger documentation.
In short, each tree predicts class probabilities and these probabilities are averaged for the forest prediction. For two classes, this is equivalent to a regression for... | How does `predict.randomForest` estimate class probabilities? | The Malley (2012) is available here: http://dx.doi.org/10.3414%2FME00-01-0052. A full reference is in the references part in the ranger documentation.
In short, each tree predicts class probabilities | How does `predict.randomForest` estimate class probabilities?
The Malley (2012) is available here: http://dx.doi.org/10.3414%2FME00-01-0052. A full reference is in the references part in the ranger documentation.
In short, each tree predicts class probabilities and these probabilities are averaged for the forest predi... | How does `predict.randomForest` estimate class probabilities?
The Malley (2012) is available here: http://dx.doi.org/10.3414%2FME00-01-0052. A full reference is in the references part in the ranger documentation.
In short, each tree predicts class probabilities |
11,546 | How does `predict.randomForest` estimate class probabilities? | If you want Out-Of-Bag probability estimates, you only can do it in randomForest package in R using model$votes. The other probability estimates are not OOB. | How does `predict.randomForest` estimate class probabilities? | If you want Out-Of-Bag probability estimates, you only can do it in randomForest package in R using model$votes. The other probability estimates are not OOB. | How does `predict.randomForest` estimate class probabilities?
If you want Out-Of-Bag probability estimates, you only can do it in randomForest package in R using model$votes. The other probability estimates are not OOB. | How does `predict.randomForest` estimate class probabilities?
If you want Out-Of-Bag probability estimates, you only can do it in randomForest package in R using model$votes. The other probability estimates are not OOB. |
11,547 | Why is the rank of covariance matrix at most $n-1$? | The unbiased estimator of the sample covariance matrix given $n$ data points $\newcommand{\x}{\mathbf x}\x_i \in \mathbb R^d$ is $$\mathbf C = \frac{1}{n-1}\sum_{i=1}^n (\x_i - \bar \x)(\x_i - \bar \x)^\top,$$ where $\bar \x = \sum \x_i /n$ is the average over all points. Let us denote $(\x_i-\bar \x)$ as $\newcommand{... | Why is the rank of covariance matrix at most $n-1$? | The unbiased estimator of the sample covariance matrix given $n$ data points $\newcommand{\x}{\mathbf x}\x_i \in \mathbb R^d$ is $$\mathbf C = \frac{1}{n-1}\sum_{i=1}^n (\x_i - \bar \x)(\x_i - \bar \x | Why is the rank of covariance matrix at most $n-1$?
The unbiased estimator of the sample covariance matrix given $n$ data points $\newcommand{\x}{\mathbf x}\x_i \in \mathbb R^d$ is $$\mathbf C = \frac{1}{n-1}\sum_{i=1}^n (\x_i - \bar \x)(\x_i - \bar \x)^\top,$$ where $\bar \x = \sum \x_i /n$ is the average over all poi... | Why is the rank of covariance matrix at most $n-1$?
The unbiased estimator of the sample covariance matrix given $n$ data points $\newcommand{\x}{\mathbf x}\x_i \in \mathbb R^d$ is $$\mathbf C = \frac{1}{n-1}\sum_{i=1}^n (\x_i - \bar \x)(\x_i - \bar \x |
11,548 | Why is the rank of covariance matrix at most $n-1$? | A bit shorter, I believe, explanation goes like this:
Let us define matrix $n$ x $m$ matrix $x$ of sample data points where
$n$ is a number of variables and $m$ is a number of samples for each variable. Let us assume that none of the variables are linearly dependent.
The rank of $x$ is $\min(n,m)$.
Let us define matrix... | Why is the rank of covariance matrix at most $n-1$? | A bit shorter, I believe, explanation goes like this:
Let us define matrix $n$ x $m$ matrix $x$ of sample data points where
$n$ is a number of variables and $m$ is a number of samples for each variabl | Why is the rank of covariance matrix at most $n-1$?
A bit shorter, I believe, explanation goes like this:
Let us define matrix $n$ x $m$ matrix $x$ of sample data points where
$n$ is a number of variables and $m$ is a number of samples for each variable. Let us assume that none of the variables are linearly dependent.
... | Why is the rank of covariance matrix at most $n-1$?
A bit shorter, I believe, explanation goes like this:
Let us define matrix $n$ x $m$ matrix $x$ of sample data points where
$n$ is a number of variables and $m$ is a number of samples for each variabl |
11,549 | Why is the rank of covariance matrix at most $n-1$? | For the same reason that you need at least two observations to estimate the variance of a single random variable. | Why is the rank of covariance matrix at most $n-1$? | For the same reason that you need at least two observations to estimate the variance of a single random variable. | Why is the rank of covariance matrix at most $n-1$?
For the same reason that you need at least two observations to estimate the variance of a single random variable. | Why is the rank of covariance matrix at most $n-1$?
For the same reason that you need at least two observations to estimate the variance of a single random variable. |
11,550 | How to apply binomial GLMM (glmer) to percentages rather than yes-no counts? | In order to use a vector of proportions as the response variable with glmer(., family = binomial), you need to set the number of trials that led to each proportion using the weights argument. For example, using the cbpp data from the lme4 package:
glmer(incidence / size ~ period + (1 | herd), weights = size,
family... | How to apply binomial GLMM (glmer) to percentages rather than yes-no counts? | In order to use a vector of proportions as the response variable with glmer(., family = binomial), you need to set the number of trials that led to each proportion using the weights argument. For exa | How to apply binomial GLMM (glmer) to percentages rather than yes-no counts?
In order to use a vector of proportions as the response variable with glmer(., family = binomial), you need to set the number of trials that led to each proportion using the weights argument. For example, using the cbpp data from the lme4 pac... | How to apply binomial GLMM (glmer) to percentages rather than yes-no counts?
In order to use a vector of proportions as the response variable with glmer(., family = binomial), you need to set the number of trials that led to each proportion using the weights argument. For exa |
11,551 | How to apply binomial GLMM (glmer) to percentages rather than yes-no counts? | If your response is a proportion, percentage or anything similiar that can only take values in $(0,1)$ you would typically use beta regression, not the binomial one. | How to apply binomial GLMM (glmer) to percentages rather than yes-no counts? | If your response is a proportion, percentage or anything similiar that can only take values in $(0,1)$ you would typically use beta regression, not the binomial one. | How to apply binomial GLMM (glmer) to percentages rather than yes-no counts?
If your response is a proportion, percentage or anything similiar that can only take values in $(0,1)$ you would typically use beta regression, not the binomial one. | How to apply binomial GLMM (glmer) to percentages rather than yes-no counts?
If your response is a proportion, percentage or anything similiar that can only take values in $(0,1)$ you would typically use beta regression, not the binomial one. |
11,552 | What is the difference between policy-based, on-policy, value-based, off-policy, model-free and model-based? | Here is a quick summary on the Reinforcement Learning taxonomy:
On-policy vs. Off-Policy
This division is based on whether you update your $Q$ values based on actions undertaken according to your current policy or not. Let's say your current policy is a completely random policy. You're in state $s$ and make an action $... | What is the difference between policy-based, on-policy, value-based, off-policy, model-free and mode | Here is a quick summary on the Reinforcement Learning taxonomy:
On-policy vs. Off-Policy
This division is based on whether you update your $Q$ values based on actions undertaken according to your curr | What is the difference between policy-based, on-policy, value-based, off-policy, model-free and model-based?
Here is a quick summary on the Reinforcement Learning taxonomy:
On-policy vs. Off-Policy
This division is based on whether you update your $Q$ values based on actions undertaken according to your current policy ... | What is the difference between policy-based, on-policy, value-based, off-policy, model-free and mode
Here is a quick summary on the Reinforcement Learning taxonomy:
On-policy vs. Off-Policy
This division is based on whether you update your $Q$ values based on actions undertaken according to your curr |
11,553 | What is the difference between policy-based, on-policy, value-based, off-policy, model-free and model-based? | You can have an on-policy RL algorithm that is value-based. An example of such algorithm is SARSA, so not all value-based algorithms are off-policy. A value-based algorithm is just an algorithm that estimates the policy by first estimating the associated value function.
To understand the difference between on-policy an... | What is the difference between policy-based, on-policy, value-based, off-policy, model-free and mode | You can have an on-policy RL algorithm that is value-based. An example of such algorithm is SARSA, so not all value-based algorithms are off-policy. A value-based algorithm is just an algorithm that e | What is the difference between policy-based, on-policy, value-based, off-policy, model-free and model-based?
You can have an on-policy RL algorithm that is value-based. An example of such algorithm is SARSA, so not all value-based algorithms are off-policy. A value-based algorithm is just an algorithm that estimates th... | What is the difference between policy-based, on-policy, value-based, off-policy, model-free and mode
You can have an on-policy RL algorithm that is value-based. An example of such algorithm is SARSA, so not all value-based algorithms are off-policy. A value-based algorithm is just an algorithm that e |
11,554 | What does a bottleneck layer mean in neural networks? | A bottleneck layer is a layer that contains few nodes compared to the previous layers. It can be used to obtain a representation of the input with reduced dimensionality. An example of this is the use of autoencoders with bottleneck layers for nonlinear dimensionality reduction.
My understanding of the quote is that pr... | What does a bottleneck layer mean in neural networks? | A bottleneck layer is a layer that contains few nodes compared to the previous layers. It can be used to obtain a representation of the input with reduced dimensionality. An example of this is the use | What does a bottleneck layer mean in neural networks?
A bottleneck layer is a layer that contains few nodes compared to the previous layers. It can be used to obtain a representation of the input with reduced dimensionality. An example of this is the use of autoencoders with bottleneck layers for nonlinear dimensionali... | What does a bottleneck layer mean in neural networks?
A bottleneck layer is a layer that contains few nodes compared to the previous layers. It can be used to obtain a representation of the input with reduced dimensionality. An example of this is the use |
11,555 | What does a bottleneck layer mean in neural networks? | Adding to the previous answer:
Bottlenecks can also be understood as a design pattern, consisting of three convolution layers, introduced by the ResNet paper.
Deeper Bottleneck Architectures. Next, we describe our deeper nets for ImageNet. Because of concerns on the training time that we can afford, we modify the buil... | What does a bottleneck layer mean in neural networks? | Adding to the previous answer:
Bottlenecks can also be understood as a design pattern, consisting of three convolution layers, introduced by the ResNet paper.
Deeper Bottleneck Architectures. Next, w | What does a bottleneck layer mean in neural networks?
Adding to the previous answer:
Bottlenecks can also be understood as a design pattern, consisting of three convolution layers, introduced by the ResNet paper.
Deeper Bottleneck Architectures. Next, we describe our deeper nets for ImageNet. Because of concerns on th... | What does a bottleneck layer mean in neural networks?
Adding to the previous answer:
Bottlenecks can also be understood as a design pattern, consisting of three convolution layers, introduced by the ResNet paper.
Deeper Bottleneck Architectures. Next, w |
11,556 | Such thing as a weighted correlation? | Formula for weighted Pearson correlation can be easily found on the web, StackOverflow, and Wikipedia and is implemented in several R packages e.g. psych, or weights and in Python's statsmodels package. It is calculated like regular correlation but with using weighted means,
$$ m_X = \frac{\sum_i w_i x_i}{\sum_i w_i}, ... | Such thing as a weighted correlation? | Formula for weighted Pearson correlation can be easily found on the web, StackOverflow, and Wikipedia and is implemented in several R packages e.g. psych, or weights and in Python's statsmodels packag | Such thing as a weighted correlation?
Formula for weighted Pearson correlation can be easily found on the web, StackOverflow, and Wikipedia and is implemented in several R packages e.g. psych, or weights and in Python's statsmodels package. It is calculated like regular correlation but with using weighted means,
$$ m_X... | Such thing as a weighted correlation?
Formula for weighted Pearson correlation can be easily found on the web, StackOverflow, and Wikipedia and is implemented in several R packages e.g. psych, or weights and in Python's statsmodels packag |
11,557 | How can I prove that the cumulative distribution function is right continuous? | To prove the right continuity of the distribution function you have to use the continuity from above of $P$, which you probably proved in one of your probability courses.
Lemma. If a sequence of events $\{A_n\}_{n\geq 1}$ is decreasing, in the sense that $A_n\supset A_{n+1}$ for every $n\geq 1$, then $P(A_n)\downarrow ... | How can I prove that the cumulative distribution function is right continuous? | To prove the right continuity of the distribution function you have to use the continuity from above of $P$, which you probably proved in one of your probability courses.
Lemma. If a sequence of event | How can I prove that the cumulative distribution function is right continuous?
To prove the right continuity of the distribution function you have to use the continuity from above of $P$, which you probably proved in one of your probability courses.
Lemma. If a sequence of events $\{A_n\}_{n\geq 1}$ is decreasing, in t... | How can I prove that the cumulative distribution function is right continuous?
To prove the right continuity of the distribution function you have to use the continuity from above of $P$, which you probably proved in one of your probability courses.
Lemma. If a sequence of event |
11,558 | How does boosting work? | In plain English: If your classifier misclassifies some data, train another copy of it mainly on this misclassified part with hope that it will discover something subtle. And then, as usual, iterate. On the way there are some voting schemes that allow to combine all those classifiers' predictions in sensible way.
Becau... | How does boosting work? | In plain English: If your classifier misclassifies some data, train another copy of it mainly on this misclassified part with hope that it will discover something subtle. And then, as usual, iterate. | How does boosting work?
In plain English: If your classifier misclassifies some data, train another copy of it mainly on this misclassified part with hope that it will discover something subtle. And then, as usual, iterate. On the way there are some voting schemes that allow to combine all those classifiers' prediction... | How does boosting work?
In plain English: If your classifier misclassifies some data, train another copy of it mainly on this misclassified part with hope that it will discover something subtle. And then, as usual, iterate. |
11,559 | How does boosting work? | Boosting employs shrinkage through the learning rate parameter, which, coupled with k-fold cross validation, "out-of-bag" (OOB) predictions or independent test set, determine the number of trees one should keep in the ensemble.
We want a model that learns slowly, hence there is a trade-off in terms of the complexity of... | How does boosting work? | Boosting employs shrinkage through the learning rate parameter, which, coupled with k-fold cross validation, "out-of-bag" (OOB) predictions or independent test set, determine the number of trees one s | How does boosting work?
Boosting employs shrinkage through the learning rate parameter, which, coupled with k-fold cross validation, "out-of-bag" (OOB) predictions or independent test set, determine the number of trees one should keep in the ensemble.
We want a model that learns slowly, hence there is a trade-off in te... | How does boosting work?
Boosting employs shrinkage through the learning rate parameter, which, coupled with k-fold cross validation, "out-of-bag" (OOB) predictions or independent test set, determine the number of trees one s |
11,560 | What is a distribution over functions? | The concept is a bit more abstract than a usual distribution. The problem is that we are used to the concept of a distribution over $\mathbb{R}$, typically shown as a line, and then expand it to a surface $\mathbb{R}^2$, and so on to distributions over $\mathbb{R}^n$. But the space of functions cannot be represented as... | What is a distribution over functions? | The concept is a bit more abstract than a usual distribution. The problem is that we are used to the concept of a distribution over $\mathbb{R}$, typically shown as a line, and then expand it to a sur | What is a distribution over functions?
The concept is a bit more abstract than a usual distribution. The problem is that we are used to the concept of a distribution over $\mathbb{R}$, typically shown as a line, and then expand it to a surface $\mathbb{R}^2$, and so on to distributions over $\mathbb{R}^n$. But the spac... | What is a distribution over functions?
The concept is a bit more abstract than a usual distribution. The problem is that we are used to the concept of a distribution over $\mathbb{R}$, typically shown as a line, and then expand it to a sur |
11,561 | What is a distribution over functions? | Your question has already been asked, and beautifully answered, on the Mathematics SE site:
https://math.stackexchange.com/questions/2297424/extending-a-distribution-over-samples-to-a-distribution-over-functions
It sounds like you're not familiar with the concepts of Gaussian measures on infinite-dimensional spaces, li... | What is a distribution over functions? | Your question has already been asked, and beautifully answered, on the Mathematics SE site:
https://math.stackexchange.com/questions/2297424/extending-a-distribution-over-samples-to-a-distribution-ove | What is a distribution over functions?
Your question has already been asked, and beautifully answered, on the Mathematics SE site:
https://math.stackexchange.com/questions/2297424/extending-a-distribution-over-samples-to-a-distribution-over-functions
It sounds like you're not familiar with the concepts of Gaussian meas... | What is a distribution over functions?
Your question has already been asked, and beautifully answered, on the Mathematics SE site:
https://math.stackexchange.com/questions/2297424/extending-a-distribution-over-samples-to-a-distribution-ove |
11,562 | How do ABC and MCMC differ in their applications? | Some additional comments on top of Björn's answer:
ABC was first introduced by Rubin (1984) as an explanation of the nature of Bayesian inference, rather than for computational purposes. In this paper he explained how the sampling distribution and the prior distribution interact to produce the posterior distribution.
... | How do ABC and MCMC differ in their applications? | Some additional comments on top of Björn's answer:
ABC was first introduced by Rubin (1984) as an explanation of the nature of Bayesian inference, rather than for computational purposes. In this pape | How do ABC and MCMC differ in their applications?
Some additional comments on top of Björn's answer:
ABC was first introduced by Rubin (1984) as an explanation of the nature of Bayesian inference, rather than for computational purposes. In this paper he explained how the sampling distribution and the prior distributio... | How do ABC and MCMC differ in their applications?
Some additional comments on top of Björn's answer:
ABC was first introduced by Rubin (1984) as an explanation of the nature of Bayesian inference, rather than for computational purposes. In this pape |
11,563 | How do ABC and MCMC differ in their applications? | The difference is that with ABC you do not need an analytic expression for $P(x|\theta)$ and instead approximate it by simulating data and seeing for which values of $\theta$ simulated data most often (approximately) matches the observed data (with proposed values e.g. drawn randomly from the prior). For simple cases, ... | How do ABC and MCMC differ in their applications? | The difference is that with ABC you do not need an analytic expression for $P(x|\theta)$ and instead approximate it by simulating data and seeing for which values of $\theta$ simulated data most often | How do ABC and MCMC differ in their applications?
The difference is that with ABC you do not need an analytic expression for $P(x|\theta)$ and instead approximate it by simulating data and seeing for which values of $\theta$ simulated data most often (approximately) matches the observed data (with proposed values e.g. ... | How do ABC and MCMC differ in their applications?
The difference is that with ABC you do not need an analytic expression for $P(x|\theta)$ and instead approximate it by simulating data and seeing for which values of $\theta$ simulated data most often |
11,564 | Methods to compute factor scores, and what is the "score coefficient" matrix in PCA or factor analysis? | Methods of computation of factor/component scores
After a series of comments I decided finally to issue an answer (based on the comments and more). It is about computing component scores in PCA and factor scores in factor analysis.
Factor/component scores are given by $\bf \hat{F}=XB$, where $\bf X$ are the analyzed va... | Methods to compute factor scores, and what is the "score coefficient" matrix in PCA or factor analys | Methods of computation of factor/component scores
After a series of comments I decided finally to issue an answer (based on the comments and more). It is about computing component scores in PCA and fa | Methods to compute factor scores, and what is the "score coefficient" matrix in PCA or factor analysis?
Methods of computation of factor/component scores
After a series of comments I decided finally to issue an answer (based on the comments and more). It is about computing component scores in PCA and factor scores in f... | Methods to compute factor scores, and what is the "score coefficient" matrix in PCA or factor analys
Methods of computation of factor/component scores
After a series of comments I decided finally to issue an answer (based on the comments and more). It is about computing component scores in PCA and fa |
11,565 | Stouffer's Z-score method: what if we sum $z^2$ instead of $z$? | One flaw that jumps out is Stouffer's method can detect systematic shifts in the $z_i$, which is what one would usually expect to happen when one alternative is consistently true, whereas the chi-squared method would appear to have less power to do so. A quick simulation shows this to be the case; the chi-squared metho... | Stouffer's Z-score method: what if we sum $z^2$ instead of $z$? | One flaw that jumps out is Stouffer's method can detect systematic shifts in the $z_i$, which is what one would usually expect to happen when one alternative is consistently true, whereas the chi-squa | Stouffer's Z-score method: what if we sum $z^2$ instead of $z$?
One flaw that jumps out is Stouffer's method can detect systematic shifts in the $z_i$, which is what one would usually expect to happen when one alternative is consistently true, whereas the chi-squared method would appear to have less power to do so. A q... | Stouffer's Z-score method: what if we sum $z^2$ instead of $z$?
One flaw that jumps out is Stouffer's method can detect systematic shifts in the $z_i$, which is what one would usually expect to happen when one alternative is consistently true, whereas the chi-squa |
11,566 | Stouffer's Z-score method: what if we sum $z^2$ instead of $z$? | One general way to gain insight into test statistics is to
derive the (usually implicit) underlying assumptions that would lead
that test statistic to be most powerful. For this particular case a student and I
have recently done this:
http://arxiv.org/abs/1111.1210v2
(a revised version is to appear in Annals of Applie... | Stouffer's Z-score method: what if we sum $z^2$ instead of $z$? | One general way to gain insight into test statistics is to
derive the (usually implicit) underlying assumptions that would lead
that test statistic to be most powerful. For this particular case a stud | Stouffer's Z-score method: what if we sum $z^2$ instead of $z$?
One general way to gain insight into test statistics is to
derive the (usually implicit) underlying assumptions that would lead
that test statistic to be most powerful. For this particular case a student and I
have recently done this:
http://arxiv.org/abs... | Stouffer's Z-score method: what if we sum $z^2$ instead of $z$?
One general way to gain insight into test statistics is to
derive the (usually implicit) underlying assumptions that would lead
that test statistic to be most powerful. For this particular case a stud |
11,567 | Stouffer's Z-score method: what if we sum $z^2$ instead of $z$? | Slightly o/t: one of the issues with both these approaches is the loss of power due to the degrees of freedom (N for stouffer's; 2N for Fisher's). There have been better meta-analytical approaches developed for this, which you may want to consider (inverse-variance weighted meta-analysis, for example).
If you're looki... | Stouffer's Z-score method: what if we sum $z^2$ instead of $z$? | Slightly o/t: one of the issues with both these approaches is the loss of power due to the degrees of freedom (N for stouffer's; 2N for Fisher's). There have been better meta-analytical approaches dev | Stouffer's Z-score method: what if we sum $z^2$ instead of $z$?
Slightly o/t: one of the issues with both these approaches is the loss of power due to the degrees of freedom (N for stouffer's; 2N for Fisher's). There have been better meta-analytical approaches developed for this, which you may want to consider (inverse... | Stouffer's Z-score method: what if we sum $z^2$ instead of $z$?
Slightly o/t: one of the issues with both these approaches is the loss of power due to the degrees of freedom (N for stouffer's; 2N for Fisher's). There have been better meta-analytical approaches dev |
11,568 | Stouffer's Z-score method: what if we sum $z^2$ instead of $z$? | To answer the question and for any further readers: is it ever used?, there is an exhaustive paper by Cousins (2008) on arXiv, which listed and reviewed a couple of alternative approaches. The proposed one does not seem to appear. | Stouffer's Z-score method: what if we sum $z^2$ instead of $z$? | To answer the question and for any further readers: is it ever used?, there is an exhaustive paper by Cousins (2008) on arXiv, which listed and reviewed a couple of alternative approaches. The propose | Stouffer's Z-score method: what if we sum $z^2$ instead of $z$?
To answer the question and for any further readers: is it ever used?, there is an exhaustive paper by Cousins (2008) on arXiv, which listed and reviewed a couple of alternative approaches. The proposed one does not seem to appear. | Stouffer's Z-score method: what if we sum $z^2$ instead of $z$?
To answer the question and for any further readers: is it ever used?, there is an exhaustive paper by Cousins (2008) on arXiv, which listed and reviewed a couple of alternative approaches. The propose |
11,569 | K successes in Bernoulli trials, or George Lucas movie experiment | Here is some R code to simulate the George Lucas experiment:
B<-20000
steps<-2*rbinom(B,1,0.5)-1
rw<-cumsum(steps)
ts.plot(rw,xlab="Number of customers",ylab="Difference")
Running it, we get pictures like these:
where the difference in sold tickets between A and B is on the y-axis.
Next, we run $10,000$ such simulate... | K successes in Bernoulli trials, or George Lucas movie experiment | Here is some R code to simulate the George Lucas experiment:
B<-20000
steps<-2*rbinom(B,1,0.5)-1
rw<-cumsum(steps)
ts.plot(rw,xlab="Number of customers",ylab="Difference")
Running it, we get pictures | K successes in Bernoulli trials, or George Lucas movie experiment
Here is some R code to simulate the George Lucas experiment:
B<-20000
steps<-2*rbinom(B,1,0.5)-1
rw<-cumsum(steps)
ts.plot(rw,xlab="Number of customers",ylab="Difference")
Running it, we get pictures like these:
where the difference in sold tickets bet... | K successes in Bernoulli trials, or George Lucas movie experiment
Here is some R code to simulate the George Lucas experiment:
B<-20000
steps<-2*rbinom(B,1,0.5)-1
rw<-cumsum(steps)
ts.plot(rw,xlab="Number of customers",ylab="Difference")
Running it, we get pictures |
11,570 | K successes in Bernoulli trials, or George Lucas movie experiment | Both A and B have a $1/2$ chance to be ahead after any odd number of trials $t$ (odd to avoid ties). However, these events are related. Whichever is ahead after $t=1$ has a $3/4$ chance to be ahead after $t=3$, and this gets more dramatic as $t$ increases.
The average number of lead changes does grow to infinity as th... | K successes in Bernoulli trials, or George Lucas movie experiment | Both A and B have a $1/2$ chance to be ahead after any odd number of trials $t$ (odd to avoid ties). However, these events are related. Whichever is ahead after $t=1$ has a $3/4$ chance to be ahead af | K successes in Bernoulli trials, or George Lucas movie experiment
Both A and B have a $1/2$ chance to be ahead after any odd number of trials $t$ (odd to avoid ties). However, these events are related. Whichever is ahead after $t=1$ has a $3/4$ chance to be ahead after $t=3$, and this gets more dramatic as $t$ increase... | K successes in Bernoulli trials, or George Lucas movie experiment
Both A and B have a $1/2$ chance to be ahead after any odd number of trials $t$ (odd to avoid ties). However, these events are related. Whichever is ahead after $t=1$ has a $3/4$ chance to be ahead af |
11,571 | K successes in Bernoulli trials, or George Lucas movie experiment | "it is 88 times more probable that one of the two films will lead through all 20,000 customers than it is that, say, the lead continuously seesaws"
In plain English: one of the movies gets an early lead. It has to, as the first customer has to go to A or B. That movie is then just as likely to keep its lead as lose it.... | K successes in Bernoulli trials, or George Lucas movie experiment | "it is 88 times more probable that one of the two films will lead through all 20,000 customers than it is that, say, the lead continuously seesaws"
In plain English: one of the movies gets an early le | K successes in Bernoulli trials, or George Lucas movie experiment
"it is 88 times more probable that one of the two films will lead through all 20,000 customers than it is that, say, the lead continuously seesaws"
In plain English: one of the movies gets an early lead. It has to, as the first customer has to go to A or... | K successes in Bernoulli trials, or George Lucas movie experiment
"it is 88 times more probable that one of the two films will lead through all 20,000 customers than it is that, say, the lead continuously seesaws"
In plain English: one of the movies gets an early le |
11,572 | Why are optimization algorithms defined in terms of other optimization problems? | You are looking at top level algorithm flow charts. Some of the individual steps in the flow chart may merit their own detailed flow charts. However, in published papers having an emphasis on brevity, many details are often omitted. Details for standard inner optimization problems, which are considered to be "old hat... | Why are optimization algorithms defined in terms of other optimization problems? | You are looking at top level algorithm flow charts. Some of the individual steps in the flow chart may merit their own detailed flow charts. However, in published papers having an emphasis on brevit | Why are optimization algorithms defined in terms of other optimization problems?
You are looking at top level algorithm flow charts. Some of the individual steps in the flow chart may merit their own detailed flow charts. However, in published papers having an emphasis on brevity, many details are often omitted. Deta... | Why are optimization algorithms defined in terms of other optimization problems?
You are looking at top level algorithm flow charts. Some of the individual steps in the flow chart may merit their own detailed flow charts. However, in published papers having an emphasis on brevit |
11,573 | Why are optimization algorithms defined in terms of other optimization problems? | I like Mark's answer, but I though I would mention "Simulated Annealing", which basically can run on top of any optimization algorithm. At a high level it works like this:
It has a "temperature" parameter which starts hot. While hot it steps frequently away and (and further away) from the where the subordinate optimiz... | Why are optimization algorithms defined in terms of other optimization problems? | I like Mark's answer, but I though I would mention "Simulated Annealing", which basically can run on top of any optimization algorithm. At a high level it works like this:
It has a "temperature" para | Why are optimization algorithms defined in terms of other optimization problems?
I like Mark's answer, but I though I would mention "Simulated Annealing", which basically can run on top of any optimization algorithm. At a high level it works like this:
It has a "temperature" parameter which starts hot. While hot it st... | Why are optimization algorithms defined in terms of other optimization problems?
I like Mark's answer, but I though I would mention "Simulated Annealing", which basically can run on top of any optimization algorithm. At a high level it works like this:
It has a "temperature" para |
11,574 | Why are optimization algorithms defined in terms of other optimization problems? | I think a reference that my satisfy your desire is here. Go to section 4 - Optimisation in Modern Bayesian Computation.
TL;DR -they discuss proximal methods. One of the advantages of such methods is splitting - you can find a solution by optimizing easier subproblems. A lot of times (or, at least, sometimes) you may ... | Why are optimization algorithms defined in terms of other optimization problems? | I think a reference that my satisfy your desire is here. Go to section 4 - Optimisation in Modern Bayesian Computation.
TL;DR -they discuss proximal methods. One of the advantages of such methods is | Why are optimization algorithms defined in terms of other optimization problems?
I think a reference that my satisfy your desire is here. Go to section 4 - Optimisation in Modern Bayesian Computation.
TL;DR -they discuss proximal methods. One of the advantages of such methods is splitting - you can find a solution by... | Why are optimization algorithms defined in terms of other optimization problems?
I think a reference that my satisfy your desire is here. Go to section 4 - Optimisation in Modern Bayesian Computation.
TL;DR -they discuss proximal methods. One of the advantages of such methods is |
11,575 | Why are optimization algorithms defined in terms of other optimization problems? | This is quite common in many optimization papers and it has to do with generality. The authors usually write the algorithms in this manner to show that they technically work for any function f. However, in practice, they are only useful for very specific functions where these sub-problems can be efficiently solved.
For... | Why are optimization algorithms defined in terms of other optimization problems? | This is quite common in many optimization papers and it has to do with generality. The authors usually write the algorithms in this manner to show that they technically work for any function f. Howeve | Why are optimization algorithms defined in terms of other optimization problems?
This is quite common in many optimization papers and it has to do with generality. The authors usually write the algorithms in this manner to show that they technically work for any function f. However, in practice, they are only useful fo... | Why are optimization algorithms defined in terms of other optimization problems?
This is quite common in many optimization papers and it has to do with generality. The authors usually write the algorithms in this manner to show that they technically work for any function f. Howeve |
11,576 | Sum or average of gradients in (mini) batch gradient decent? [duplicate] | Average.
Examples: Notes to Andrew Ng's Machine Learning Course on Coursera compiled by Alex Holehouse.
Summing the gradients due to individual samples you get a much smoother gradient. The larger the batch the smoother the resulting gradient used in updating the weight.
Dividing the sum by the batch size and taking th... | Sum or average of gradients in (mini) batch gradient decent? [duplicate] | Average.
Examples: Notes to Andrew Ng's Machine Learning Course on Coursera compiled by Alex Holehouse.
Summing the gradients due to individual samples you get a much smoother gradient. The larger the | Sum or average of gradients in (mini) batch gradient decent? [duplicate]
Average.
Examples: Notes to Andrew Ng's Machine Learning Course on Coursera compiled by Alex Holehouse.
Summing the gradients due to individual samples you get a much smoother gradient. The larger the batch the smoother the resulting gradient used... | Sum or average of gradients in (mini) batch gradient decent? [duplicate]
Average.
Examples: Notes to Andrew Ng's Machine Learning Course on Coursera compiled by Alex Holehouse.
Summing the gradients due to individual samples you get a much smoother gradient. The larger the |
11,577 | Regression with only categorical variables [duplicate] | We need to be clear on our terms here, but in general, yes:
If your dependent variable is continuous (and the residuals are normally distributed—see here), but all of your independent variables are categorical, this is just an ANOVA.
If your dependent variable is categorical and your independent variables are cont... | Regression with only categorical variables [duplicate] | We need to be clear on our terms here, but in general, yes:
If your dependent variable is continuous (and the residuals are normally distributed—see here), but all of your independent variables are | Regression with only categorical variables [duplicate]
We need to be clear on our terms here, but in general, yes:
If your dependent variable is continuous (and the residuals are normally distributed—see here), but all of your independent variables are categorical, this is just an ANOVA.
If your dependent variable... | Regression with only categorical variables [duplicate]
We need to be clear on our terms here, but in general, yes:
If your dependent variable is continuous (and the residuals are normally distributed—see here), but all of your independent variables are |
11,578 | Linear regression prediction interval | @whuber has pointed you to three good answers, but perhaps I can still write something of value. Your explicit question, as I understand it, is:
Given my fitted model, $\hat y_i=\hat mx_i + \hat b$ (notice I added 'hats'), and assuming my residuals are normally distributed, $\mathcal N(0, \hat\sigma^2_e)$, can I pre... | Linear regression prediction interval | @whuber has pointed you to three good answers, but perhaps I can still write something of value. Your explicit question, as I understand it, is:
Given my fitted model, $\hat y_i=\hat mx_i + \hat b$ | Linear regression prediction interval
@whuber has pointed you to three good answers, but perhaps I can still write something of value. Your explicit question, as I understand it, is:
Given my fitted model, $\hat y_i=\hat mx_i + \hat b$ (notice I added 'hats'), and assuming my residuals are normally distributed, $\ma... | Linear regression prediction interval
@whuber has pointed you to three good answers, but perhaps I can still write something of value. Your explicit question, as I understand it, is:
Given my fitted model, $\hat y_i=\hat mx_i + \hat b$ |
11,579 | Is it possible to understand pareto/nbd model conceptually? | Imagine you're the newly appointed manager of a flower shop. You've got a record of last year's customers – the frequency with which they shop and how long since their last visit. You want to know how much business the listed customers are likely to bring in this year. There are a few things to consider:
[assumption (i... | Is it possible to understand pareto/nbd model conceptually? | Imagine you're the newly appointed manager of a flower shop. You've got a record of last year's customers – the frequency with which they shop and how long since their last visit. You want to know how | Is it possible to understand pareto/nbd model conceptually?
Imagine you're the newly appointed manager of a flower shop. You've got a record of last year's customers – the frequency with which they shop and how long since their last visit. You want to know how much business the listed customers are likely to bring in t... | Is it possible to understand pareto/nbd model conceptually?
Imagine you're the newly appointed manager of a flower shop. You've got a record of last year's customers – the frequency with which they shop and how long since their last visit. You want to know how |
11,580 | In neural nets, why use gradient methods rather than other metaheuristics? | Extending @Dikran Marsupial's answer....
Anna Choromanska and her colleagues in Yan LeCunn's group at NYU, address this in their 2014 AISTATS paper "The Loss Surface of Multilayer Nets". Using random matrix theory, along with some experiments, they argue that:
For large-size networks, most local minima are equivalent... | In neural nets, why use gradient methods rather than other metaheuristics? | Extending @Dikran Marsupial's answer....
Anna Choromanska and her colleagues in Yan LeCunn's group at NYU, address this in their 2014 AISTATS paper "The Loss Surface of Multilayer Nets". Using random | In neural nets, why use gradient methods rather than other metaheuristics?
Extending @Dikran Marsupial's answer....
Anna Choromanska and her colleagues in Yan LeCunn's group at NYU, address this in their 2014 AISTATS paper "The Loss Surface of Multilayer Nets". Using random matrix theory, along with some experiments, t... | In neural nets, why use gradient methods rather than other metaheuristics?
Extending @Dikran Marsupial's answer....
Anna Choromanska and her colleagues in Yan LeCunn's group at NYU, address this in their 2014 AISTATS paper "The Loss Surface of Multilayer Nets". Using random |
11,581 | In neural nets, why use gradient methods rather than other metaheuristics? | Local minima are not really as great a problem with neural nets as is often suggested. Some of the local minima are due to the symmetry of the network (i.e. you can permute the hidden neurons and leave the function of the network unchanged. All that is necessary is to find a good local minima, rather than the global ... | In neural nets, why use gradient methods rather than other metaheuristics? | Local minima are not really as great a problem with neural nets as is often suggested. Some of the local minima are due to the symmetry of the network (i.e. you can permute the hidden neurons and lea | In neural nets, why use gradient methods rather than other metaheuristics?
Local minima are not really as great a problem with neural nets as is often suggested. Some of the local minima are due to the symmetry of the network (i.e. you can permute the hidden neurons and leave the function of the network unchanged. Al... | In neural nets, why use gradient methods rather than other metaheuristics?
Local minima are not really as great a problem with neural nets as is often suggested. Some of the local minima are due to the symmetry of the network (i.e. you can permute the hidden neurons and lea |
11,582 | What does the name "Logistic Regression" mean? | As it has been already pointed out, ''logistic'' comes from logistic curve/function/distribution (which is underlying logistic regression). So the question is: where is logistic coming in their names?
The reference to Verhulst (i.e. Wikipedia's statement) seems a bit false. While it is clearly true that it is most wide... | What does the name "Logistic Regression" mean? | As it has been already pointed out, ''logistic'' comes from logistic curve/function/distribution (which is underlying logistic regression). So the question is: where is logistic coming in their names? | What does the name "Logistic Regression" mean?
As it has been already pointed out, ''logistic'' comes from logistic curve/function/distribution (which is underlying logistic regression). So the question is: where is logistic coming in their names?
The reference to Verhulst (i.e. Wikipedia's statement) seems a bit false... | What does the name "Logistic Regression" mean?
As it has been already pointed out, ''logistic'' comes from logistic curve/function/distribution (which is underlying logistic regression). So the question is: where is logistic coming in their names? |
11,583 | What does the name "Logistic Regression" mean? | Its related to the LOGISTIC distribution, which has an S-shaped curve. | What does the name "Logistic Regression" mean? | Its related to the LOGISTIC distribution, which has an S-shaped curve. | What does the name "Logistic Regression" mean?
Its related to the LOGISTIC distribution, which has an S-shaped curve. | What does the name "Logistic Regression" mean?
Its related to the LOGISTIC distribution, which has an S-shaped curve. |
11,584 | Is a weighted $R^2$ in robust linear model meaningful for goodness of fit analysis? | The following answer is based on: (1) my interpretation of Willett and Singer (1988) Another Cautionary Note about R-squared: It's use in weighted least squates regression analysis. The American Statistician. 42(3). pp236-238, and (2) the premise that robust linear regression is essentially weighted least squares regr... | Is a weighted $R^2$ in robust linear model meaningful for goodness of fit analysis? | The following answer is based on: (1) my interpretation of Willett and Singer (1988) Another Cautionary Note about R-squared: It's use in weighted least squates regression analysis. The American Stat | Is a weighted $R^2$ in robust linear model meaningful for goodness of fit analysis?
The following answer is based on: (1) my interpretation of Willett and Singer (1988) Another Cautionary Note about R-squared: It's use in weighted least squates regression analysis. The American Statistician. 42(3). pp236-238, and (2) ... | Is a weighted $R^2$ in robust linear model meaningful for goodness of fit analysis?
The following answer is based on: (1) my interpretation of Willett and Singer (1988) Another Cautionary Note about R-squared: It's use in weighted least squates regression analysis. The American Stat |
11,585 | Is a weighted $R^2$ in robust linear model meaningful for goodness of fit analysis? | @CraigMilligan.
Shouldn't:
the weight be outside of the squared parenthesis
the weighted mean be calculated as sum(x$w*observed)/sum(x$w) for which we can also use weighted.mean(observed,x$w)
Something like this:
r2ww <- function(x){
SSe <- sum(x$w*(x$resid)^2)
observed <- x$resid+x$fitted
SSt <- sum(x$w*(obser... | Is a weighted $R^2$ in robust linear model meaningful for goodness of fit analysis? | @CraigMilligan.
Shouldn't:
the weight be outside of the squared parenthesis
the weighted mean be calculated as sum(x$w*observed)/sum(x$w) for which we can also use weighted.mean(observed,x$w)
Someth | Is a weighted $R^2$ in robust linear model meaningful for goodness of fit analysis?
@CraigMilligan.
Shouldn't:
the weight be outside of the squared parenthesis
the weighted mean be calculated as sum(x$w*observed)/sum(x$w) for which we can also use weighted.mean(observed,x$w)
Something like this:
r2ww <- function(x){
... | Is a weighted $R^2$ in robust linear model meaningful for goodness of fit analysis?
@CraigMilligan.
Shouldn't:
the weight be outside of the squared parenthesis
the weighted mean be calculated as sum(x$w*observed)/sum(x$w) for which we can also use weighted.mean(observed,x$w)
Someth |
11,586 | How to test for differences between two group means when the data is not normally distributed? | The idea that the t-test is only for small samples is a historical hold over. Yes it was originally developed for small samples, but there is nothing in the theory that distinguishes small from large. In the days before computers were common for doing statistics the t-tables often only went up to around 30 degrees of... | How to test for differences between two group means when the data is not normally distributed? | The idea that the t-test is only for small samples is a historical hold over. Yes it was originally developed for small samples, but there is nothing in the theory that distinguishes small from large | How to test for differences between two group means when the data is not normally distributed?
The idea that the t-test is only for small samples is a historical hold over. Yes it was originally developed for small samples, but there is nothing in the theory that distinguishes small from large. In the days before com... | How to test for differences between two group means when the data is not normally distributed?
The idea that the t-test is only for small samples is a historical hold over. Yes it was originally developed for small samples, but there is nothing in the theory that distinguishes small from large |
11,587 | How to test for differences between two group means when the data is not normally distributed? | One addition to Greg's already very comprehensive answer.
If I understand you the right way, your point 3 states the following procedure:
Observe $n$ samples of a distribution $X$.
Then, draw $m$ of those $n$ values and compute their mean.
Repeat this 1000 times, save the corresponding means
Finally, compute the mean... | How to test for differences between two group means when the data is not normally distributed? | One addition to Greg's already very comprehensive answer.
If I understand you the right way, your point 3 states the following procedure:
Observe $n$ samples of a distribution $X$.
Then, draw $m$ of | How to test for differences between two group means when the data is not normally distributed?
One addition to Greg's already very comprehensive answer.
If I understand you the right way, your point 3 states the following procedure:
Observe $n$ samples of a distribution $X$.
Then, draw $m$ of those $n$ values and comp... | How to test for differences between two group means when the data is not normally distributed?
One addition to Greg's already very comprehensive answer.
If I understand you the right way, your point 3 states the following procedure:
Observe $n$ samples of a distribution $X$.
Then, draw $m$ of |
11,588 | What non-Bayesian methods are there for predictive inference? | Non-Bayesian predictive inference (apart from the SLR case) is a relatively recent field. Under the heading of "non-Bayesian" we can subdivide the approaches into those that are "classical" frequentist vs those that are "likelihood" based.
Classical Frequentist Prediction
As you know, the "gold standard" in frequentism... | What non-Bayesian methods are there for predictive inference? | Non-Bayesian predictive inference (apart from the SLR case) is a relatively recent field. Under the heading of "non-Bayesian" we can subdivide the approaches into those that are "classical" frequentis | What non-Bayesian methods are there for predictive inference?
Non-Bayesian predictive inference (apart from the SLR case) is a relatively recent field. Under the heading of "non-Bayesian" we can subdivide the approaches into those that are "classical" frequentist vs those that are "likelihood" based.
Classical Frequent... | What non-Bayesian methods are there for predictive inference?
Non-Bayesian predictive inference (apart from the SLR case) is a relatively recent field. Under the heading of "non-Bayesian" we can subdivide the approaches into those that are "classical" frequentis |
11,589 | What non-Bayesian methods are there for predictive inference? | I'll address my answer specifically to the question, "What non-Bayesian methods for predictive inference are there that take into account uncertainty in parameter estimates?" I will organize my answer around expanding the meaning of uncertainty.
We hope statistical analyses provide support for various kinds of claims, ... | What non-Bayesian methods are there for predictive inference? | I'll address my answer specifically to the question, "What non-Bayesian methods for predictive inference are there that take into account uncertainty in parameter estimates?" I will organize my answer | What non-Bayesian methods are there for predictive inference?
I'll address my answer specifically to the question, "What non-Bayesian methods for predictive inference are there that take into account uncertainty in parameter estimates?" I will organize my answer around expanding the meaning of uncertainty.
We hope stat... | What non-Bayesian methods are there for predictive inference?
I'll address my answer specifically to the question, "What non-Bayesian methods for predictive inference are there that take into account uncertainty in parameter estimates?" I will organize my answer |
11,590 | A proof for the stationarity of an AR(2) | My guess is that the characteristic equation you are departing from is different from mine. Let me proceed in a couple of steps to see whether we agree.
Consider the equation
$$
\lambda^2-\phi_1\lambda-\phi_2=0
$$
If $z$ is a root of the "standard" characteristic equation $1-\phi_1 z-\phi_2 z^2=0$ and setting $z^{-1}=\... | A proof for the stationarity of an AR(2) | My guess is that the characteristic equation you are departing from is different from mine. Let me proceed in a couple of steps to see whether we agree.
Consider the equation
$$
\lambda^2-\phi_1\lambd | A proof for the stationarity of an AR(2)
My guess is that the characteristic equation you are departing from is different from mine. Let me proceed in a couple of steps to see whether we agree.
Consider the equation
$$
\lambda^2-\phi_1\lambda-\phi_2=0
$$
If $z$ is a root of the "standard" characteristic equation $1-\ph... | A proof for the stationarity of an AR(2)
My guess is that the characteristic equation you are departing from is different from mine. Let me proceed in a couple of steps to see whether we agree.
Consider the equation
$$
\lambda^2-\phi_1\lambd |
11,591 | k-fold Cross validation of ensemble learning | Ensemble learning refers to quite a few different methods. Boosting and bagging are probably the two most common ones. It seems that you are attempting to implement an ensemble learning method called stacking. Stacking aims to improve accuracy by combining predictions from several learning algorithms. There are quite a... | k-fold Cross validation of ensemble learning | Ensemble learning refers to quite a few different methods. Boosting and bagging are probably the two most common ones. It seems that you are attempting to implement an ensemble learning method called | k-fold Cross validation of ensemble learning
Ensemble learning refers to quite a few different methods. Boosting and bagging are probably the two most common ones. It seems that you are attempting to implement an ensemble learning method called stacking. Stacking aims to improve accuracy by combining predictions from s... | k-fold Cross validation of ensemble learning
Ensemble learning refers to quite a few different methods. Boosting and bagging are probably the two most common ones. It seems that you are attempting to implement an ensemble learning method called |
11,592 | How many times should we repeat a K-fold CV? | The influencing factor is how stable your model - or, more precisely: the predictions of the surrogates are.
If the models are completely stable, all surrogate models will yield the same prediction for the same test case. In that case, iterations/repetitions are not needed, and they don't yield any improvements.
As you... | How many times should we repeat a K-fold CV? | The influencing factor is how stable your model - or, more precisely: the predictions of the surrogates are.
If the models are completely stable, all surrogate models will yield the same prediction fo | How many times should we repeat a K-fold CV?
The influencing factor is how stable your model - or, more precisely: the predictions of the surrogates are.
If the models are completely stable, all surrogate models will yield the same prediction for the same test case. In that case, iterations/repetitions are not needed, ... | How many times should we repeat a K-fold CV?
The influencing factor is how stable your model - or, more precisely: the predictions of the surrogates are.
If the models are completely stable, all surrogate models will yield the same prediction fo |
11,593 | How many times should we repeat a K-fold CV? | Ask a statistician any question and their answer will be some form of "it depends".
It depends. Apart from the type of model (good point cbeleites!), the number of training set points and the number of predictors? If the model is for classification, a large class imbalance would cause me to increase the number of repet... | How many times should we repeat a K-fold CV? | Ask a statistician any question and their answer will be some form of "it depends".
It depends. Apart from the type of model (good point cbeleites!), the number of training set points and the number o | How many times should we repeat a K-fold CV?
Ask a statistician any question and their answer will be some form of "it depends".
It depends. Apart from the type of model (good point cbeleites!), the number of training set points and the number of predictors? If the model is for classification, a large class imbalance w... | How many times should we repeat a K-fold CV?
Ask a statistician any question and their answer will be some form of "it depends".
It depends. Apart from the type of model (good point cbeleites!), the number of training set points and the number o |
11,594 | Why doesn't k-means give the global minimum? | You can see k-means as a special version of the EM algorithm, which may help a little.
Say you are estimating a multivariate normal distribution for each cluster with the covariance matrix fixed to the identity matrix for all, but variable mean $\mu_i$ where $i$ is the cluster's index. Clearly, if the parameters $\{\m... | Why doesn't k-means give the global minimum? | You can see k-means as a special version of the EM algorithm, which may help a little.
Say you are estimating a multivariate normal distribution for each cluster with the covariance matrix fixed to t | Why doesn't k-means give the global minimum?
You can see k-means as a special version of the EM algorithm, which may help a little.
Say you are estimating a multivariate normal distribution for each cluster with the covariance matrix fixed to the identity matrix for all, but variable mean $\mu_i$ where $i$ is the clus... | Why doesn't k-means give the global minimum?
You can see k-means as a special version of the EM algorithm, which may help a little.
Say you are estimating a multivariate normal distribution for each cluster with the covariance matrix fixed to t |
11,595 | Why doesn't k-means give the global minimum? | This is the problem that you want to solve:
\begin{align}
&\min_{x} \sum_{i=1}^n \sum_{j=1}^k x_{ij} || p_i - c_j||^2\\
&\text{subject to:} \\
&\sum_{j=1}^k x_{ij} = 1 \quad \forall i\\
& c_j\textit{ is the centroid of cluster j}\\
&x_{ij} \in \{0,1\} \quad \forall i, j \\
\end{align}
The binary variable $x_{ij}$ indi... | Why doesn't k-means give the global minimum? | This is the problem that you want to solve:
\begin{align}
&\min_{x} \sum_{i=1}^n \sum_{j=1}^k x_{ij} || p_i - c_j||^2\\
&\text{subject to:} \\
&\sum_{j=1}^k x_{ij} = 1 \quad \forall i\\
& c_j\textit{ | Why doesn't k-means give the global minimum?
This is the problem that you want to solve:
\begin{align}
&\min_{x} \sum_{i=1}^n \sum_{j=1}^k x_{ij} || p_i - c_j||^2\\
&\text{subject to:} \\
&\sum_{j=1}^k x_{ij} = 1 \quad \forall i\\
& c_j\textit{ is the centroid of cluster j}\\
&x_{ij} \in \{0,1\} \quad \forall i, j \\
... | Why doesn't k-means give the global minimum?
This is the problem that you want to solve:
\begin{align}
&\min_{x} \sum_{i=1}^n \sum_{j=1}^k x_{ij} || p_i - c_j||^2\\
&\text{subject to:} \\
&\sum_{j=1}^k x_{ij} = 1 \quad \forall i\\
& c_j\textit{ |
11,596 | Why doesn't k-means give the global minimum? | A simple example might help.
Let us define the set of points to be clustered as A = {1,2,3,4}.
Say you're trying to find 2 appropriate clusters for A (2-means). There are (at least) two different settings which satisfy the stationary condition of k-means.
Setting 1:
Center1 = 1, Cluster1 = {1}
Center2 = 3, Cluster1 = ... | Why doesn't k-means give the global minimum? | A simple example might help.
Let us define the set of points to be clustered as A = {1,2,3,4}.
Say you're trying to find 2 appropriate clusters for A (2-means). There are (at least) two different set | Why doesn't k-means give the global minimum?
A simple example might help.
Let us define the set of points to be clustered as A = {1,2,3,4}.
Say you're trying to find 2 appropriate clusters for A (2-means). There are (at least) two different settings which satisfy the stationary condition of k-means.
Setting 1:
Center1... | Why doesn't k-means give the global minimum?
A simple example might help.
Let us define the set of points to be clustered as A = {1,2,3,4}.
Say you're trying to find 2 appropriate clusters for A (2-means). There are (at least) two different set |
11,597 | Why doesn't k-means give the global minimum? | [This was before @Peter answered]
After a small discussion (in the comments section), I feel I have to answer my own question.
I believe that when I partially differentiate the objective function with respect to one centroid, the points in the cluster of another centroid vanish in the derivative. So, the centroid we ... | Why doesn't k-means give the global minimum? | [This was before @Peter answered]
After a small discussion (in the comments section), I feel I have to answer my own question.
I believe that when I partially differentiate the objective function wi | Why doesn't k-means give the global minimum?
[This was before @Peter answered]
After a small discussion (in the comments section), I feel I have to answer my own question.
I believe that when I partially differentiate the objective function with respect to one centroid, the points in the cluster of another centroid v... | Why doesn't k-means give the global minimum?
[This was before @Peter answered]
After a small discussion (in the comments section), I feel I have to answer my own question.
I believe that when I partially differentiate the objective function wi |
11,598 | Why doesn't k-means give the global minimum? | Everybody has explained everything, but I would like to add that if a sample data is not distributed as a Gaussian distribution then it can stuck to a local minima. In the K-means algorithm we are actually trying to get that. | Why doesn't k-means give the global minimum? | Everybody has explained everything, but I would like to add that if a sample data is not distributed as a Gaussian distribution then it can stuck to a local minima. In the K-means algorithm we are act | Why doesn't k-means give the global minimum?
Everybody has explained everything, but I would like to add that if a sample data is not distributed as a Gaussian distribution then it can stuck to a local minima. In the K-means algorithm we are actually trying to get that. | Why doesn't k-means give the global minimum?
Everybody has explained everything, but I would like to add that if a sample data is not distributed as a Gaussian distribution then it can stuck to a local minima. In the K-means algorithm we are act |
11,599 | Why doesn't k-means give the global minimum? | Also, the global minimum depends on the type of error function you define to minimize.
For K-Means algorithm I found the way to get to global minima would be by brute-force.
suppose you have k = 2 and points = 6 the way you can initialize them is a max of 2^6 ways.
Solving k-means for that will give me all the local mi... | Why doesn't k-means give the global minimum? | Also, the global minimum depends on the type of error function you define to minimize.
For K-Means algorithm I found the way to get to global minima would be by brute-force.
suppose you have k = 2 and | Why doesn't k-means give the global minimum?
Also, the global minimum depends on the type of error function you define to minimize.
For K-Means algorithm I found the way to get to global minima would be by brute-force.
suppose you have k = 2 and points = 6 the way you can initialize them is a max of 2^6 ways.
Solving k... | Why doesn't k-means give the global minimum?
Also, the global minimum depends on the type of error function you define to minimize.
For K-Means algorithm I found the way to get to global minima would be by brute-force.
suppose you have k = 2 and |
11,600 | Mother milk of 6 Corona-positive (COVID-19) women does not contain the virus - can we make a confidence statement about this? | There is the rule of three saying
if a certain event did not occur in a sample with $n$ subjects, the interval from $0$ to $3/n$ is a 95% confidence interval for the rate of occurrences in the population.
You have $n=6$, so says $[0, 3/6=0.5]$ is a 95% confidence interval for the binomial $p$ of transmission. In non... | Mother milk of 6 Corona-positive (COVID-19) women does not contain the virus - can we make a confide | There is the rule of three saying
if a certain event did not occur in a sample with $n$ subjects, the interval from $0$ to $3/n$ is a 95% confidence interval for the rate of occurrences in the popul | Mother milk of 6 Corona-positive (COVID-19) women does not contain the virus - can we make a confidence statement about this?
There is the rule of three saying
if a certain event did not occur in a sample with $n$ subjects, the interval from $0$ to $3/n$ is a 95% confidence interval for the rate of occurrences in the... | Mother milk of 6 Corona-positive (COVID-19) women does not contain the virus - can we make a confide
There is the rule of three saying
if a certain event did not occur in a sample with $n$ subjects, the interval from $0$ to $3/n$ is a 95% confidence interval for the rate of occurrences in the popul |
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