idx int64 1 56k | question stringlengths 15 155 | answer stringlengths 2 29.2k ⌀ | question_cut stringlengths 15 100 | answer_cut stringlengths 2 200 ⌀ | conversation stringlengths 47 29.3k | conversation_cut stringlengths 47 301 |
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55,101 | Can we correctly identify all the non-zero coefficients in the linear regression model? | I do not have a good answer, but let me rephrase some of you thoughts and questions and give comments.
<...> what is the point of those $p$−values of each individual coefficient?
A $p$-value is a valid tool when assessing the significance of a single regressor individually. If you care about whether $X_i$ has a non-z... | Can we correctly identify all the non-zero coefficients in the linear regression model? | I do not have a good answer, but let me rephrase some of you thoughts and questions and give comments.
<...> what is the point of those $p$−values of each individual coefficient?
A $p$-value is a va | Can we correctly identify all the non-zero coefficients in the linear regression model?
I do not have a good answer, but let me rephrase some of you thoughts and questions and give comments.
<...> what is the point of those $p$−values of each individual coefficient?
A $p$-value is a valid tool when assessing the sign... | Can we correctly identify all the non-zero coefficients in the linear regression model?
I do not have a good answer, but let me rephrase some of you thoughts and questions and give comments.
<...> what is the point of those $p$−values of each individual coefficient?
A $p$-value is a va |
55,102 | Can we correctly identify all the non-zero coefficients in the linear regression model? | Running statistical algorithms to find the "correct" variables is almost futile. A relevant simulation is in Section 4.3 of my Regression Modeling Strategies course notes at http://biostat.mc.vanderbilt.edu/RmS#Materials
The simplest way to look at the difficulty of the task is to use the bootstrap to get confidence i... | Can we correctly identify all the non-zero coefficients in the linear regression model? | Running statistical algorithms to find the "correct" variables is almost futile. A relevant simulation is in Section 4.3 of my Regression Modeling Strategies course notes at http://biostat.mc.vanderb | Can we correctly identify all the non-zero coefficients in the linear regression model?
Running statistical algorithms to find the "correct" variables is almost futile. A relevant simulation is in Section 4.3 of my Regression Modeling Strategies course notes at http://biostat.mc.vanderbilt.edu/RmS#Materials
The simple... | Can we correctly identify all the non-zero coefficients in the linear regression model?
Running statistical algorithms to find the "correct" variables is almost futile. A relevant simulation is in Section 4.3 of my Regression Modeling Strategies course notes at http://biostat.mc.vanderb |
55,103 | What optimization (maximization/minimization) methods exist contours with lots of kinks? | The state-of-the-art for non-convex optimization in a complex, ill-conditioned and multi-modal landscape is Covariance Matrix Adaptation - Evolution Strategies, aka CMA-ES, which in various versions (such as BIPOP-CMA-ES) has scored first in several global optimization contests (see e.g. the Black-Box Optimization Benc... | What optimization (maximization/minimization) methods exist contours with lots of kinks? | The state-of-the-art for non-convex optimization in a complex, ill-conditioned and multi-modal landscape is Covariance Matrix Adaptation - Evolution Strategies, aka CMA-ES, which in various versions ( | What optimization (maximization/minimization) methods exist contours with lots of kinks?
The state-of-the-art for non-convex optimization in a complex, ill-conditioned and multi-modal landscape is Covariance Matrix Adaptation - Evolution Strategies, aka CMA-ES, which in various versions (such as BIPOP-CMA-ES) has score... | What optimization (maximization/minimization) methods exist contours with lots of kinks?
The state-of-the-art for non-convex optimization in a complex, ill-conditioned and multi-modal landscape is Covariance Matrix Adaptation - Evolution Strategies, aka CMA-ES, which in various versions ( |
55,104 | Interpreting accuracy results for an ARIMA model fit | Here are a few points.
Your ARIMA model is not "estimating a second time series", it is filtering it.
The function accuracy gives you multiple measures of accuracy of the model fit: mean error (ME), root mean squared error (RMSE), mean absolute error (MAE), mean percentage error (MPE), mean absolute percentage error ... | Interpreting accuracy results for an ARIMA model fit | Here are a few points.
Your ARIMA model is not "estimating a second time series", it is filtering it.
The function accuracy gives you multiple measures of accuracy of the model fit: mean error (ME), | Interpreting accuracy results for an ARIMA model fit
Here are a few points.
Your ARIMA model is not "estimating a second time series", it is filtering it.
The function accuracy gives you multiple measures of accuracy of the model fit: mean error (ME), root mean squared error (RMSE), mean absolute error (MAE), mean pe... | Interpreting accuracy results for an ARIMA model fit
Here are a few points.
Your ARIMA model is not "estimating a second time series", it is filtering it.
The function accuracy gives you multiple measures of accuracy of the model fit: mean error (ME), |
55,105 | Interpreting accuracy results for an ARIMA model fit | Out of all the one simplest to understand is MAPE (Mean absolute percentage error). It considers actual values fed into model and fitted values from the model and calculates absolute difference between the two as a percentage of actual value and finally calculates mean of that.
For example if below are your actual data... | Interpreting accuracy results for an ARIMA model fit | Out of all the one simplest to understand is MAPE (Mean absolute percentage error). It considers actual values fed into model and fitted values from the model and calculates absolute difference betwee | Interpreting accuracy results for an ARIMA model fit
Out of all the one simplest to understand is MAPE (Mean absolute percentage error). It considers actual values fed into model and fitted values from the model and calculates absolute difference between the two as a percentage of actual value and finally calculates me... | Interpreting accuracy results for an ARIMA model fit
Out of all the one simplest to understand is MAPE (Mean absolute percentage error). It considers actual values fed into model and fitted values from the model and calculates absolute difference betwee |
55,106 | Interpreting accuracy results for an ARIMA model fit | I was searching myself how to interpret these indices.
Note that the best method remains to plot the predictions over the real data of the same period.
I found these information on various websites including Wikipedia, stackexchange / stackoverflow, statisticshowto and other web places:
-You may "Ecosia" some of the... | Interpreting accuracy results for an ARIMA model fit | I was searching myself how to interpret these indices.
Note that the best method remains to plot the predictions over the real data of the same period.
I found these information on various websites | Interpreting accuracy results for an ARIMA model fit
I was searching myself how to interpret these indices.
Note that the best method remains to plot the predictions over the real data of the same period.
I found these information on various websites including Wikipedia, stackexchange / stackoverflow, statisticshowto... | Interpreting accuracy results for an ARIMA model fit
I was searching myself how to interpret these indices.
Note that the best method remains to plot the predictions over the real data of the same period.
I found these information on various websites |
55,107 | What is the definition of "death rate" in survival analysis? | A rate has a specific definition of $\frac{\# \mbox{events}}{\# \mbox{person-years}}$. A risk on the other hand refers to a particular individual's risk of experiencing an outcome of interest, and it is risk which is intrinsically related to the hazard (instantaneous risk). The language the question uses is consistent ... | What is the definition of "death rate" in survival analysis? | A rate has a specific definition of $\frac{\# \mbox{events}}{\# \mbox{person-years}}$. A risk on the other hand refers to a particular individual's risk of experiencing an outcome of interest, and it | What is the definition of "death rate" in survival analysis?
A rate has a specific definition of $\frac{\# \mbox{events}}{\# \mbox{person-years}}$. A risk on the other hand refers to a particular individual's risk of experiencing an outcome of interest, and it is risk which is intrinsically related to the hazard (insta... | What is the definition of "death rate" in survival analysis?
A rate has a specific definition of $\frac{\# \mbox{events}}{\# \mbox{person-years}}$. A risk on the other hand refers to a particular individual's risk of experiencing an outcome of interest, and it |
55,108 | What is the definition of "death rate" in survival analysis? | By "death rate", they essentially mean hazard rate. Death rates are often reported as deaths per 100,000 subjects per year, making the death rate proportional to the hazard rate, so they are not necessarily exactly alike.
In regards to the book, part "i" of the problem is quite easy as you said. Using what they ask you... | What is the definition of "death rate" in survival analysis? | By "death rate", they essentially mean hazard rate. Death rates are often reported as deaths per 100,000 subjects per year, making the death rate proportional to the hazard rate, so they are not neces | What is the definition of "death rate" in survival analysis?
By "death rate", they essentially mean hazard rate. Death rates are often reported as deaths per 100,000 subjects per year, making the death rate proportional to the hazard rate, so they are not necessarily exactly alike.
In regards to the book, part "i" of t... | What is the definition of "death rate" in survival analysis?
By "death rate", they essentially mean hazard rate. Death rates are often reported as deaths per 100,000 subjects per year, making the death rate proportional to the hazard rate, so they are not neces |
55,109 | Definition of residuals versus prediction errors? | I find your post quite confusing, especially the part about the statistic and the example; how are they relevant here? Instead, let me provide my own understanding of [model] residuals and prediction errors.
A stochastic model includes an error term to allow the relationship between the variables to be stochastic (hav... | Definition of residuals versus prediction errors? | I find your post quite confusing, especially the part about the statistic and the example; how are they relevant here? Instead, let me provide my own understanding of [model] residuals and prediction | Definition of residuals versus prediction errors?
I find your post quite confusing, especially the part about the statistic and the example; how are they relevant here? Instead, let me provide my own understanding of [model] residuals and prediction errors.
A stochastic model includes an error term to allow the relati... | Definition of residuals versus prediction errors?
I find your post quite confusing, especially the part about the statistic and the example; how are they relevant here? Instead, let me provide my own understanding of [model] residuals and prediction |
55,110 | increase in number of filters in convolutional neural nets | Here is an example of what a convolutional network might be looking for, layer by layer.
Layer 1: simple edges at various orientations
Layer 2: combinations of simple edges that form more complex edges and textures such as rounded edges or multiple edges touching
Layer 3: combinations of complex edges that form parts o... | increase in number of filters in convolutional neural nets | Here is an example of what a convolutional network might be looking for, layer by layer.
Layer 1: simple edges at various orientations
Layer 2: combinations of simple edges that form more complex edge | increase in number of filters in convolutional neural nets
Here is an example of what a convolutional network might be looking for, layer by layer.
Layer 1: simple edges at various orientations
Layer 2: combinations of simple edges that form more complex edges and textures such as rounded edges or multiple edges touchi... | increase in number of filters in convolutional neural nets
Here is an example of what a convolutional network might be looking for, layer by layer.
Layer 1: simple edges at various orientations
Layer 2: combinations of simple edges that form more complex edge |
55,111 | Understanding probabilistic neural networks | PNN are easy to understand when taking an example. So let's say I want to classify with a PNN points in 2D and my training points are the blue and red dots in the figure:
I can take as base function a gaussian of variance, say 0.1. There's no training in a PNN as soon as the variance $\sigma$ of the Gaussian is fixed,... | Understanding probabilistic neural networks | PNN are easy to understand when taking an example. So let's say I want to classify with a PNN points in 2D and my training points are the blue and red dots in the figure:
I can take as base function | Understanding probabilistic neural networks
PNN are easy to understand when taking an example. So let's say I want to classify with a PNN points in 2D and my training points are the blue and red dots in the figure:
I can take as base function a gaussian of variance, say 0.1. There's no training in a PNN as soon as the... | Understanding probabilistic neural networks
PNN are easy to understand when taking an example. So let's say I want to classify with a PNN points in 2D and my training points are the blue and red dots in the figure:
I can take as base function |
55,112 | How to interpret Mann-Whitney's statistical significance if median is equal? | The Mann-Whitney is not a test of medians. At best, the Mann-Whitney test can only be claimed to a be a test of differences in mean-rank between two populations' pooled ranking.
You can easily calculate medians empirically and perform a basic Wald test if you need a test of medians.
The Mann-Whitney test happens to be... | How to interpret Mann-Whitney's statistical significance if median is equal? | The Mann-Whitney is not a test of medians. At best, the Mann-Whitney test can only be claimed to a be a test of differences in mean-rank between two populations' pooled ranking.
You can easily calcula | How to interpret Mann-Whitney's statistical significance if median is equal?
The Mann-Whitney is not a test of medians. At best, the Mann-Whitney test can only be claimed to a be a test of differences in mean-rank between two populations' pooled ranking.
You can easily calculate medians empirically and perform a basic ... | How to interpret Mann-Whitney's statistical significance if median is equal?
The Mann-Whitney is not a test of medians. At best, the Mann-Whitney test can only be claimed to a be a test of differences in mean-rank between two populations' pooled ranking.
You can easily calcula |
55,113 | How to interpret Mann-Whitney's statistical significance if median is equal? | Mann-Whitney U test is a rank-sum test, hence it doesn't really care about distribution properties such as mean, media, etc, it only cares that one of your variables tends to have higher values than the other, hence the former has a higher sum of ranks. Nevertheless, if you look closely at this table:
Variable | Me... | How to interpret Mann-Whitney's statistical significance if median is equal? | Mann-Whitney U test is a rank-sum test, hence it doesn't really care about distribution properties such as mean, media, etc, it only cares that one of your variables tends to have higher values than t | How to interpret Mann-Whitney's statistical significance if median is equal?
Mann-Whitney U test is a rank-sum test, hence it doesn't really care about distribution properties such as mean, media, etc, it only cares that one of your variables tends to have higher values than the other, hence the former has a higher sum... | How to interpret Mann-Whitney's statistical significance if median is equal?
Mann-Whitney U test is a rank-sum test, hence it doesn't really care about distribution properties such as mean, media, etc, it only cares that one of your variables tends to have higher values than t |
55,114 | Expected value of a function including the cumulative normal distribution | As $C$ varies from $-1$ to $+1$, the function
$\Phi\left(\frac{C-\mu}{\sigma}\right)$ is a slowly increasing
function whose value increases from varies
$\Phi\left(\frac{-1-\mu}{\sigma}\right)$ to
$\Phi\left(\frac{1-\mu}{\sigma}\right)$.
A more generic question is:
What is $E[\Phi(X)]$ when $X$ is uniformly distrib... | Expected value of a function including the cumulative normal distribution | As $C$ varies from $-1$ to $+1$, the function
$\Phi\left(\frac{C-\mu}{\sigma}\right)$ is a slowly increasing
function whose value increases from varies
$\Phi\left(\frac{-1-\mu}{\sigma}\right)$ to
$ | Expected value of a function including the cumulative normal distribution
As $C$ varies from $-1$ to $+1$, the function
$\Phi\left(\frac{C-\mu}{\sigma}\right)$ is a slowly increasing
function whose value increases from varies
$\Phi\left(\frac{-1-\mu}{\sigma}\right)$ to
$\Phi\left(\frac{1-\mu}{\sigma}\right)$.
A mor... | Expected value of a function including the cumulative normal distribution
As $C$ varies from $-1$ to $+1$, the function
$\Phi\left(\frac{C-\mu}{\sigma}\right)$ is a slowly increasing
function whose value increases from varies
$\Phi\left(\frac{-1-\mu}{\sigma}\right)$ to
$ |
55,115 | Expected value of a function including the cumulative normal distribution | Random variable $Y$ can be expressed as:
where Erf[z] denotes the error function $\frac{2}{\sqrt{\pi }}\int _0^z e^{-t^2}d t$, and where $X \sim \text{Uniform}(-1,1)$ with pdf $f(x)$:
Then, $E[Y]$ can be solved analytically as:
where I am using the Expect function from the mathStatica add-on to Mathematica to do the... | Expected value of a function including the cumulative normal distribution | Random variable $Y$ can be expressed as:
where Erf[z] denotes the error function $\frac{2}{\sqrt{\pi }}\int _0^z e^{-t^2}d t$, and where $X \sim \text{Uniform}(-1,1)$ with pdf $f(x)$:
Then, $E[Y]$ c | Expected value of a function including the cumulative normal distribution
Random variable $Y$ can be expressed as:
where Erf[z] denotes the error function $\frac{2}{\sqrt{\pi }}\int _0^z e^{-t^2}d t$, and where $X \sim \text{Uniform}(-1,1)$ with pdf $f(x)$:
Then, $E[Y]$ can be solved analytically as:
where I am usin... | Expected value of a function including the cumulative normal distribution
Random variable $Y$ can be expressed as:
where Erf[z] denotes the error function $\frac{2}{\sqrt{\pi }}\int _0^z e^{-t^2}d t$, and where $X \sim \text{Uniform}(-1,1)$ with pdf $f(x)$:
Then, $E[Y]$ c |
55,116 | What can we conclude from a Bayesian credible interval? | Confidence intervals can be used equivalently to hypothesis tests, but highest density intervals are not the same as confidence intervals. Let's start with what $p$-value is by quoting Cohen (1994)
What we want to know is "Given this data what is the probability that
$H_0$ is true?" But as most of us know, what it $... | What can we conclude from a Bayesian credible interval? | Confidence intervals can be used equivalently to hypothesis tests, but highest density intervals are not the same as confidence intervals. Let's start with what $p$-value is by quoting Cohen (1994)
W | What can we conclude from a Bayesian credible interval?
Confidence intervals can be used equivalently to hypothesis tests, but highest density intervals are not the same as confidence intervals. Let's start with what $p$-value is by quoting Cohen (1994)
What we want to know is "Given this data what is the probability ... | What can we conclude from a Bayesian credible interval?
Confidence intervals can be used equivalently to hypothesis tests, but highest density intervals are not the same as confidence intervals. Let's start with what $p$-value is by quoting Cohen (1994)
W |
55,117 | Maximizing likelihood vs. minimizing cost [duplicate] | You already know a lot. Two observations.
Take linear regression. Minimizing the squared error turns out to be equivalent to maximizing the likelihood. Loosely one could say that minimizing the squared error is an intuitive method, and maximizing the likelihood a more formal approach that allows for proofs using prope... | Maximizing likelihood vs. minimizing cost [duplicate] | You already know a lot. Two observations.
Take linear regression. Minimizing the squared error turns out to be equivalent to maximizing the likelihood. Loosely one could say that minimizing the squar | Maximizing likelihood vs. minimizing cost [duplicate]
You already know a lot. Two observations.
Take linear regression. Minimizing the squared error turns out to be equivalent to maximizing the likelihood. Loosely one could say that minimizing the squared error is an intuitive method, and maximizing the likelihood a m... | Maximizing likelihood vs. minimizing cost [duplicate]
You already know a lot. Two observations.
Take linear regression. Minimizing the squared error turns out to be equivalent to maximizing the likelihood. Loosely one could say that minimizing the squar |
55,118 | Bivariate normal distribution with $|\rho|=1$ | A simple-minded (that is, non-measure-theoretic) version of the answer is as follows.
If random variables $X$ and $Y$ are such
that
every point $(x,y)$ in a region $\mathcal A$
of the plane is a possible realization of $(X,Y)$
The area of $\mathcal A$ is greater than $0$
and
$P\{(X,Y) \in \mathcal A\} = 1$
then $X... | Bivariate normal distribution with $|\rho|=1$ | A simple-minded (that is, non-measure-theoretic) version of the answer is as follows.
If random variables $X$ and $Y$ are such
that
every point $(x,y)$ in a region $\mathcal A$
of the plane is a pos | Bivariate normal distribution with $|\rho|=1$
A simple-minded (that is, non-measure-theoretic) version of the answer is as follows.
If random variables $X$ and $Y$ are such
that
every point $(x,y)$ in a region $\mathcal A$
of the plane is a possible realization of $(X,Y)$
The area of $\mathcal A$ is greater than $0$
... | Bivariate normal distribution with $|\rho|=1$
A simple-minded (that is, non-measure-theoretic) version of the answer is as follows.
If random variables $X$ and $Y$ are such
that
every point $(x,y)$ in a region $\mathcal A$
of the plane is a pos |
55,119 | Bivariate normal distribution with $|\rho|=1$ | The Pearson product moment correlation coefficient is a measure of linear dependence. At its extremes, one of the random variables is a linear function of the other with probability one and so there is no randomness. | Bivariate normal distribution with $|\rho|=1$ | The Pearson product moment correlation coefficient is a measure of linear dependence. At its extremes, one of the random variables is a linear function of the other with probability one and so there i | Bivariate normal distribution with $|\rho|=1$
The Pearson product moment correlation coefficient is a measure of linear dependence. At its extremes, one of the random variables is a linear function of the other with probability one and so there is no randomness. | Bivariate normal distribution with $|\rho|=1$
The Pearson product moment correlation coefficient is a measure of linear dependence. At its extremes, one of the random variables is a linear function of the other with probability one and so there i |
55,120 | Estimating a cumulative distribution function from a mixture model | Such mixture models are prominently featured in the theory of multiple testing. Here again you have such a mixture; the so-called "two-groups" model. The one group corresponds to hypotheses drawn from the null distribution and the other to hypotheses drawn from the alternative distribution. Indeed, there are people cr... | Estimating a cumulative distribution function from a mixture model | Such mixture models are prominently featured in the theory of multiple testing. Here again you have such a mixture; the so-called "two-groups" model. The one group corresponds to hypotheses drawn fro | Estimating a cumulative distribution function from a mixture model
Such mixture models are prominently featured in the theory of multiple testing. Here again you have such a mixture; the so-called "two-groups" model. The one group corresponds to hypotheses drawn from the null distribution and the other to hypotheses d... | Estimating a cumulative distribution function from a mixture model
Such mixture models are prominently featured in the theory of multiple testing. Here again you have such a mixture; the so-called "two-groups" model. The one group corresponds to hypotheses drawn fro |
55,121 | Programming probability distribution in R | This answer walks you through steps that are common to most stochastic simulations, showing how to create the code in small, simple, easily-tested chunks on any software platform. The process is illustrated with R code. You can run the code snippets as you go along to see what they produce.
FWIW, here's a compact, qu... | Programming probability distribution in R | This answer walks you through steps that are common to most stochastic simulations, showing how to create the code in small, simple, easily-tested chunks on any software platform. The process is illu | Programming probability distribution in R
This answer walks you through steps that are common to most stochastic simulations, showing how to create the code in small, simple, easily-tested chunks on any software platform. The process is illustrated with R code. You can run the code snippets as you go along to see wha... | Programming probability distribution in R
This answer walks you through steps that are common to most stochastic simulations, showing how to create the code in small, simple, easily-tested chunks on any software platform. The process is illu |
55,122 | Programming probability distribution in R | Here is a possible solution to your question
prop=0
T=1e6
for (t in 1:T){
insrd=sample(0:1,4,rep=TRUE,prob=c(8,2))
prop=prop+(sum(insrd)>1)}
print(prop/T)
with answer 0.1809. But you can compute the exact value [0.1808] of this probability by realising that the draw of four farmers is a Binomial B(4,0.2) random va... | Programming probability distribution in R | Here is a possible solution to your question
prop=0
T=1e6
for (t in 1:T){
insrd=sample(0:1,4,rep=TRUE,prob=c(8,2))
prop=prop+(sum(insrd)>1)}
print(prop/T)
with answer 0.1809. But you can compute | Programming probability distribution in R
Here is a possible solution to your question
prop=0
T=1e6
for (t in 1:T){
insrd=sample(0:1,4,rep=TRUE,prob=c(8,2))
prop=prop+(sum(insrd)>1)}
print(prop/T)
with answer 0.1809. But you can compute the exact value [0.1808] of this probability by realising that the draw of fou... | Programming probability distribution in R
Here is a possible solution to your question
prop=0
T=1e6
for (t in 1:T){
insrd=sample(0:1,4,rep=TRUE,prob=c(8,2))
prop=prop+(sum(insrd)>1)}
print(prop/T)
with answer 0.1809. But you can compute |
55,123 | Variational Bayes: Understanding Mean field approximation | Taking the equation from Wikipedia
$D_{KL}(Q||P) = \sum_\limits{z}Q(Z)\log\frac{Q(Z)}{P(Z,X)} +\log P(X)$
What we want is to minimize KL distance wrt $Q$ distribution.
Since $P(X)$ is independent of $Q$ we need to care only about the first term.
Substituting the factored approximation, $Q=\prod\limits_{i=1}^M q(Z_i|X... | Variational Bayes: Understanding Mean field approximation | Taking the equation from Wikipedia
$D_{KL}(Q||P) = \sum_\limits{z}Q(Z)\log\frac{Q(Z)}{P(Z,X)} +\log P(X)$
What we want is to minimize KL distance wrt $Q$ distribution.
Since $P(X)$ is independent of | Variational Bayes: Understanding Mean field approximation
Taking the equation from Wikipedia
$D_{KL}(Q||P) = \sum_\limits{z}Q(Z)\log\frac{Q(Z)}{P(Z,X)} +\log P(X)$
What we want is to minimize KL distance wrt $Q$ distribution.
Since $P(X)$ is independent of $Q$ we need to care only about the first term.
Substituting t... | Variational Bayes: Understanding Mean field approximation
Taking the equation from Wikipedia
$D_{KL}(Q||P) = \sum_\limits{z}Q(Z)\log\frac{Q(Z)}{P(Z,X)} +\log P(X)$
What we want is to minimize KL distance wrt $Q$ distribution.
Since $P(X)$ is independent of |
55,124 | Creating interaction terms for regression | In theory there is no problem creating an interaction by multiplying values of two variables (componentwise), but in practice there can be, depending on your software. Since this question concerns questionable software--a private package (coded by who knows who) or (perhaps worse) Excel, as suggested in another answer... | Creating interaction terms for regression | In theory there is no problem creating an interaction by multiplying values of two variables (componentwise), but in practice there can be, depending on your software. Since this question concerns qu | Creating interaction terms for regression
In theory there is no problem creating an interaction by multiplying values of two variables (componentwise), but in practice there can be, depending on your software. Since this question concerns questionable software--a private package (coded by who knows who) or (perhaps wo... | Creating interaction terms for regression
In theory there is no problem creating an interaction by multiplying values of two variables (componentwise), but in practice there can be, depending on your software. Since this question concerns qu |
55,125 | Creating interaction terms for regression | Nothing wrong with using interaction term in the model, if theory suggests so. How to include interaction term in the model will depend on the software you are using.
In R, you can directly use interaction term using x1:x2 (only the product term) or x1*x2 (interaction as well as the main effects). In other softwares, ... | Creating interaction terms for regression | Nothing wrong with using interaction term in the model, if theory suggests so. How to include interaction term in the model will depend on the software you are using.
In R, you can directly use inter | Creating interaction terms for regression
Nothing wrong with using interaction term in the model, if theory suggests so. How to include interaction term in the model will depend on the software you are using.
In R, you can directly use interaction term using x1:x2 (only the product term) or x1*x2 (interaction as well ... | Creating interaction terms for regression
Nothing wrong with using interaction term in the model, if theory suggests so. How to include interaction term in the model will depend on the software you are using.
In R, you can directly use inter |
55,126 | Appropriate application of Poisson regression? | A couple of thoughts that may or may not help below. It's a bit hard for us to be helpful without seeing your actual data...
First of all, your data rather obviously does not follow a standard regression model form: observations are integer, residuals will certainly not be normally distributed, and so forth. This is a... | Appropriate application of Poisson regression? | A couple of thoughts that may or may not help below. It's a bit hard for us to be helpful without seeing your actual data...
First of all, your data rather obviously does not follow a standard regres | Appropriate application of Poisson regression?
A couple of thoughts that may or may not help below. It's a bit hard for us to be helpful without seeing your actual data...
First of all, your data rather obviously does not follow a standard regression model form: observations are integer, residuals will certainly not b... | Appropriate application of Poisson regression?
A couple of thoughts that may or may not help below. It's a bit hard for us to be helpful without seeing your actual data...
First of all, your data rather obviously does not follow a standard regres |
55,127 | Why should the roots of an ARMA (p,q) process be different? | If the roots are the same, the two cancel out. Consider an ARMA model of the form
$y_t = \frac{\Theta(B)}{\Phi(B)}\varepsilon_t$
that is both stationary and invertible.
Write the numerator and denominator characteristic polynomials as products of factors (i.e. factorize the polynomials). Divide through by a constant so... | Why should the roots of an ARMA (p,q) process be different? | If the roots are the same, the two cancel out. Consider an ARMA model of the form
$y_t = \frac{\Theta(B)}{\Phi(B)}\varepsilon_t$
that is both stationary and invertible.
Write the numerator and denomin | Why should the roots of an ARMA (p,q) process be different?
If the roots are the same, the two cancel out. Consider an ARMA model of the form
$y_t = \frac{\Theta(B)}{\Phi(B)}\varepsilon_t$
that is both stationary and invertible.
Write the numerator and denominator characteristic polynomials as products of factors (i.e.... | Why should the roots of an ARMA (p,q) process be different?
If the roots are the same, the two cancel out. Consider an ARMA model of the form
$y_t = \frac{\Theta(B)}{\Phi(B)}\varepsilon_t$
that is both stationary and invertible.
Write the numerator and denomin |
55,128 | Logistic Regression in R and How to deal with 0 and 1 | That is very strange advice, I am forced to wonder who in the world advanced it.
The correct way to fit a logistic regression leaves the zeros and ones alone, and determines the parameters that minimize the log likelihood function:
$$ f(\beta) = \sum_i y_i \log(p_i) + (1 - y_i) \log(1 - p_i) $$
Where $p_i$ is shorthand... | Logistic Regression in R and How to deal with 0 and 1 | That is very strange advice, I am forced to wonder who in the world advanced it.
The correct way to fit a logistic regression leaves the zeros and ones alone, and determines the parameters that minimi | Logistic Regression in R and How to deal with 0 and 1
That is very strange advice, I am forced to wonder who in the world advanced it.
The correct way to fit a logistic regression leaves the zeros and ones alone, and determines the parameters that minimize the log likelihood function:
$$ f(\beta) = \sum_i y_i \log(p_i)... | Logistic Regression in R and How to deal with 0 and 1
That is very strange advice, I am forced to wonder who in the world advanced it.
The correct way to fit a logistic regression leaves the zeros and ones alone, and determines the parameters that minimi |
55,129 | Is there any modality summary statistic? | Simple summary statistic? Not really.
Any sort of summary statistic? Yes, but I'm guessing it's a harder problem than you may expect (and that the answers given by these methods are less reliable than you want).
To help motivate the difficulty, consider the following histogram:
I believe looking at this plot, you wo... | Is there any modality summary statistic? | Simple summary statistic? Not really.
Any sort of summary statistic? Yes, but I'm guessing it's a harder problem than you may expect (and that the answers given by these methods are less reliable tha | Is there any modality summary statistic?
Simple summary statistic? Not really.
Any sort of summary statistic? Yes, but I'm guessing it's a harder problem than you may expect (and that the answers given by these methods are less reliable than you want).
To help motivate the difficulty, consider the following histogram... | Is there any modality summary statistic?
Simple summary statistic? Not really.
Any sort of summary statistic? Yes, but I'm guessing it's a harder problem than you may expect (and that the answers given by these methods are less reliable tha |
55,130 | Lagrangian multiplier: role of the constraint sign | There is no sign restriction for the Lagrange multiplier of an equality constraint. Lagrange multipliers of inequality constraints do have a sign restriction.
You should really look at the Karush-Kuhn-tucker conditions if you want to understand Lagrange multipliers https://en.wikipedia.org/wiki/Karush%E2%80%93Kuhn%E... | Lagrangian multiplier: role of the constraint sign | There is no sign restriction for the Lagrange multiplier of an equality constraint. Lagrange multipliers of inequality constraints do have a sign restriction.
You should really look at the Karush-K | Lagrangian multiplier: role of the constraint sign
There is no sign restriction for the Lagrange multiplier of an equality constraint. Lagrange multipliers of inequality constraints do have a sign restriction.
You should really look at the Karush-Kuhn-tucker conditions if you want to understand Lagrange multipliers ... | Lagrangian multiplier: role of the constraint sign
There is no sign restriction for the Lagrange multiplier of an equality constraint. Lagrange multipliers of inequality constraints do have a sign restriction.
You should really look at the Karush-K |
55,131 | Should we report R-squared or adjusted R-squared in non-linear regression? | You are fitting multiple parameters in your model. (Usually, you fit one parameter for every variable, but your model is non-linear so that isn't the case, even though you have only one $X$ variable.) With every additional parameter, your model has the opportunity to fit the data better, even if that parameter should... | Should we report R-squared or adjusted R-squared in non-linear regression? | You are fitting multiple parameters in your model. (Usually, you fit one parameter for every variable, but your model is non-linear so that isn't the case, even though you have only one $X$ variable. | Should we report R-squared or adjusted R-squared in non-linear regression?
You are fitting multiple parameters in your model. (Usually, you fit one parameter for every variable, but your model is non-linear so that isn't the case, even though you have only one $X$ variable.) With every additional parameter, your mode... | Should we report R-squared or adjusted R-squared in non-linear regression?
You are fitting multiple parameters in your model. (Usually, you fit one parameter for every variable, but your model is non-linear so that isn't the case, even though you have only one $X$ variable. |
55,132 | Should we report R-squared or adjusted R-squared in non-linear regression? | You should use neither of those. This is because neither $R^2$ nor adjusted $R^2$ (for handling multiple explanatory variables) are well defined for non-linear regression. If the purpose is for reporting the accuracy of the models, I would suggest to use cross validation errors, MSE, on a hold out test set instead. | Should we report R-squared or adjusted R-squared in non-linear regression? | You should use neither of those. This is because neither $R^2$ nor adjusted $R^2$ (for handling multiple explanatory variables) are well defined for non-linear regression. If the purpose is for report | Should we report R-squared or adjusted R-squared in non-linear regression?
You should use neither of those. This is because neither $R^2$ nor adjusted $R^2$ (for handling multiple explanatory variables) are well defined for non-linear regression. If the purpose is for reporting the accuracy of the models, I would sugge... | Should we report R-squared or adjusted R-squared in non-linear regression?
You should use neither of those. This is because neither $R^2$ nor adjusted $R^2$ (for handling multiple explanatory variables) are well defined for non-linear regression. If the purpose is for report |
55,133 | Frequentist statistics | It sounds like your objection is to the use of complete datasets, rather than an objection to the statistical methodology used on those datasets. While you are correct that datasets used in university courses are usually much cleaner than real-life datasets (in particular, they often do not have missing data), this is... | Frequentist statistics | It sounds like your objection is to the use of complete datasets, rather than an objection to the statistical methodology used on those datasets. While you are correct that datasets used in universit | Frequentist statistics
It sounds like your objection is to the use of complete datasets, rather than an objection to the statistical methodology used on those datasets. While you are correct that datasets used in university courses are usually much cleaner than real-life datasets (in particular, they often do not have... | Frequentist statistics
It sounds like your objection is to the use of complete datasets, rather than an objection to the statistical methodology used on those datasets. While you are correct that datasets used in universit |
55,134 | Frequentist statistics | As Ben mentioned there are often a variety of methods available to approach a problem (including missing data), each with a different set of assumptions (frequentist or not). I realize your question is asking about where frequentist methods will fail, but I will provide my rationale for why many adhere to frequentist ... | Frequentist statistics | As Ben mentioned there are often a variety of methods available to approach a problem (including missing data), each with a different set of assumptions (frequentist or not). I realize your question | Frequentist statistics
As Ben mentioned there are often a variety of methods available to approach a problem (including missing data), each with a different set of assumptions (frequentist or not). I realize your question is asking about where frequentist methods will fail, but I will provide my rationale for why many... | Frequentist statistics
As Ben mentioned there are often a variety of methods available to approach a problem (including missing data), each with a different set of assumptions (frequentist or not). I realize your question |
55,135 | Frequentist statistics | This post is about 2800 words long in order to handle the response to comments. It looks much larger due to the size of the graphics. About half the post in length is graphics. Nonetheless, a comment makes mention that with my edit, the whole is difficult to consume. So what I am doing is providing an outline and a... | Frequentist statistics | This post is about 2800 words long in order to handle the response to comments. It looks much larger due to the size of the graphics. About half the post in length is graphics. Nonetheless, a comme | Frequentist statistics
This post is about 2800 words long in order to handle the response to comments. It looks much larger due to the size of the graphics. About half the post in length is graphics. Nonetheless, a comment makes mention that with my edit, the whole is difficult to consume. So what I am doing is pro... | Frequentist statistics
This post is about 2800 words long in order to handle the response to comments. It looks much larger due to the size of the graphics. About half the post in length is graphics. Nonetheless, a comme |
55,136 | Basic intuition about minimal sufficient statistic | Let the sample space be $\mathcal{X}$. Then a sufficient statistic $T$ can be seen as indexing a partition of $\mathcal{X}$, that is, $T(x)=T(y)$ iff (if and only if) $x,y$ belongs to the same element of the partition. A minimallly sufficient statistic is then giving a maximal reduction of the data. That is to say, if... | Basic intuition about minimal sufficient statistic | Let the sample space be $\mathcal{X}$. Then a sufficient statistic $T$ can be seen as indexing a partition of $\mathcal{X}$, that is, $T(x)=T(y)$ iff (if and only if) $x,y$ belongs to the same element | Basic intuition about minimal sufficient statistic
Let the sample space be $\mathcal{X}$. Then a sufficient statistic $T$ can be seen as indexing a partition of $\mathcal{X}$, that is, $T(x)=T(y)$ iff (if and only if) $x,y$ belongs to the same element of the partition. A minimallly sufficient statistic is then giving ... | Basic intuition about minimal sufficient statistic
Let the sample space be $\mathcal{X}$. Then a sufficient statistic $T$ can be seen as indexing a partition of $\mathcal{X}$, that is, $T(x)=T(y)$ iff (if and only if) $x,y$ belongs to the same element |
55,137 | Best way to bin continuous data | You might try a regression tree with party as response and age as independent variable.
>temp <- rpart(Party ~ Age)
>plot(temp)
>text(temp)
The algorithm will find suitable places to split the Age variable, if these exist. If not, the tree won't grow past the root stage, which would tell you something. | Best way to bin continuous data | You might try a regression tree with party as response and age as independent variable.
>temp <- rpart(Party ~ Age)
>plot(temp)
>text(temp)
The algorithm will find suitable places to split the Age v | Best way to bin continuous data
You might try a regression tree with party as response and age as independent variable.
>temp <- rpart(Party ~ Age)
>plot(temp)
>text(temp)
The algorithm will find suitable places to split the Age variable, if these exist. If not, the tree won't grow past the root stage, which would te... | Best way to bin continuous data
You might try a regression tree with party as response and age as independent variable.
>temp <- rpart(Party ~ Age)
>plot(temp)
>text(temp)
The algorithm will find suitable places to split the Age v |
55,138 | Best way to bin continuous data | (For the record, I agree with @dsaxton. But just to give you something, here is a quick demonstration of using LDA to optimally bin a continuous variable based on a factor.)
library(MASS)
Iris = iris[,c(1,5)]
model = lda(Species~Sepal.Length, Iris)
range(Iris$Sepal.Length) # [1] 4.3 7.9
cbind(seq(4, 8, .1),
... | Best way to bin continuous data | (For the record, I agree with @dsaxton. But just to give you something, here is a quick demonstration of using LDA to optimally bin a continuous variable based on a factor.)
library(MASS)
Iris = i | Best way to bin continuous data
(For the record, I agree with @dsaxton. But just to give you something, here is a quick demonstration of using LDA to optimally bin a continuous variable based on a factor.)
library(MASS)
Iris = iris[,c(1,5)]
model = lda(Species~Sepal.Length, Iris)
range(Iris$Sepal.Length) # [1] 4.3... | Best way to bin continuous data
(For the record, I agree with @dsaxton. But just to give you something, here is a quick demonstration of using LDA to optimally bin a continuous variable based on a factor.)
library(MASS)
Iris = i |
55,139 | How to plot algorithm runtime for huge input set? | Continuing the comment theme, you should find an explanation for your outliers to know whether to include them or segregate them. I notice that the outliers are oddly clumped. An outlier for one input set row seems to often go along with an outlier for the same row in another input set.
Regarding your graph, once you'... | How to plot algorithm runtime for huge input set? | Continuing the comment theme, you should find an explanation for your outliers to know whether to include them or segregate them. I notice that the outliers are oddly clumped. An outlier for one input | How to plot algorithm runtime for huge input set?
Continuing the comment theme, you should find an explanation for your outliers to know whether to include them or segregate them. I notice that the outliers are oddly clumped. An outlier for one input set row seems to often go along with an outlier for the same row in a... | How to plot algorithm runtime for huge input set?
Continuing the comment theme, you should find an explanation for your outliers to know whether to include them or segregate them. I notice that the outliers are oddly clumped. An outlier for one input |
55,140 | How to plot algorithm runtime for huge input set? | The minimum values for each input set might be the most informative. A lot of nuisance factors can slow down your benchmark, but very few can cause the code to run faster The docs for the python benchmarking module timeit say:
It’s tempting to calculate mean and standard deviation from the result vector and report the... | How to plot algorithm runtime for huge input set? | The minimum values for each input set might be the most informative. A lot of nuisance factors can slow down your benchmark, but very few can cause the code to run faster The docs for the python bench | How to plot algorithm runtime for huge input set?
The minimum values for each input set might be the most informative. A lot of nuisance factors can slow down your benchmark, but very few can cause the code to run faster The docs for the python benchmarking module timeit say:
It’s tempting to calculate mean and standa... | How to plot algorithm runtime for huge input set?
The minimum values for each input set might be the most informative. A lot of nuisance factors can slow down your benchmark, but very few can cause the code to run faster The docs for the python bench |
55,141 | How to plot algorithm runtime for huge input set? | I have a strong suspicion that your raw data are not normally distributed, given that your data are right-skewed and they cannot possibly be skewed left (bounded by zero). As you mentioned, assuming normality here results in error estimates which extend below zero, which I believe is inappropriate. You may want to cons... | How to plot algorithm runtime for huge input set? | I have a strong suspicion that your raw data are not normally distributed, given that your data are right-skewed and they cannot possibly be skewed left (bounded by zero). As you mentioned, assuming n | How to plot algorithm runtime for huge input set?
I have a strong suspicion that your raw data are not normally distributed, given that your data are right-skewed and they cannot possibly be skewed left (bounded by zero). As you mentioned, assuming normality here results in error estimates which extend below zero, whic... | How to plot algorithm runtime for huge input set?
I have a strong suspicion that your raw data are not normally distributed, given that your data are right-skewed and they cannot possibly be skewed left (bounded by zero). As you mentioned, assuming n |
55,142 | How to plot algorithm runtime for huge input set? | For my part, I would find the following most intuitive and illustrative: A stack of three plots, each corresponding to a subset, showing estimated density curves of both algorithms. (Example below, but note that they're simple pdfs, rather than estimated curves.)
To add more detail, you could include vertical lines dem... | How to plot algorithm runtime for huge input set? | For my part, I would find the following most intuitive and illustrative: A stack of three plots, each corresponding to a subset, showing estimated density curves of both algorithms. (Example below, bu | How to plot algorithm runtime for huge input set?
For my part, I would find the following most intuitive and illustrative: A stack of three plots, each corresponding to a subset, showing estimated density curves of both algorithms. (Example below, but note that they're simple pdfs, rather than estimated curves.)
To add... | How to plot algorithm runtime for huge input set?
For my part, I would find the following most intuitive and illustrative: A stack of three plots, each corresponding to a subset, showing estimated density curves of both algorithms. (Example below, bu |
55,143 | topic similarity semantic PMI between two words wikipedia | You might compute PMI using Wikipedia, as following:
1) Using Lucene to index a Wikipedia dump
2) Using Lucene API, it is straightforward to get:
The number (N1) of documents containing word1 and the number (N2) of documents containing word2. So, Prob(word1) = (N1 + 1) / N and Prob(word2) = (N2 + 1) / N, where N is th... | topic similarity semantic PMI between two words wikipedia | You might compute PMI using Wikipedia, as following:
1) Using Lucene to index a Wikipedia dump
2) Using Lucene API, it is straightforward to get:
The number (N1) of documents containing word1 and the | topic similarity semantic PMI between two words wikipedia
You might compute PMI using Wikipedia, as following:
1) Using Lucene to index a Wikipedia dump
2) Using Lucene API, it is straightforward to get:
The number (N1) of documents containing word1 and the number (N2) of documents containing word2. So, Prob(word1) = ... | topic similarity semantic PMI between two words wikipedia
You might compute PMI using Wikipedia, as following:
1) Using Lucene to index a Wikipedia dump
2) Using Lucene API, it is straightforward to get:
The number (N1) of documents containing word1 and the |
55,144 | Categorical Predictors and categorical responses | You use logistic regression. All these forms of regression/ANOVA depend only on the nature of the dependent variable. ANOVA is the same thing as linear regression. So, here are starting places for various types of DV
Continuous, unbounded response with normal errors: Linear regression/ANOVA
Binary, categorical or or... | Categorical Predictors and categorical responses | You use logistic regression. All these forms of regression/ANOVA depend only on the nature of the dependent variable. ANOVA is the same thing as linear regression. So, here are starting places for v | Categorical Predictors and categorical responses
You use logistic regression. All these forms of regression/ANOVA depend only on the nature of the dependent variable. ANOVA is the same thing as linear regression. So, here are starting places for various types of DV
Continuous, unbounded response with normal errors: ... | Categorical Predictors and categorical responses
You use logistic regression. All these forms of regression/ANOVA depend only on the nature of the dependent variable. ANOVA is the same thing as linear regression. So, here are starting places for v |
55,145 | Categorical Predictors and categorical responses | First: independent of the predictors, if your response has
2 classes (binary), we would usually use a logistic regression
2 classes, we are speaking about a multinomial regression.
Second: regardless of what regression model you use (linear, logistic, multinomial), if you have categorical predictors, most software... | Categorical Predictors and categorical responses | First: independent of the predictors, if your response has
2 classes (binary), we would usually use a logistic regression
2 classes, we are speaking about a multinomial regression.
Second: regard | Categorical Predictors and categorical responses
First: independent of the predictors, if your response has
2 classes (binary), we would usually use a logistic regression
2 classes, we are speaking about a multinomial regression.
Second: regardless of what regression model you use (linear, logistic, multinomial), ... | Categorical Predictors and categorical responses
First: independent of the predictors, if your response has
2 classes (binary), we would usually use a logistic regression
2 classes, we are speaking about a multinomial regression.
Second: regard |
55,146 | How does one extract the final equation from glm poisson model? | The equation is
$$\log(\mu_i) = \beta_0 + \beta_1 x_i$$
where $\mu_i$ is the conditional expectation of $y_i$, $E(y | x)$, $\beta_0$ is the coefficient marked Intercept and $\beta_1$ the coefficient marked x. The $\log$ bit is the link function you specified. Hence to get actual predictions on the scale of your respons... | How does one extract the final equation from glm poisson model? | The equation is
$$\log(\mu_i) = \beta_0 + \beta_1 x_i$$
where $\mu_i$ is the conditional expectation of $y_i$, $E(y | x)$, $\beta_0$ is the coefficient marked Intercept and $\beta_1$ the coefficient m | How does one extract the final equation from glm poisson model?
The equation is
$$\log(\mu_i) = \beta_0 + \beta_1 x_i$$
where $\mu_i$ is the conditional expectation of $y_i$, $E(y | x)$, $\beta_0$ is the coefficient marked Intercept and $\beta_1$ the coefficient marked x. The $\log$ bit is the link function you specifi... | How does one extract the final equation from glm poisson model?
The equation is
$$\log(\mu_i) = \beta_0 + \beta_1 x_i$$
where $\mu_i$ is the conditional expectation of $y_i$, $E(y | x)$, $\beta_0$ is the coefficient marked Intercept and $\beta_1$ the coefficient m |
55,147 | How does one extract the final equation from glm poisson model? | This is great, and I have used it to verify part of a plot in which I am modeling the number of trees counted at certain elevations. However, I am using a zero-inflated Poisson model through zeroinfl() in pscl and the predicted values of zeroinfl() begin to deviate from the equation provided by Gavin after about 1000m ... | How does one extract the final equation from glm poisson model? | This is great, and I have used it to verify part of a plot in which I am modeling the number of trees counted at certain elevations. However, I am using a zero-inflated Poisson model through zeroinfl( | How does one extract the final equation from glm poisson model?
This is great, and I have used it to verify part of a plot in which I am modeling the number of trees counted at certain elevations. However, I am using a zero-inflated Poisson model through zeroinfl() in pscl and the predicted values of zeroinfl() begin t... | How does one extract the final equation from glm poisson model?
This is great, and I have used it to verify part of a plot in which I am modeling the number of trees counted at certain elevations. However, I am using a zero-inflated Poisson model through zeroinfl( |
55,148 | How to do hypothesis testing in this case? | You only have a single sample, so when you call wilcox.test, that's not doing a Wilcoxon-Mann-Whitney, it's doing (as it tells you in the output!) a Wilcoxon signed-rank test.
That doesn't look to me to be directly relevant to the hypothesis in question. With additional assumptions (that don't hold) it could be relevan... | How to do hypothesis testing in this case? | You only have a single sample, so when you call wilcox.test, that's not doing a Wilcoxon-Mann-Whitney, it's doing (as it tells you in the output!) a Wilcoxon signed-rank test.
That doesn't look to me | How to do hypothesis testing in this case?
You only have a single sample, so when you call wilcox.test, that's not doing a Wilcoxon-Mann-Whitney, it's doing (as it tells you in the output!) a Wilcoxon signed-rank test.
That doesn't look to me to be directly relevant to the hypothesis in question. With additional assump... | How to do hypothesis testing in this case?
You only have a single sample, so when you call wilcox.test, that's not doing a Wilcoxon-Mann-Whitney, it's doing (as it tells you in the output!) a Wilcoxon signed-rank test.
That doesn't look to me |
55,149 | How to do hypothesis testing in this case? | By your data 17 of 27 have less than 55 marks, hence failed. This is 63% with a 95% confidence interval of 42.3% to 80.6%. Hence, the hypothesis that MORE THAN 50% will fail with this teaching methodology is still not proven (the confidence interval is going across 50% meaning that the true rate could be LESS THAN 50%)... | How to do hypothesis testing in this case? | By your data 17 of 27 have less than 55 marks, hence failed. This is 63% with a 95% confidence interval of 42.3% to 80.6%. Hence, the hypothesis that MORE THAN 50% will fail with this teaching methodo | How to do hypothesis testing in this case?
By your data 17 of 27 have less than 55 marks, hence failed. This is 63% with a 95% confidence interval of 42.3% to 80.6%. Hence, the hypothesis that MORE THAN 50% will fail with this teaching methodology is still not proven (the confidence interval is going across 50% meaning... | How to do hypothesis testing in this case?
By your data 17 of 27 have less than 55 marks, hence failed. This is 63% with a 95% confidence interval of 42.3% to 80.6%. Hence, the hypothesis that MORE THAN 50% will fail with this teaching methodo |
55,150 | use standard deviation as predictor? | Going by your picture, it looks like what you are proposing is to stratify your data into layers depending on the value of $Y$, then compute the standard deviation of $X$ in each layer, then use that computed group standard deviation as a predictor.
This leaks the true value of $Y$ into your predictors. Of course your... | use standard deviation as predictor? | Going by your picture, it looks like what you are proposing is to stratify your data into layers depending on the value of $Y$, then compute the standard deviation of $X$ in each layer, then use that | use standard deviation as predictor?
Going by your picture, it looks like what you are proposing is to stratify your data into layers depending on the value of $Y$, then compute the standard deviation of $X$ in each layer, then use that computed group standard deviation as a predictor.
This leaks the true value of $Y$ ... | use standard deviation as predictor?
Going by your picture, it looks like what you are proposing is to stratify your data into layers depending on the value of $Y$, then compute the standard deviation of $X$ in each layer, then use that |
55,151 | use standard deviation as predictor? | I understood agenis to say that, in creating the std dev, he wanted to base them on bucketed X values, not Y values. If he were asking about bucketing the Y values, then Matthew Drury would be correct that this would "leak" Y into the predictors. In addition, agenis hasn't said whether or not there is a temporal dimens... | use standard deviation as predictor? | I understood agenis to say that, in creating the std dev, he wanted to base them on bucketed X values, not Y values. If he were asking about bucketing the Y values, then Matthew Drury would be correct | use standard deviation as predictor?
I understood agenis to say that, in creating the std dev, he wanted to base them on bucketed X values, not Y values. If he were asking about bucketing the Y values, then Matthew Drury would be correct that this would "leak" Y into the predictors. In addition, agenis hasn't said whet... | use standard deviation as predictor?
I understood agenis to say that, in creating the std dev, he wanted to base them on bucketed X values, not Y values. If he were asking about bucketing the Y values, then Matthew Drury would be correct |
55,152 | LASSO with two predictors | The two formulas
$$\hat\beta_1=[s/2+(\hat\beta^{(ols)}_1-\hat\beta^{(ols)}_2)/2]^+\qquad\qquad(1)$$
and
$$\hat\beta_2=[s/2-(\hat\beta^{(ols)}_1-\hat\beta^{(ols)}_2)/2]^+\qquad\qquad(2)$$
are inconsistent with the budget equation
$$\hat\beta_1+\hat\beta_2 = s$$
in the case where only one predictor is in the model. Not... | LASSO with two predictors | The two formulas
$$\hat\beta_1=[s/2+(\hat\beta^{(ols)}_1-\hat\beta^{(ols)}_2)/2]^+\qquad\qquad(1)$$
and
$$\hat\beta_2=[s/2-(\hat\beta^{(ols)}_1-\hat\beta^{(ols)}_2)/2]^+\qquad\qquad(2)$$
are inconsist | LASSO with two predictors
The two formulas
$$\hat\beta_1=[s/2+(\hat\beta^{(ols)}_1-\hat\beta^{(ols)}_2)/2]^+\qquad\qquad(1)$$
and
$$\hat\beta_2=[s/2-(\hat\beta^{(ols)}_1-\hat\beta^{(ols)}_2)/2]^+\qquad\qquad(2)$$
are inconsistent with the budget equation
$$\hat\beta_1+\hat\beta_2 = s$$
in the case where only one predi... | LASSO with two predictors
The two formulas
$$\hat\beta_1=[s/2+(\hat\beta^{(ols)}_1-\hat\beta^{(ols)}_2)/2]^+\qquad\qquad(1)$$
and
$$\hat\beta_2=[s/2-(\hat\beta^{(ols)}_1-\hat\beta^{(ols)}_2)/2]^+\qquad\qquad(2)$$
are inconsist |
55,153 | How to detect noisy datasets (bias and variance trade-off) | When noise is "large" then learning is not pointless, but it's "expensive" in some sense. For instance, you know the expression "house always wins". It means that the odds favor the casino against the gambler. However, the odds can be very close to 1:1, they may only so slightly be tilted towards the "house", e.g. 0.5%... | How to detect noisy datasets (bias and variance trade-off) | When noise is "large" then learning is not pointless, but it's "expensive" in some sense. For instance, you know the expression "house always wins". It means that the odds favor the casino against the | How to detect noisy datasets (bias and variance trade-off)
When noise is "large" then learning is not pointless, but it's "expensive" in some sense. For instance, you know the expression "house always wins". It means that the odds favor the casino against the gambler. However, the odds can be very close to 1:1, they ma... | How to detect noisy datasets (bias and variance trade-off)
When noise is "large" then learning is not pointless, but it's "expensive" in some sense. For instance, you know the expression "house always wins". It means that the odds favor the casino against the |
55,154 | Is it possible for an expected value not to exist? [duplicate] | You can find the answer on Wikipedia http://en.wikipedia.org/wiki/Cauchy_distribution. However, you are right, the integral for $E(X)$ does not converge, hence it means that $E(X)$ is undefined. Whereas for $E(X^2)$ it evaluates to infinity, e.g. $E(X^2)=\infty$. Therefore, in this case $Var(X) = E(X^2)-E(X)^2$ is unde... | Is it possible for an expected value not to exist? [duplicate] | You can find the answer on Wikipedia http://en.wikipedia.org/wiki/Cauchy_distribution. However, you are right, the integral for $E(X)$ does not converge, hence it means that $E(X)$ is undefined. Where | Is it possible for an expected value not to exist? [duplicate]
You can find the answer on Wikipedia http://en.wikipedia.org/wiki/Cauchy_distribution. However, you are right, the integral for $E(X)$ does not converge, hence it means that $E(X)$ is undefined. Whereas for $E(X^2)$ it evaluates to infinity, e.g. $E(X^2)=\i... | Is it possible for an expected value not to exist? [duplicate]
You can find the answer on Wikipedia http://en.wikipedia.org/wiki/Cauchy_distribution. However, you are right, the integral for $E(X)$ does not converge, hence it means that $E(X)$ is undefined. Where |
55,155 | LASSO and related path algorithms | The Lasso is the solution to
$$\hat{\beta} \in argmin_\beta \frac{1}{2n}\Vert y-X\beta\Vert_2^2 + \lambda\Vert\beta\Vert_1$$
Evidently, $\hat{\beta}$ also depends on $\lambda$, so really, we could write this dependence explicitly: $\hat{\beta}(\lambda)$. Thus, we can interpret $\hat{\beta}$ as a function $\lambda\maps... | LASSO and related path algorithms | The Lasso is the solution to
$$\hat{\beta} \in argmin_\beta \frac{1}{2n}\Vert y-X\beta\Vert_2^2 + \lambda\Vert\beta\Vert_1$$
Evidently, $\hat{\beta}$ also depends on $\lambda$, so really, we could wr | LASSO and related path algorithms
The Lasso is the solution to
$$\hat{\beta} \in argmin_\beta \frac{1}{2n}\Vert y-X\beta\Vert_2^2 + \lambda\Vert\beta\Vert_1$$
Evidently, $\hat{\beta}$ also depends on $\lambda$, so really, we could write this dependence explicitly: $\hat{\beta}(\lambda)$. Thus, we can interpret $\hat{\... | LASSO and related path algorithms
The Lasso is the solution to
$$\hat{\beta} \in argmin_\beta \frac{1}{2n}\Vert y-X\beta\Vert_2^2 + \lambda\Vert\beta\Vert_1$$
Evidently, $\hat{\beta}$ also depends on $\lambda$, so really, we could wr |
55,156 | Standard error of the combination of estimated parameters | Usually when you estimate the model you get the covariance matrix of the parameter estimates. If you assume that the parameter estimates are normally distributed (a standard assumption for large samples and small samples with normal errors), then you have the correlation coefficient between parameter estimates, their m... | Standard error of the combination of estimated parameters | Usually when you estimate the model you get the covariance matrix of the parameter estimates. If you assume that the parameter estimates are normally distributed (a standard assumption for large sampl | Standard error of the combination of estimated parameters
Usually when you estimate the model you get the covariance matrix of the parameter estimates. If you assume that the parameter estimates are normally distributed (a standard assumption for large samples and small samples with normal errors), then you have the co... | Standard error of the combination of estimated parameters
Usually when you estimate the model you get the covariance matrix of the parameter estimates. If you assume that the parameter estimates are normally distributed (a standard assumption for large sampl |
55,157 | Standard error of the combination of estimated parameters | We usually use the exact same symbol to denote the obtained estimate of a parameter (a number) and the estimator we used, which is a random variable (a function). To distinguish, I will use the following notation:
True values of unknown paramters : $\alpha,\beta$
Obtained estimates from a specific sample: $\hat \alpha,... | Standard error of the combination of estimated parameters | We usually use the exact same symbol to denote the obtained estimate of a parameter (a number) and the estimator we used, which is a random variable (a function). To distinguish, I will use the follow | Standard error of the combination of estimated parameters
We usually use the exact same symbol to denote the obtained estimate of a parameter (a number) and the estimator we used, which is a random variable (a function). To distinguish, I will use the following notation:
True values of unknown paramters : $\alpha,\beta... | Standard error of the combination of estimated parameters
We usually use the exact same symbol to denote the obtained estimate of a parameter (a number) and the estimator we used, which is a random variable (a function). To distinguish, I will use the follow |
55,158 | Modelling a binary outcome when census interval varies | An alternative and slightly easier approach is to use a complementary log-log link (cloglog), which estimates the log-hazard rather than the log-odds of outcomes such as mortality. Copying from rpubs:
A very common situation in ecology (and elsewhere) is a survival/binary-outcome model where individuals (each measured... | Modelling a binary outcome when census interval varies | An alternative and slightly easier approach is to use a complementary log-log link (cloglog), which estimates the log-hazard rather than the log-odds of outcomes such as mortality. Copying from rpubs | Modelling a binary outcome when census interval varies
An alternative and slightly easier approach is to use a complementary log-log link (cloglog), which estimates the log-hazard rather than the log-odds of outcomes such as mortality. Copying from rpubs:
A very common situation in ecology (and elsewhere) is a surviva... | Modelling a binary outcome when census interval varies
An alternative and slightly easier approach is to use a complementary log-log link (cloglog), which estimates the log-hazard rather than the log-odds of outcomes such as mortality. Copying from rpubs |
55,159 | Interpreting prior and posterior | Using the same approach, you can compute the posterior probability that the coin is fair. (Do the exercise!) What do you make of the result? | Interpreting prior and posterior | Using the same approach, you can compute the posterior probability that the coin is fair. (Do the exercise!) What do you make of the result? | Interpreting prior and posterior
Using the same approach, you can compute the posterior probability that the coin is fair. (Do the exercise!) What do you make of the result? | Interpreting prior and posterior
Using the same approach, you can compute the posterior probability that the coin is fair. (Do the exercise!) What do you make of the result? |
55,160 | Interpretation of continuous variable in dummy-continuous interaction | Yes, that is correct in your case. A good way to convince yourself of that statement follows.
Say you want to find the impact of the pollution level on the log of house prices.
$$ \dfrac{\partial \ ln(housePrice)} {\partial \ pollutionLevel} = \beta_1 + \beta_3 \times D_N $$
where the impact of the pollution level on t... | Interpretation of continuous variable in dummy-continuous interaction | Yes, that is correct in your case. A good way to convince yourself of that statement follows.
Say you want to find the impact of the pollution level on the log of house prices.
$$ \dfrac{\partial \ ln | Interpretation of continuous variable in dummy-continuous interaction
Yes, that is correct in your case. A good way to convince yourself of that statement follows.
Say you want to find the impact of the pollution level on the log of house prices.
$$ \dfrac{\partial \ ln(housePrice)} {\partial \ pollutionLevel} = \beta_... | Interpretation of continuous variable in dummy-continuous interaction
Yes, that is correct in your case. A good way to convince yourself of that statement follows.
Say you want to find the impact of the pollution level on the log of house prices.
$$ \dfrac{\partial \ ln |
55,161 | Interpretation of continuous variable in dummy-continuous interaction | One way to generally look at this is via marginal effects as in @Giaco.Metrics' response. Another general technique is a distinction of cases.
For $D_N = 0$ (no school nearby, reference group), your equation simplifies to:
$\ln(housePrice) = \beta_1 \times pollutionLevel + u$,
i.e., you have intercept 0 and slope $\bet... | Interpretation of continuous variable in dummy-continuous interaction | One way to generally look at this is via marginal effects as in @Giaco.Metrics' response. Another general technique is a distinction of cases.
For $D_N = 0$ (no school nearby, reference group), your e | Interpretation of continuous variable in dummy-continuous interaction
One way to generally look at this is via marginal effects as in @Giaco.Metrics' response. Another general technique is a distinction of cases.
For $D_N = 0$ (no school nearby, reference group), your equation simplifies to:
$\ln(housePrice) = \beta_1 ... | Interpretation of continuous variable in dummy-continuous interaction
One way to generally look at this is via marginal effects as in @Giaco.Metrics' response. Another general technique is a distinction of cases.
For $D_N = 0$ (no school nearby, reference group), your e |
55,162 | Why do we need PCA whitening before feeding into autoencoder? | Natural images have a lot of variance/energy in low spatial frequency components and little variance/energy in high spatial frequency components*. When using squared Euclidean distance to evaluate the reconstruction of an autoencoder, this means that the network will focus on getting the low spatial frequencies right, ... | Why do we need PCA whitening before feeding into autoencoder? | Natural images have a lot of variance/energy in low spatial frequency components and little variance/energy in high spatial frequency components*. When using squared Euclidean distance to evaluate the | Why do we need PCA whitening before feeding into autoencoder?
Natural images have a lot of variance/energy in low spatial frequency components and little variance/energy in high spatial frequency components*. When using squared Euclidean distance to evaluate the reconstruction of an autoencoder, this means that the net... | Why do we need PCA whitening before feeding into autoencoder?
Natural images have a lot of variance/energy in low spatial frequency components and little variance/energy in high spatial frequency components*. When using squared Euclidean distance to evaluate the |
55,163 | Why do we need PCA whitening before feeding into autoencoder? | The tutorial only said "each variable comes from an IID Gaussian independent of the other features". Independence implies uncorrelation, but uncorrelation does not imply independence. Even if data get processed by PCA, features become uncorrelated, but it does not imply features become independent of each other. | Why do we need PCA whitening before feeding into autoencoder? | The tutorial only said "each variable comes from an IID Gaussian independent of the other features". Independence implies uncorrelation, but uncorrelation does not imply independence. Even if data get | Why do we need PCA whitening before feeding into autoencoder?
The tutorial only said "each variable comes from an IID Gaussian independent of the other features". Independence implies uncorrelation, but uncorrelation does not imply independence. Even if data get processed by PCA, features become uncorrelated, but it do... | Why do we need PCA whitening before feeding into autoencoder?
The tutorial only said "each variable comes from an IID Gaussian independent of the other features". Independence implies uncorrelation, but uncorrelation does not imply independence. Even if data get |
55,164 | R mtcars dataset - linear regression of MPG in Auto and Manual transmission mode | The models are equivalent. The misconception here is that overlapping confidence intervals do not mean you "failed to reject the null hypothesis." You do not compare the upper/lower bounds of confidence intervals and call it a day. Thomas' comment links1 to a good general explanation of why this is, though it doesn't d... | R mtcars dataset - linear regression of MPG in Auto and Manual transmission mode | The models are equivalent. The misconception here is that overlapping confidence intervals do not mean you "failed to reject the null hypothesis." You do not compare the upper/lower bounds of confiden | R mtcars dataset - linear regression of MPG in Auto and Manual transmission mode
The models are equivalent. The misconception here is that overlapping confidence intervals do not mean you "failed to reject the null hypothesis." You do not compare the upper/lower bounds of confidence intervals and call it a day. Thomas'... | R mtcars dataset - linear regression of MPG in Auto and Manual transmission mode
The models are equivalent. The misconception here is that overlapping confidence intervals do not mean you "failed to reject the null hypothesis." You do not compare the upper/lower bounds of confiden |
55,165 | R mtcars dataset - linear regression of MPG in Auto and Manual transmission mode | In these linear models, the null hypothesis is actually that there is no effect,i.e. the coefficient is equal to zero. Therefore, in the output of summary(lm()) the conclusion is that there is no significant difference between automatic and manual transmission. And this is in line with your observation that the confide... | R mtcars dataset - linear regression of MPG in Auto and Manual transmission mode | In these linear models, the null hypothesis is actually that there is no effect,i.e. the coefficient is equal to zero. Therefore, in the output of summary(lm()) the conclusion is that there is no sign | R mtcars dataset - linear regression of MPG in Auto and Manual transmission mode
In these linear models, the null hypothesis is actually that there is no effect,i.e. the coefficient is equal to zero. Therefore, in the output of summary(lm()) the conclusion is that there is no significant difference between automatic an... | R mtcars dataset - linear regression of MPG in Auto and Manual transmission mode
In these linear models, the null hypothesis is actually that there is no effect,i.e. the coefficient is equal to zero. Therefore, in the output of summary(lm()) the conclusion is that there is no sign |
55,166 | Why does Pearson's r have a non-normal sampling distribution at high values of ρ? | This is just a short answer without mathematical details, but:
Because if your $r$ is high you get a non-symmetric distribution. For example, if the real correlation is $0.9$ you might, by chance, observe a sample correlation of $0.75$. But you will never observe a sample correlation of $1.05$. Generally many normal a... | Why does Pearson's r have a non-normal sampling distribution at high values of ρ? | This is just a short answer without mathematical details, but:
Because if your $r$ is high you get a non-symmetric distribution. For example, if the real correlation is $0.9$ you might, by chance, ob | Why does Pearson's r have a non-normal sampling distribution at high values of ρ?
This is just a short answer without mathematical details, but:
Because if your $r$ is high you get a non-symmetric distribution. For example, if the real correlation is $0.9$ you might, by chance, observe a sample correlation of $0.75$. ... | Why does Pearson's r have a non-normal sampling distribution at high values of ρ?
This is just a short answer without mathematical details, but:
Because if your $r$ is high you get a non-symmetric distribution. For example, if the real correlation is $0.9$ you might, by chance, ob |
55,167 | Finding UMVUE of Bernoulli random variables | The idea is that you can start with any estimator of $(1-\theta)^2$, no matter how awful, provided it is unbiased. The Rao-Blackwell process will almost magically turn it into a uniformly minimum-variance unbiased estimator (UMVUE).
There are many ways to proceed. One fruitful idea is systematically to remove the com... | Finding UMVUE of Bernoulli random variables | The idea is that you can start with any estimator of $(1-\theta)^2$, no matter how awful, provided it is unbiased. The Rao-Blackwell process will almost magically turn it into a uniformly minimum-var | Finding UMVUE of Bernoulli random variables
The idea is that you can start with any estimator of $(1-\theta)^2$, no matter how awful, provided it is unbiased. The Rao-Blackwell process will almost magically turn it into a uniformly minimum-variance unbiased estimator (UMVUE).
There are many ways to proceed. One fruit... | Finding UMVUE of Bernoulli random variables
The idea is that you can start with any estimator of $(1-\theta)^2$, no matter how awful, provided it is unbiased. The Rao-Blackwell process will almost magically turn it into a uniformly minimum-var |
55,168 | Definition of $X_t$ in the context of Stochastic process and Time Series | Parameters in a statistical sense are not realizations of a random variable:
A statistical parameter is a parameter that indexes a family of
probability distributions. It can be regarded as a numerical
characteristic of a population or a statistical model.
So $T$ will simply be some parameter space (for stochasti... | Definition of $X_t$ in the context of Stochastic process and Time Series | Parameters in a statistical sense are not realizations of a random variable:
A statistical parameter is a parameter that indexes a family of
probability distributions. It can be regarded as a numer | Definition of $X_t$ in the context of Stochastic process and Time Series
Parameters in a statistical sense are not realizations of a random variable:
A statistical parameter is a parameter that indexes a family of
probability distributions. It can be regarded as a numerical
characteristic of a population or a stat... | Definition of $X_t$ in the context of Stochastic process and Time Series
Parameters in a statistical sense are not realizations of a random variable:
A statistical parameter is a parameter that indexes a family of
probability distributions. It can be regarded as a numer |
55,169 | Definition of $X_t$ in the context of Stochastic process and Time Series | The term parameter can different meanings in different settings. In statistics it is a usually a property of random variable which we want to estimate. In mathematics it is a simply a property of a mathematical object which is not constant. The stochastic processes literature usually follows mathematical conventions, s... | Definition of $X_t$ in the context of Stochastic process and Time Series | The term parameter can different meanings in different settings. In statistics it is a usually a property of random variable which we want to estimate. In mathematics it is a simply a property of a ma | Definition of $X_t$ in the context of Stochastic process and Time Series
The term parameter can different meanings in different settings. In statistics it is a usually a property of random variable which we want to estimate. In mathematics it is a simply a property of a mathematical object which is not constant. The st... | Definition of $X_t$ in the context of Stochastic process and Time Series
The term parameter can different meanings in different settings. In statistics it is a usually a property of random variable which we want to estimate. In mathematics it is a simply a property of a ma |
55,170 | Is the cumulative incidence function just an inverted Kaplan-Meier survival curve? | If you're talking about the cumulative incidence function that arises from a Kaplan-Meier estimator, then it's just $1 - S(t)$ where $t$ is time. In R:
library(survival)
fit <- survfit(Surv(time, status) ~ x, data = aml)
plot(fit) # the standard survival curve
plot(fit, fun="event") # the cumulative incidence curve
Bu... | Is the cumulative incidence function just an inverted Kaplan-Meier survival curve? | If you're talking about the cumulative incidence function that arises from a Kaplan-Meier estimator, then it's just $1 - S(t)$ where $t$ is time. In R:
library(survival)
fit <- survfit(Surv(time, stat | Is the cumulative incidence function just an inverted Kaplan-Meier survival curve?
If you're talking about the cumulative incidence function that arises from a Kaplan-Meier estimator, then it's just $1 - S(t)$ where $t$ is time. In R:
library(survival)
fit <- survfit(Surv(time, status) ~ x, data = aml)
plot(fit) # the ... | Is the cumulative incidence function just an inverted Kaplan-Meier survival curve?
If you're talking about the cumulative incidence function that arises from a Kaplan-Meier estimator, then it's just $1 - S(t)$ where $t$ is time. In R:
library(survival)
fit <- survfit(Surv(time, stat |
55,171 | Estimating conditional effect of logistic regression | You can include terms with fixed coefficients using an offset. Technically, an offset is a predictor with coefficient fixed at 1, so you will first need to create a new variable that has the linear combination of the $X$'s with coefficients estimated from the first model.
Model for first data set:
$$logit(P(Y=1)) = \be... | Estimating conditional effect of logistic regression | You can include terms with fixed coefficients using an offset. Technically, an offset is a predictor with coefficient fixed at 1, so you will first need to create a new variable that has the linear co | Estimating conditional effect of logistic regression
You can include terms with fixed coefficients using an offset. Technically, an offset is a predictor with coefficient fixed at 1, so you will first need to create a new variable that has the linear combination of the $X$'s with coefficients estimated from the first m... | Estimating conditional effect of logistic regression
You can include terms with fixed coefficients using an offset. Technically, an offset is a predictor with coefficient fixed at 1, so you will first need to create a new variable that has the linear co |
55,172 | Why is the p-value for Cohen's $d$ not equal to the p-value of a t-test? | Cohen's d is a measure of the standardized difference in means.
(mean($X_1$)-mean ($X_2$))/sigma
So the null hypothesis tests whether this standardized difference is equal to zero. This is different from the original null hypothesis which tests whether the non-standardized difference in means is equal to zero.
It migh... | Why is the p-value for Cohen's $d$ not equal to the p-value of a t-test? | Cohen's d is a measure of the standardized difference in means.
(mean($X_1$)-mean ($X_2$))/sigma
So the null hypothesis tests whether this standardized difference is equal to zero. This is different | Why is the p-value for Cohen's $d$ not equal to the p-value of a t-test?
Cohen's d is a measure of the standardized difference in means.
(mean($X_1$)-mean ($X_2$))/sigma
So the null hypothesis tests whether this standardized difference is equal to zero. This is different from the original null hypothesis which tests w... | Why is the p-value for Cohen's $d$ not equal to the p-value of a t-test?
Cohen's d is a measure of the standardized difference in means.
(mean($X_1$)-mean ($X_2$))/sigma
So the null hypothesis tests whether this standardized difference is equal to zero. This is different |
55,173 | Some basic questions related to the moments of a probability distribution | Existence. If we have a random variable $x$ with the density function $f(x)$, then we know that $$\int_{-\infty}^\infty f(x) dx=1$$ rewrite this as follows $$1=\int_{-\infty}^\infty 1\cdot f(x) dx\ge |\int_{-\infty}^\infty(\cos tx + i \sin tx)\cdot f(x) dx|$$ simply because $$1\ge |\cos tx + i \sin tx|$$
Hence, charac... | Some basic questions related to the moments of a probability distribution | Existence. If we have a random variable $x$ with the density function $f(x)$, then we know that $$\int_{-\infty}^\infty f(x) dx=1$$ rewrite this as follows $$1=\int_{-\infty}^\infty 1\cdot f(x) dx\ge | Some basic questions related to the moments of a probability distribution
Existence. If we have a random variable $x$ with the density function $f(x)$, then we know that $$\int_{-\infty}^\infty f(x) dx=1$$ rewrite this as follows $$1=\int_{-\infty}^\infty 1\cdot f(x) dx\ge |\int_{-\infty}^\infty(\cos tx + i \sin tx)\cd... | Some basic questions related to the moments of a probability distribution
Existence. If we have a random variable $x$ with the density function $f(x)$, then we know that $$\int_{-\infty}^\infty f(x) dx=1$$ rewrite this as follows $$1=\int_{-\infty}^\infty 1\cdot f(x) dx\ge |
55,174 | Biostatistics book for mathematician | In addition to the already recommended Frank Harrell's nice book (which I look forward to reading), I would like to share the following - and hopefully relevant - resources:
Book "Regression Methods in Biostatistics: Linear, Logistic, Survival, and Repeated Measures Models". The examples are in Stata, in case, if you ... | Biostatistics book for mathematician | In addition to the already recommended Frank Harrell's nice book (which I look forward to reading), I would like to share the following - and hopefully relevant - resources:
Book "Regression Methods | Biostatistics book for mathematician
In addition to the already recommended Frank Harrell's nice book (which I look forward to reading), I would like to share the following - and hopefully relevant - resources:
Book "Regression Methods in Biostatistics: Linear, Logistic, Survival, and Repeated Measures Models". The ex... | Biostatistics book for mathematician
In addition to the already recommended Frank Harrell's nice book (which I look forward to reading), I would like to share the following - and hopefully relevant - resources:
Book "Regression Methods |
55,175 | Biostatistics book for mathematician | you mention at the end of your Q that "I am thinking of selling myself as a biostatistician" in the industry in europe. In that case, it would make more sense to read the regulatory guidelines and books about the drug development process, and to sharpen your SAS skills and knowledge of cdisc, sdtm, adam. Large randomis... | Biostatistics book for mathematician | you mention at the end of your Q that "I am thinking of selling myself as a biostatistician" in the industry in europe. In that case, it would make more sense to read the regulatory guidelines and boo | Biostatistics book for mathematician
you mention at the end of your Q that "I am thinking of selling myself as a biostatistician" in the industry in europe. In that case, it would make more sense to read the regulatory guidelines and books about the drug development process, and to sharpen your SAS skills and knowledge... | Biostatistics book for mathematician
you mention at the end of your Q that "I am thinking of selling myself as a biostatistician" in the industry in europe. In that case, it would make more sense to read the regulatory guidelines and boo |
55,176 | Biostatistics book for mathematician | You need to start with something on the applied side, like Frank Harrell: "Regression Modeling Strategies: With Applications to Linear Models, Logistic Regression, and Survival Analysis (Springer Series in Statistics) "
Then you can go deep into the underlying mathematics wih somethingh like PER KRAGH ANDERSEN and Ørnu... | Biostatistics book for mathematician | You need to start with something on the applied side, like Frank Harrell: "Regression Modeling Strategies: With Applications to Linear Models, Logistic Regression, and Survival Analysis (Springer Seri | Biostatistics book for mathematician
You need to start with something on the applied side, like Frank Harrell: "Regression Modeling Strategies: With Applications to Linear Models, Logistic Regression, and Survival Analysis (Springer Series in Statistics) "
Then you can go deep into the underlying mathematics wih someth... | Biostatistics book for mathematician
You need to start with something on the applied side, like Frank Harrell: "Regression Modeling Strategies: With Applications to Linear Models, Logistic Regression, and Survival Analysis (Springer Seri |
55,177 | Should I find this big parameter suspicious? | If $X$ has a logistic distribution with location parameter $\mu$ and scale parameter $\sigma$
$$\newcommand{\e}{\mathrm{e}}f(x) = \frac{\exp\left(\frac{x-\mu}{\sigma}\right)}{\sigma \left[1+ \exp\left(\frac{x-\mu}{\sigma}\right)\right]^2}$$
then $Y=\log(X)$ has a log-logistic distribution
$$f(y) = \frac{ \frac{\sigma^{... | Should I find this big parameter suspicious? | If $X$ has a logistic distribution with location parameter $\mu$ and scale parameter $\sigma$
$$\newcommand{\e}{\mathrm{e}}f(x) = \frac{\exp\left(\frac{x-\mu}{\sigma}\right)}{\sigma \left[1+ \exp\left | Should I find this big parameter suspicious?
If $X$ has a logistic distribution with location parameter $\mu$ and scale parameter $\sigma$
$$\newcommand{\e}{\mathrm{e}}f(x) = \frac{\exp\left(\frac{x-\mu}{\sigma}\right)}{\sigma \left[1+ \exp\left(\frac{x-\mu}{\sigma}\right)\right]^2}$$
then $Y=\log(X)$ has a log-logisti... | Should I find this big parameter suspicious?
If $X$ has a logistic distribution with location parameter $\mu$ and scale parameter $\sigma$
$$\newcommand{\e}{\mathrm{e}}f(x) = \frac{\exp\left(\frac{x-\mu}{\sigma}\right)}{\sigma \left[1+ \exp\left |
55,178 | Derivation of cumulative Binomial Distribution expression | I think you'll find it difficult to prove, because it is not true unless $p = 0.5$.
Consider the simple case of $n = 1$, $r = 1$. Then:
$P(Y \geq r) = P(Y = 1) = p$
$P(Y \leq n - r) = P(Y = 0) = 1 - p$.
Starting with the LHS of your second equation, if you substitute $j = n - x$ and use ${n \choose j} = {n \choose {n-j... | Derivation of cumulative Binomial Distribution expression | I think you'll find it difficult to prove, because it is not true unless $p = 0.5$.
Consider the simple case of $n = 1$, $r = 1$. Then:
$P(Y \geq r) = P(Y = 1) = p$
$P(Y \leq n - r) = P(Y = 0) = 1 - p | Derivation of cumulative Binomial Distribution expression
I think you'll find it difficult to prove, because it is not true unless $p = 0.5$.
Consider the simple case of $n = 1$, $r = 1$. Then:
$P(Y \geq r) = P(Y = 1) = p$
$P(Y \leq n - r) = P(Y = 0) = 1 - p$.
Starting with the LHS of your second equation, if you subst... | Derivation of cumulative Binomial Distribution expression
I think you'll find it difficult to prove, because it is not true unless $p = 0.5$.
Consider the simple case of $n = 1$, $r = 1$. Then:
$P(Y \geq r) = P(Y = 1) = p$
$P(Y \leq n - r) = P(Y = 0) = 1 - p |
55,179 | Is it an assumption of the normal linear model that explanatory variables are uncorrelated with the errors? | I wouldn't quite call this an assumption of the linear model. Instead, I would say that this is an assumption you are making when you interpret the results of a linear model in a particular way. In other words, when the stated condition holds, there may be multiple possible interpretations of which some are legitimat... | Is it an assumption of the normal linear model that explanatory variables are uncorrelated with the | I wouldn't quite call this an assumption of the linear model. Instead, I would say that this is an assumption you are making when you interpret the results of a linear model in a particular way. In | Is it an assumption of the normal linear model that explanatory variables are uncorrelated with the errors?
I wouldn't quite call this an assumption of the linear model. Instead, I would say that this is an assumption you are making when you interpret the results of a linear model in a particular way. In other words,... | Is it an assumption of the normal linear model that explanatory variables are uncorrelated with the
I wouldn't quite call this an assumption of the linear model. Instead, I would say that this is an assumption you are making when you interpret the results of a linear model in a particular way. In |
55,180 | Is it an assumption of the normal linear model that explanatory variables are uncorrelated with the errors? | I find the phrase "no correlation" potentially misleading, because I have noticed that sometimes the word correlation is used narrowly, to refer to the covariance between two random variables and whether it is zero or not, and sometimes it is used more broadly, to indicate whether there exists (or not) some unspecified... | Is it an assumption of the normal linear model that explanatory variables are uncorrelated with the | I find the phrase "no correlation" potentially misleading, because I have noticed that sometimes the word correlation is used narrowly, to refer to the covariance between two random variables and whet | Is it an assumption of the normal linear model that explanatory variables are uncorrelated with the errors?
I find the phrase "no correlation" potentially misleading, because I have noticed that sometimes the word correlation is used narrowly, to refer to the covariance between two random variables and whether it is ze... | Is it an assumption of the normal linear model that explanatory variables are uncorrelated with the
I find the phrase "no correlation" potentially misleading, because I have noticed that sometimes the word correlation is used narrowly, to refer to the covariance between two random variables and whet |
55,181 | Endogeneity test instrumental variables | What you are looking at is formally known as the control function approach. When you run your first stage
$$x_3 = b_0 + b_1x_1 +b_2x_2 + b_3z + u$$
you basically split the variation in $x_3$ into exogenous variation (that comes from the exogenous and instrumental variables), and you leave the "bad" variation that is co... | Endogeneity test instrumental variables | What you are looking at is formally known as the control function approach. When you run your first stage
$$x_3 = b_0 + b_1x_1 +b_2x_2 + b_3z + u$$
you basically split the variation in $x_3$ into exog | Endogeneity test instrumental variables
What you are looking at is formally known as the control function approach. When you run your first stage
$$x_3 = b_0 + b_1x_1 +b_2x_2 + b_3z + u$$
you basically split the variation in $x_3$ into exogenous variation (that comes from the exogenous and instrumental variables), and ... | Endogeneity test instrumental variables
What you are looking at is formally known as the control function approach. When you run your first stage
$$x_3 = b_0 + b_1x_1 +b_2x_2 + b_3z + u$$
you basically split the variation in $x_3$ into exog |
55,182 | Which statistical test to use to test differences in multiple means (multiple populations) | If you want a multi-group analog of a t-test it sounds like you just want ANOVA (analysis of variance) or something similar to it. That's exactly what it's for - comparing group means.
Specifically, you seem to be asking for one-way analysis of variance.
Any decent statistics package does ANOVA.
If you don't want to ... | Which statistical test to use to test differences in multiple means (multiple populations) | If you want a multi-group analog of a t-test it sounds like you just want ANOVA (analysis of variance) or something similar to it. That's exactly what it's for - comparing group means.
Specifically, | Which statistical test to use to test differences in multiple means (multiple populations)
If you want a multi-group analog of a t-test it sounds like you just want ANOVA (analysis of variance) or something similar to it. That's exactly what it's for - comparing group means.
Specifically, you seem to be asking for one... | Which statistical test to use to test differences in multiple means (multiple populations)
If you want a multi-group analog of a t-test it sounds like you just want ANOVA (analysis of variance) or something similar to it. That's exactly what it's for - comparing group means.
Specifically, |
55,183 | How to detect random clicks on a page? | I presume your intent is to identify the agent as human or random by choosing the one with the smaller chi-square (assuming you can get an expected human pattern), essentially treating it as a classification problem. If you are treating it as one, you might want to consider the costs of the two types of misclassificati... | How to detect random clicks on a page? | I presume your intent is to identify the agent as human or random by choosing the one with the smaller chi-square (assuming you can get an expected human pattern), essentially treating it as a classif | How to detect random clicks on a page?
I presume your intent is to identify the agent as human or random by choosing the one with the smaller chi-square (assuming you can get an expected human pattern), essentially treating it as a classification problem. If you are treating it as one, you might want to consider the co... | How to detect random clicks on a page?
I presume your intent is to identify the agent as human or random by choosing the one with the smaller chi-square (assuming you can get an expected human pattern), essentially treating it as a classif |
55,184 | Transformation of variables (Metropolis Hastings) | You do not need the $\alpha$ since it is a parameter. The change of variables formula applies to the variable with respect to which you are "integrating". It is $x$ in your case. So MH is right to demand that you remove the excess factor.
So what you really have is:
$$
p(X|\alpha) = \frac{\exp(-\exp(\alpha))\exp(\alpha... | Transformation of variables (Metropolis Hastings) | You do not need the $\alpha$ since it is a parameter. The change of variables formula applies to the variable with respect to which you are "integrating". It is $x$ in your case. So MH is right to dem | Transformation of variables (Metropolis Hastings)
You do not need the $\alpha$ since it is a parameter. The change of variables formula applies to the variable with respect to which you are "integrating". It is $x$ in your case. So MH is right to demand that you remove the excess factor.
So what you really have is:
$$
... | Transformation of variables (Metropolis Hastings)
You do not need the $\alpha$ since it is a parameter. The change of variables formula applies to the variable with respect to which you are "integrating". It is $x$ in your case. So MH is right to dem |
55,185 | Transformation of variables (Metropolis Hastings) | Check your code, particularly the factors of N (number of data points) appearing in the likelihood. I find consistent results with the Jacobian factor (so the extra alpha) included in the log-posterior, and inconsistent inferences when I do not include the Jacobian (the opposite to what you say you are finding). The Ja... | Transformation of variables (Metropolis Hastings) | Check your code, particularly the factors of N (number of data points) appearing in the likelihood. I find consistent results with the Jacobian factor (so the extra alpha) included in the log-posterio | Transformation of variables (Metropolis Hastings)
Check your code, particularly the factors of N (number of data points) appearing in the likelihood. I find consistent results with the Jacobian factor (so the extra alpha) included in the log-posterior, and inconsistent inferences when I do not include the Jacobian (the... | Transformation of variables (Metropolis Hastings)
Check your code, particularly the factors of N (number of data points) appearing in the likelihood. I find consistent results with the Jacobian factor (so the extra alpha) included in the log-posterio |
55,186 | Example of dependence with zero covariance | Among spherically symmetric distributions, i.e. distributions of the form $f(\boldsymbol x) = \varphi(\|\boldsymbol x\|)$ where $f$ is the density with respect to Lebesgue measure, it can be shown that the coordinates always have zero correlation, essentially due to the fact that the distribution is invariant under ort... | Example of dependence with zero covariance | Among spherically symmetric distributions, i.e. distributions of the form $f(\boldsymbol x) = \varphi(\|\boldsymbol x\|)$ where $f$ is the density with respect to Lebesgue measure, it can be shown tha | Example of dependence with zero covariance
Among spherically symmetric distributions, i.e. distributions of the form $f(\boldsymbol x) = \varphi(\|\boldsymbol x\|)$ where $f$ is the density with respect to Lebesgue measure, it can be shown that the coordinates always have zero correlation, essentially due to the fact t... | Example of dependence with zero covariance
Among spherically symmetric distributions, i.e. distributions of the form $f(\boldsymbol x) = \varphi(\|\boldsymbol x\|)$ where $f$ is the density with respect to Lebesgue measure, it can be shown tha |
55,187 | Example of dependence with zero covariance | The last row of the first image of https://en.wikipedia.org/wiki/Correlation_and_dependence provide exemple where the Pearson correlation is 0 but there is strong non-linear dependance between X and Y.
The relation $\rho=0$ is quite strong in general but easily obtainable considering discrete and / or symetrical distr... | Example of dependence with zero covariance | The last row of the first image of https://en.wikipedia.org/wiki/Correlation_and_dependence provide exemple where the Pearson correlation is 0 but there is strong non-linear dependance between X and Y | Example of dependence with zero covariance
The last row of the first image of https://en.wikipedia.org/wiki/Correlation_and_dependence provide exemple where the Pearson correlation is 0 but there is strong non-linear dependance between X and Y.
The relation $\rho=0$ is quite strong in general but easily obtainable con... | Example of dependence with zero covariance
The last row of the first image of https://en.wikipedia.org/wiki/Correlation_and_dependence provide exemple where the Pearson correlation is 0 but there is strong non-linear dependance between X and Y |
55,188 | What is the deal with $p$-value when generating Pearson's $r$ correlation coefficient? | [Fixed/improved, based on the feedback from @Momo and @whuber]
I believe that in the context of regression the relationship between $p$-value and Pearson's correlation coefficient is the following: $p$-value can be interpreted as probability that correlation (coefficient), determined in a random sampling-based experime... | What is the deal with $p$-value when generating Pearson's $r$ correlation coefficient? | [Fixed/improved, based on the feedback from @Momo and @whuber]
I believe that in the context of regression the relationship between $p$-value and Pearson's correlation coefficient is the following: $p | What is the deal with $p$-value when generating Pearson's $r$ correlation coefficient?
[Fixed/improved, based on the feedback from @Momo and @whuber]
I believe that in the context of regression the relationship between $p$-value and Pearson's correlation coefficient is the following: $p$-value can be interpreted as pro... | What is the deal with $p$-value when generating Pearson's $r$ correlation coefficient?
[Fixed/improved, based on the feedback from @Momo and @whuber]
I believe that in the context of regression the relationship between $p$-value and Pearson's correlation coefficient is the following: $p |
55,189 | What is a Dirichlet prior | Let me try to respond your very last question about understanding the Dirichlet distribution, its relation to the Multinomial, and what I suspect is what you really would like to know is how this could be explained in an applied context, such as your genomics problem.
Now I am going to explain all this using my vague r... | What is a Dirichlet prior | Let me try to respond your very last question about understanding the Dirichlet distribution, its relation to the Multinomial, and what I suspect is what you really would like to know is how this coul | What is a Dirichlet prior
Let me try to respond your very last question about understanding the Dirichlet distribution, its relation to the Multinomial, and what I suspect is what you really would like to know is how this could be explained in an applied context, such as your genomics problem.
Now I am going to explain... | What is a Dirichlet prior
Let me try to respond your very last question about understanding the Dirichlet distribution, its relation to the Multinomial, and what I suspect is what you really would like to know is how this coul |
55,190 | What is a Dirichlet prior | There is a good explanation in this presentation.
https://www.slideshare.net/g33ktalk/machine-learning-meetup-12182013
You can watch the whole presentation if you want (it is a good explanation of the Dirichlet distribution) but I think the slides will get the concept across pretty quickly.
Slides 32-35 Explains the m... | What is a Dirichlet prior | There is a good explanation in this presentation.
https://www.slideshare.net/g33ktalk/machine-learning-meetup-12182013
You can watch the whole presentation if you want (it is a good explanation of th | What is a Dirichlet prior
There is a good explanation in this presentation.
https://www.slideshare.net/g33ktalk/machine-learning-meetup-12182013
You can watch the whole presentation if you want (it is a good explanation of the Dirichlet distribution) but I think the slides will get the concept across pretty quickly.
S... | What is a Dirichlet prior
There is a good explanation in this presentation.
https://www.slideshare.net/g33ktalk/machine-learning-meetup-12182013
You can watch the whole presentation if you want (it is a good explanation of th |
55,191 | Comparing 2 time series in R | There are a number of possible models at a variety of levels of complexity. These include
(some are very closely related):
Time series regression with lagged variables
Lagged regression models. See also distributed lag models
Regression with autocorrelated errors
Transfer function modelling /lagged regression with a... | Comparing 2 time series in R | There are a number of possible models at a variety of levels of complexity. These include
(some are very closely related):
Time series regression with lagged variables
Lagged regression models. See | Comparing 2 time series in R
There are a number of possible models at a variety of levels of complexity. These include
(some are very closely related):
Time series regression with lagged variables
Lagged regression models. See also distributed lag models
Regression with autocorrelated errors
Transfer function modell... | Comparing 2 time series in R
There are a number of possible models at a variety of levels of complexity. These include
(some are very closely related):
Time series regression with lagged variables
Lagged regression models. See |
55,192 | Comparing 2 time series in R | In addition to the very nice answer by @Glen_b, I would like to suggest some complementary information and resources on time series analysis (mostly in R!), which might be useful to you. Please find them in my related answers, as follows: on general time series analysis and on time series classification and clustering.... | Comparing 2 time series in R | In addition to the very nice answer by @Glen_b, I would like to suggest some complementary information and resources on time series analysis (mostly in R!), which might be useful to you. Please find t | Comparing 2 time series in R
In addition to the very nice answer by @Glen_b, I would like to suggest some complementary information and resources on time series analysis (mostly in R!), which might be useful to you. Please find them in my related answers, as follows: on general time series analysis and on time series c... | Comparing 2 time series in R
In addition to the very nice answer by @Glen_b, I would like to suggest some complementary information and resources on time series analysis (mostly in R!), which might be useful to you. Please find t |
55,193 | How to determine whether a variable is significant using Pr (>Chi) and Df? | This actually appears to be an analysis of deviance table, but the principle is the same, and people still call it an 'ANalysis Of VAriance' table. The table presents information about a series of sequentially nested model fits. In the first row is the null model (without any of the variables included). Each subsequ... | How to determine whether a variable is significant using Pr (>Chi) and Df? | This actually appears to be an analysis of deviance table, but the principle is the same, and people still call it an 'ANalysis Of VAriance' table. The table presents information about a series of se | How to determine whether a variable is significant using Pr (>Chi) and Df?
This actually appears to be an analysis of deviance table, but the principle is the same, and people still call it an 'ANalysis Of VAriance' table. The table presents information about a series of sequentially nested model fits. In the first r... | How to determine whether a variable is significant using Pr (>Chi) and Df?
This actually appears to be an analysis of deviance table, but the principle is the same, and people still call it an 'ANalysis Of VAriance' table. The table presents information about a series of se |
55,194 | How to determine whether a variable is significant using Pr (>Chi) and Df? | You would most easily judge significance for one of those variables by checking whether the p-value was $\leq \alpha$, your previously chosen significance level.
This is true of essentially any hypothesis test, not just chi-square tests.
You haven't stated your significance level, so I can't talk about which of those c... | How to determine whether a variable is significant using Pr (>Chi) and Df? | You would most easily judge significance for one of those variables by checking whether the p-value was $\leq \alpha$, your previously chosen significance level.
This is true of essentially any hypoth | How to determine whether a variable is significant using Pr (>Chi) and Df?
You would most easily judge significance for one of those variables by checking whether the p-value was $\leq \alpha$, your previously chosen significance level.
This is true of essentially any hypothesis test, not just chi-square tests.
You hav... | How to determine whether a variable is significant using Pr (>Chi) and Df?
You would most easily judge significance for one of those variables by checking whether the p-value was $\leq \alpha$, your previously chosen significance level.
This is true of essentially any hypoth |
55,195 | A guide to regularization strategies in regression | From The Elements of Statistical Learning, as suggested by goangit, section 3.6 is a one page discussion comparing selection and shrinkage methods which points to a paper by Frank and Friedman (1993) A Statistical View of Some Chemometrics Regression Tools. Section 5 of their paper (page 125) performed a Monte Carlo st... | A guide to regularization strategies in regression | From The Elements of Statistical Learning, as suggested by goangit, section 3.6 is a one page discussion comparing selection and shrinkage methods which points to a paper by Frank and Friedman (1993) | A guide to regularization strategies in regression
From The Elements of Statistical Learning, as suggested by goangit, section 3.6 is a one page discussion comparing selection and shrinkage methods which points to a paper by Frank and Friedman (1993) A Statistical View of Some Chemometrics Regression Tools. Section 5 o... | A guide to regularization strategies in regression
From The Elements of Statistical Learning, as suggested by goangit, section 3.6 is a one page discussion comparing selection and shrinkage methods which points to a paper by Frank and Friedman (1993) |
55,196 | A guide to regularization strategies in regression | You could try Introduction to Statistical Learning by Gareth James et al. It's freely available, contains introductory-level review and discusion of all the topics you mention (in particular Chapter 6 deals with regularization), is well-supported by the ISLwR package in R and provides a gateway to the more advanced cou... | A guide to regularization strategies in regression | You could try Introduction to Statistical Learning by Gareth James et al. It's freely available, contains introductory-level review and discusion of all the topics you mention (in particular Chapter 6 | A guide to regularization strategies in regression
You could try Introduction to Statistical Learning by Gareth James et al. It's freely available, contains introductory-level review and discusion of all the topics you mention (in particular Chapter 6 deals with regularization), is well-supported by the ISLwR package i... | A guide to regularization strategies in regression
You could try Introduction to Statistical Learning by Gareth James et al. It's freely available, contains introductory-level review and discusion of all the topics you mention (in particular Chapter 6 |
55,197 | Initialize AR(p) process by using Arima.sim | You have the following system:
\begin{eqnarray}
\left\{
\begin{array}{lcl}
y_5 &=& 0.67 y_4 - 0.51 y_1 + \epsilon_5 \\
y_6 &=& 0.67 y_5 - 0.51 y_2 + \epsilon_6 \\
y_7 &=& 0.67 y_6 - 0.51 y_3 + \epsilon_7 \\
y_8 &=& 0.67 y_7 - 0.51 y_4 + \epsilon_8
\end{array}
\right.
\end{eqnarray}
with $\epsilon_t \sim NID(0, 1)$. In... | Initialize AR(p) process by using Arima.sim | You have the following system:
\begin{eqnarray}
\left\{
\begin{array}{lcl}
y_5 &=& 0.67 y_4 - 0.51 y_1 + \epsilon_5 \\
y_6 &=& 0.67 y_5 - 0.51 y_2 + \epsilon_6 \\
y_7 &=& 0.67 y_6 - 0.51 y_3 + \epsil | Initialize AR(p) process by using Arima.sim
You have the following system:
\begin{eqnarray}
\left\{
\begin{array}{lcl}
y_5 &=& 0.67 y_4 - 0.51 y_1 + \epsilon_5 \\
y_6 &=& 0.67 y_5 - 0.51 y_2 + \epsilon_6 \\
y_7 &=& 0.67 y_6 - 0.51 y_3 + \epsilon_7 \\
y_8 &=& 0.67 y_7 - 0.51 y_4 + \epsilon_8
\end{array}
\right.
\end{eq... | Initialize AR(p) process by using Arima.sim
You have the following system:
\begin{eqnarray}
\left\{
\begin{array}{lcl}
y_5 &=& 0.67 y_4 - 0.51 y_1 + \epsilon_5 \\
y_6 &=& 0.67 y_5 - 0.51 y_2 + \epsilon_6 \\
y_7 &=& 0.67 y_6 - 0.51 y_3 + \epsil |
55,198 | interrupted time series in R | One usually distinguishes two patterns of change (continuous with change in slope only, abrupt with shift plus change in slope) and whether or not the breakpoint is known.
If the breakpoint (= timing where the intervention became effective) were known, then the formula for the regression without intervation would be so... | interrupted time series in R | One usually distinguishes two patterns of change (continuous with change in slope only, abrupt with shift plus change in slope) and whether or not the breakpoint is known.
If the breakpoint (= timing | interrupted time series in R
One usually distinguishes two patterns of change (continuous with change in slope only, abrupt with shift plus change in slope) and whether or not the breakpoint is known.
If the breakpoint (= timing where the intervention became effective) were known, then the formula for the regression wi... | interrupted time series in R
One usually distinguishes two patterns of change (continuous with change in slope only, abrupt with shift plus change in slope) and whether or not the breakpoint is known.
If the breakpoint (= timing |
55,199 | Expected proportion of the sample when bootstrapping | This is related to collision-counting in the birthday problem.
Imagine you walk into a room of $k$ people. The probability at least one shares a birthday with you is $q(k;n) = 1 - \left( \frac{n-1}{n} \right)^k$, where $n$ is the number of different birthday slots (days in the year).
The expected number you add to the... | Expected proportion of the sample when bootstrapping | This is related to collision-counting in the birthday problem.
Imagine you walk into a room of $k$ people. The probability at least one shares a birthday with you is $q(k;n) = 1 - \left( \frac{n-1}{n | Expected proportion of the sample when bootstrapping
This is related to collision-counting in the birthday problem.
Imagine you walk into a room of $k$ people. The probability at least one shares a birthday with you is $q(k;n) = 1 - \left( \frac{n-1}{n} \right)^k$, where $n$ is the number of different birthday slots (... | Expected proportion of the sample when bootstrapping
This is related to collision-counting in the birthday problem.
Imagine you walk into a room of $k$ people. The probability at least one shares a birthday with you is $q(k;n) = 1 - \left( \frac{n-1}{n |
55,200 | Expected proportion of the sample when bootstrapping | I would like to corroborate again the answer from @glen-b with some experimental results.
I wrote a function $p(n,m,k)$ that tells the exact probability (is not based on simulations) of getting exactly $k$ unique elements after choosing $m$ samples with replacement from a set of $n$ elements. Notice $p$ is a pdf on $k$... | Expected proportion of the sample when bootstrapping | I would like to corroborate again the answer from @glen-b with some experimental results.
I wrote a function $p(n,m,k)$ that tells the exact probability (is not based on simulations) of getting exactl | Expected proportion of the sample when bootstrapping
I would like to corroborate again the answer from @glen-b with some experimental results.
I wrote a function $p(n,m,k)$ that tells the exact probability (is not based on simulations) of getting exactly $k$ unique elements after choosing $m$ samples with replacement f... | Expected proportion of the sample when bootstrapping
I would like to corroborate again the answer from @glen-b with some experimental results.
I wrote a function $p(n,m,k)$ that tells the exact probability (is not based on simulations) of getting exactl |
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