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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54,901 | What are drawbacks of isotonic regression? | Isotonic regression
By Alexeicolin - Own work, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=23732999
As seen in the image, and suggested (partly) by the name, isotonic regression is monotonic increasing or monotonic decreasing. Thus, it would not be appropriate for fitting distributions that have left... | What are drawbacks of isotonic regression? | Isotonic regression
By Alexeicolin - Own work, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=23732999
As seen in the image, and suggested (partly) by the name, isotonic regression is | What are drawbacks of isotonic regression?
Isotonic regression
By Alexeicolin - Own work, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=23732999
As seen in the image, and suggested (partly) by the name, isotonic regression is monotonic increasing or monotonic decreasing. Thus, it would not be appropria... | What are drawbacks of isotonic regression?
Isotonic regression
By Alexeicolin - Own work, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=23732999
As seen in the image, and suggested (partly) by the name, isotonic regression is |
54,902 | Confidence interval on the percentage difference of two binomial distributions | You can use profile likelihood methods (other answers are surely possible, but I will show that.)
You have binomial counts from two groups, men and women. We write
$$
M \sim \mathcal{Bin}(m, p_m) \\
W \sim \mathcal{Bin}(w, p_w)
$$
and the focus (or interest) parameter is $Q=\frac{p_w-p_m}{p_m}$. Assuming (reasona... | Confidence interval on the percentage difference of two binomial distributions | You can use profile likelihood methods (other answers are surely possible, but I will show that.)
You have binomial counts from two groups, men and women. We write
$$
M \sim \mathcal{Bin}(m, p_m) \ | Confidence interval on the percentage difference of two binomial distributions
You can use profile likelihood methods (other answers are surely possible, but I will show that.)
You have binomial counts from two groups, men and women. We write
$$
M \sim \mathcal{Bin}(m, p_m) \\
W \sim \mathcal{Bin}(w, p_w)
$$
and ... | Confidence interval on the percentage difference of two binomial distributions
You can use profile likelihood methods (other answers are surely possible, but I will show that.)
You have binomial counts from two groups, men and women. We write
$$
M \sim \mathcal{Bin}(m, p_m) \ |
54,903 | Confidence interval on the percentage difference of two binomial distributions | Unfortunately there is no universally accepted way for computing a confidence interval for a difference in binomial proportions. The R function BinomDiffCI in the package DescTools offers eleven different options, and its help page gives references to publications.
Newcombe recommends the methods by Miettinen and Nurmi... | Confidence interval on the percentage difference of two binomial distributions | Unfortunately there is no universally accepted way for computing a confidence interval for a difference in binomial proportions. The R function BinomDiffCI in the package DescTools offers eleven diffe | Confidence interval on the percentage difference of two binomial distributions
Unfortunately there is no universally accepted way for computing a confidence interval for a difference in binomial proportions. The R function BinomDiffCI in the package DescTools offers eleven different options, and its help page gives ref... | Confidence interval on the percentage difference of two binomial distributions
Unfortunately there is no universally accepted way for computing a confidence interval for a difference in binomial proportions. The R function BinomDiffCI in the package DescTools offers eleven diffe |
54,904 | When is a stochastic process not differentiable? | (1) Forget about random variables for a second. You have a function $Y_t=Y(t,X_t):=\ln(X_t)$. Then as a function it's partial derivative is defined in the usual sense: $\frac{\partial Y_t}{\partial X_t}=\frac{1}{X_t}$. The fact that $Y_t$ is a random variable makes no difference: your $X_t=X(t,\omega)$, but you're stil... | When is a stochastic process not differentiable? | (1) Forget about random variables for a second. You have a function $Y_t=Y(t,X_t):=\ln(X_t)$. Then as a function it's partial derivative is defined in the usual sense: $\frac{\partial Y_t}{\partial X_ | When is a stochastic process not differentiable?
(1) Forget about random variables for a second. You have a function $Y_t=Y(t,X_t):=\ln(X_t)$. Then as a function it's partial derivative is defined in the usual sense: $\frac{\partial Y_t}{\partial X_t}=\frac{1}{X_t}$. The fact that $Y_t$ is a random variable makes no di... | When is a stochastic process not differentiable?
(1) Forget about random variables for a second. You have a function $Y_t=Y(t,X_t):=\ln(X_t)$. Then as a function it's partial derivative is defined in the usual sense: $\frac{\partial Y_t}{\partial X_ |
54,905 | Motivation for Ward's definition of error sum of squares (ESS) | \begin{align}
\operatorname{Var}(\vec x) \propto \sum_{i=1}^n(x_i - \bar x)^2 &= \sum_i x_i^2 - 2\bar x \sum_ix_i + n \bar x^2 \\
&= \sum_i x_i^2 - n \bar x^2 = \sum_i x_i^2 - \frac 1n \left(\sum_i x_i\right)^2 = \text{ESS}.
\end{align}
I think $ESS$ is more sensible when talking about compression because $ESS = ||\ve... | Motivation for Ward's definition of error sum of squares (ESS) | \begin{align}
\operatorname{Var}(\vec x) \propto \sum_{i=1}^n(x_i - \bar x)^2 &= \sum_i x_i^2 - 2\bar x \sum_ix_i + n \bar x^2 \\
&= \sum_i x_i^2 - n \bar x^2 = \sum_i x_i^2 - \frac 1n \left(\sum_i x | Motivation for Ward's definition of error sum of squares (ESS)
\begin{align}
\operatorname{Var}(\vec x) \propto \sum_{i=1}^n(x_i - \bar x)^2 &= \sum_i x_i^2 - 2\bar x \sum_ix_i + n \bar x^2 \\
&= \sum_i x_i^2 - n \bar x^2 = \sum_i x_i^2 - \frac 1n \left(\sum_i x_i\right)^2 = \text{ESS}.
\end{align}
I think $ESS$ is mo... | Motivation for Ward's definition of error sum of squares (ESS)
\begin{align}
\operatorname{Var}(\vec x) \propto \sum_{i=1}^n(x_i - \bar x)^2 &= \sum_i x_i^2 - 2\bar x \sum_ix_i + n \bar x^2 \\
&= \sum_i x_i^2 - n \bar x^2 = \sum_i x_i^2 - \frac 1n \left(\sum_i x |
54,906 | Motivation for Ward's definition of error sum of squares (ESS) | Ward's ESS is the same as the SS you mention. If you distribute the terms in your formula you get:
$ \sum(x_i - \bar x)^2 = \sum x_i^2 + \sum \bar x^2 - 2 \bar x \sum x_i = \sum x_i^2 - n \bar x ^2 = \sum x_i^2 - (\sum x_i)^2 / n$ | Motivation for Ward's definition of error sum of squares (ESS) | Ward's ESS is the same as the SS you mention. If you distribute the terms in your formula you get:
$ \sum(x_i - \bar x)^2 = \sum x_i^2 + \sum \bar x^2 - 2 \bar x \sum x_i = \sum x_i^2 - n \bar x ^2 = | Motivation for Ward's definition of error sum of squares (ESS)
Ward's ESS is the same as the SS you mention. If you distribute the terms in your formula you get:
$ \sum(x_i - \bar x)^2 = \sum x_i^2 + \sum \bar x^2 - 2 \bar x \sum x_i = \sum x_i^2 - n \bar x ^2 = \sum x_i^2 - (\sum x_i)^2 / n$ | Motivation for Ward's definition of error sum of squares (ESS)
Ward's ESS is the same as the SS you mention. If you distribute the terms in your formula you get:
$ \sum(x_i - \bar x)^2 = \sum x_i^2 + \sum \bar x^2 - 2 \bar x \sum x_i = \sum x_i^2 - n \bar x ^2 = |
54,907 | Interpreting PCA figures in layman terms | The link ( http://stats.stackexchange.com/questions/141085 ) provided in the comments give great insight. In this post I place some additions and specific comments on the particular biplot function used
I especially recommend you to look at the documentation of the biplot function (in a R console type "?biplot.princom... | Interpreting PCA figures in layman terms | The link ( http://stats.stackexchange.com/questions/141085 ) provided in the comments give great insight. In this post I place some additions and specific comments on the particular biplot function us | Interpreting PCA figures in layman terms
The link ( http://stats.stackexchange.com/questions/141085 ) provided in the comments give great insight. In this post I place some additions and specific comments on the particular biplot function used
I especially recommend you to look at the documentation of the biplot funct... | Interpreting PCA figures in layman terms
The link ( http://stats.stackexchange.com/questions/141085 ) provided in the comments give great insight. In this post I place some additions and specific comments on the particular biplot function us |
54,908 | How to sample uniformly points around a neighborhood of a point lying on a n-sphere? | Sample in a neighborhood of $e_{n+1}=(0,0,\ldots,0,1)$ in $\mathbb{R}^{n+1}$ and then apply any orthogonal transformation (that is, isometry of the sphere) that sends $e_{n+1}$ to $x_k$. This reduces the problem to sampling around $e_{n+1}$.
Geometry shows that the last coordinate of the points, $Z$, will range from... | How to sample uniformly points around a neighborhood of a point lying on a n-sphere? | Sample in a neighborhood of $e_{n+1}=(0,0,\ldots,0,1)$ in $\mathbb{R}^{n+1}$ and then apply any orthogonal transformation (that is, isometry of the sphere) that sends $e_{n+1}$ to $x_k$. This reduces | How to sample uniformly points around a neighborhood of a point lying on a n-sphere?
Sample in a neighborhood of $e_{n+1}=(0,0,\ldots,0,1)$ in $\mathbb{R}^{n+1}$ and then apply any orthogonal transformation (that is, isometry of the sphere) that sends $e_{n+1}$ to $x_k$. This reduces the problem to sampling around $e_... | How to sample uniformly points around a neighborhood of a point lying on a n-sphere?
Sample in a neighborhood of $e_{n+1}=(0,0,\ldots,0,1)$ in $\mathbb{R}^{n+1}$ and then apply any orthogonal transformation (that is, isometry of the sphere) that sends $e_{n+1}$ to $x_k$. This reduces |
54,909 | How to sample uniformly points around a neighborhood of a point lying on a n-sphere? | Adding to @whuber's answer here is python code to reproduce the ideas he explained, as well to validate the results.
from scipy.stats import beta
import numpy as np
def rsphere(n,n_dim,rad=1.0):
X = np.random.normal(size=(n,n_dim+1))
X_norm=np.divide(np.linalg.norm(X,axis=1),rad)
X = np.divide(X.T,X_norm).... | How to sample uniformly points around a neighborhood of a point lying on a n-sphere? | Adding to @whuber's answer here is python code to reproduce the ideas he explained, as well to validate the results.
from scipy.stats import beta
import numpy as np
def rsphere(n,n_dim,rad=1.0):
| How to sample uniformly points around a neighborhood of a point lying on a n-sphere?
Adding to @whuber's answer here is python code to reproduce the ideas he explained, as well to validate the results.
from scipy.stats import beta
import numpy as np
def rsphere(n,n_dim,rad=1.0):
X = np.random.normal(size=(n,n_dim+... | How to sample uniformly points around a neighborhood of a point lying on a n-sphere?
Adding to @whuber's answer here is python code to reproduce the ideas he explained, as well to validate the results.
from scipy.stats import beta
import numpy as np
def rsphere(n,n_dim,rad=1.0):
|
54,910 | Why are we interested in asymptotics if the real-world data is almost always finite? [duplicate] | Asymptotic theory tells us about the statistical properties of a sample as it grows to an arbitrarily large size $n$. Often datasets are sufficiently large that theorems like the law of large numbers and the central limit theorem apply in practice. Think of doing a census of tree heights in a forest or the number of ti... | Why are we interested in asymptotics if the real-world data is almost always finite? [duplicate] | Asymptotic theory tells us about the statistical properties of a sample as it grows to an arbitrarily large size $n$. Often datasets are sufficiently large that theorems like the law of large numbers | Why are we interested in asymptotics if the real-world data is almost always finite? [duplicate]
Asymptotic theory tells us about the statistical properties of a sample as it grows to an arbitrarily large size $n$. Often datasets are sufficiently large that theorems like the law of large numbers and the central limit t... | Why are we interested in asymptotics if the real-world data is almost always finite? [duplicate]
Asymptotic theory tells us about the statistical properties of a sample as it grows to an arbitrarily large size $n$. Often datasets are sufficiently large that theorems like the law of large numbers |
54,911 | Expectation of $X$ given $X < c$ | A general solution: let $X$ be a random vector with density $f$ and $A=\{X\in B_0\}$, for some $n$-dimensional Borel set $B_0$, with $\Pr(A)>0$. The conditional density denoted by $f(x\mid A)$ must be such that
$$
\Pr\{X\in B\mid A\} = \int_B f(x\mid A)\,dx \, \qquad (*)
$$
for every $n$-dimensional Borel set $B$. Fr... | Expectation of $X$ given $X < c$ | A general solution: let $X$ be a random vector with density $f$ and $A=\{X\in B_0\}$, for some $n$-dimensional Borel set $B_0$, with $\Pr(A)>0$. The conditional density denoted by $f(x\mid A)$ must be | Expectation of $X$ given $X < c$
A general solution: let $X$ be a random vector with density $f$ and $A=\{X\in B_0\}$, for some $n$-dimensional Borel set $B_0$, with $\Pr(A)>0$. The conditional density denoted by $f(x\mid A)$ must be such that
$$
\Pr\{X\in B\mid A\} = \int_B f(x\mid A)\,dx \, \qquad (*)
$$
for every ... | Expectation of $X$ given $X < c$
A general solution: let $X$ be a random vector with density $f$ and $A=\{X\in B_0\}$, for some $n$-dimensional Borel set $B_0$, with $\Pr(A)>0$. The conditional density denoted by $f(x\mid A)$ must be |
54,912 | Expectation of $X$ given $X < c$ | Here is another approach for a continuous random variable, less rigorous than Zen's beautiful solution.
Fix $x:x< c$, then
$P(X\leq x|X<c)=\frac{P(X\leq x,X <c)}{P(X<c)}\overset{x<c}{=} \frac{P(X <x)}{P(X<c)}=\frac{F_X(x)}{F_X(c)}$
Fix $x:x>c$, then
$P(X\leq x|X<c)=\frac{P(X\leq x,X <c)}{P(X<c)}\overset{x>c}{=} \frac{P... | Expectation of $X$ given $X < c$ | Here is another approach for a continuous random variable, less rigorous than Zen's beautiful solution.
Fix $x:x< c$, then
$P(X\leq x|X<c)=\frac{P(X\leq x,X <c)}{P(X<c)}\overset{x<c}{=} \frac{P(X <x)} | Expectation of $X$ given $X < c$
Here is another approach for a continuous random variable, less rigorous than Zen's beautiful solution.
Fix $x:x< c$, then
$P(X\leq x|X<c)=\frac{P(X\leq x,X <c)}{P(X<c)}\overset{x<c}{=} \frac{P(X <x)}{P(X<c)}=\frac{F_X(x)}{F_X(c)}$
Fix $x:x>c$, then
$P(X\leq x|X<c)=\frac{P(X\leq x,X <c)... | Expectation of $X$ given $X < c$
Here is another approach for a continuous random variable, less rigorous than Zen's beautiful solution.
Fix $x:x< c$, then
$P(X\leq x|X<c)=\frac{P(X\leq x,X <c)}{P(X<c)}\overset{x<c}{=} \frac{P(X <x)} |
54,913 | Models to use Predict time till next purchase | The basic strategy would be to assume that the activity is distributed according to some family of distributions, and then estimate the parameters based on the data. This wouldn’t really be regression, since the feature variables and the response variables are basically the same. Also, the really basic analysis would b... | Models to use Predict time till next purchase | The basic strategy would be to assume that the activity is distributed according to some family of distributions, and then estimate the parameters based on the data. This wouldn’t really be regression | Models to use Predict time till next purchase
The basic strategy would be to assume that the activity is distributed according to some family of distributions, and then estimate the parameters based on the data. This wouldn’t really be regression, since the feature variables and the response variables are basically the... | Models to use Predict time till next purchase
The basic strategy would be to assume that the activity is distributed according to some family of distributions, and then estimate the parameters based on the data. This wouldn’t really be regression |
54,914 | Models to use Predict time till next purchase | It depends on what you want to use and what assumptions you want to make. If you assume that the purchases are stochastically independent then you're looking for the the Poisson Point Process. An accessible introduction can be found here.
More generally, the Exponential Distribution predicts the time between successive... | Models to use Predict time till next purchase | It depends on what you want to use and what assumptions you want to make. If you assume that the purchases are stochastically independent then you're looking for the the Poisson Point Process. An acce | Models to use Predict time till next purchase
It depends on what you want to use and what assumptions you want to make. If you assume that the purchases are stochastically independent then you're looking for the the Poisson Point Process. An accessible introduction can be found here.
More generally, the Exponential Dis... | Models to use Predict time till next purchase
It depends on what you want to use and what assumptions you want to make. If you assume that the purchases are stochastically independent then you're looking for the the Poisson Point Process. An acce |
54,915 | Models to use Predict time till next purchase | This is an example of Survival Analysis, and yes, that can be done with regression. You can start at Wikipedia. Start with figuring out how to create a Kaplan Meier curve, maybe compare it for some subgroups, if you've never heard of this area. | Models to use Predict time till next purchase | This is an example of Survival Analysis, and yes, that can be done with regression. You can start at Wikipedia. Start with figuring out how to create a Kaplan Meier curve, maybe compare it for some su | Models to use Predict time till next purchase
This is an example of Survival Analysis, and yes, that can be done with regression. You can start at Wikipedia. Start with figuring out how to create a Kaplan Meier curve, maybe compare it for some subgroups, if you've never heard of this area. | Models to use Predict time till next purchase
This is an example of Survival Analysis, and yes, that can be done with regression. You can start at Wikipedia. Start with figuring out how to create a Kaplan Meier curve, maybe compare it for some su |
54,916 | Models to use Predict time till next purchase | This is point process modeling. One simple way to use regression is to regress the next interval of purchase as a function of history and other covariates. In general, you can fit a parametric form of conditional intensity function. A popular choice in neuroscience is to use a linear-nonlinear functional form. | Models to use Predict time till next purchase | This is point process modeling. One simple way to use regression is to regress the next interval of purchase as a function of history and other covariates. In general, you can fit a parametric form of | Models to use Predict time till next purchase
This is point process modeling. One simple way to use regression is to regress the next interval of purchase as a function of history and other covariates. In general, you can fit a parametric form of conditional intensity function. A popular choice in neuroscience is to us... | Models to use Predict time till next purchase
This is point process modeling. One simple way to use regression is to regress the next interval of purchase as a function of history and other covariates. In general, you can fit a parametric form of |
54,917 | Variance of set of subsets | You are looking for "measure of similarity" between the sets of commenting friends. One of the most popular measures is Jaccard index:
$$
J=\frac{|\bigcap_{i=1}^{n} A_i|}{|\bigcup_{i=1}^{n} A_i|}
$$
$A_i$ is a set of friends that commented on post i.
If most friends that commented are the same, the intersection count w... | Variance of set of subsets | You are looking for "measure of similarity" between the sets of commenting friends. One of the most popular measures is Jaccard index:
$$
J=\frac{|\bigcap_{i=1}^{n} A_i|}{|\bigcup_{i=1}^{n} A_i|}
$$
$ | Variance of set of subsets
You are looking for "measure of similarity" between the sets of commenting friends. One of the most popular measures is Jaccard index:
$$
J=\frac{|\bigcap_{i=1}^{n} A_i|}{|\bigcup_{i=1}^{n} A_i|}
$$
$A_i$ is a set of friends that commented on post i.
If most friends that commented are the sam... | Variance of set of subsets
You are looking for "measure of similarity" between the sets of commenting friends. One of the most popular measures is Jaccard index:
$$
J=\frac{|\bigcap_{i=1}^{n} A_i|}{|\bigcup_{i=1}^{n} A_i|}
$$
$ |
54,918 | Variance of set of subsets | What about this: suppose the set of friends you have is $\mathcal{A}$ and $\mathcal{A}_i\subset\mathcal{A}$ is the set of friends commenting on post $i$, $i=1,\ldots,n$. Then
$$
\text{KPI} = \frac{\big|\bigcup_{i=1}^n \mathcal{A}_i \big|}{\sum_{i=1}^n |\mathcal{A}_i|}
$$
would be high if always different friends commen... | Variance of set of subsets | What about this: suppose the set of friends you have is $\mathcal{A}$ and $\mathcal{A}_i\subset\mathcal{A}$ is the set of friends commenting on post $i$, $i=1,\ldots,n$. Then
$$
\text{KPI} = \frac{\bi | Variance of set of subsets
What about this: suppose the set of friends you have is $\mathcal{A}$ and $\mathcal{A}_i\subset\mathcal{A}$ is the set of friends commenting on post $i$, $i=1,\ldots,n$. Then
$$
\text{KPI} = \frac{\big|\bigcup_{i=1}^n \mathcal{A}_i \big|}{\sum_{i=1}^n |\mathcal{A}_i|}
$$
would be high if alwa... | Variance of set of subsets
What about this: suppose the set of friends you have is $\mathcal{A}$ and $\mathcal{A}_i\subset\mathcal{A}$ is the set of friends commenting on post $i$, $i=1,\ldots,n$. Then
$$
\text{KPI} = \frac{\bi |
54,919 | Variance of set of subsets | StijnDeVuyst, and repeated by igrinis, provides a good measure and concept for the 'variance among subsets' you were looking for.
In relation to your task to find 'turnover' and not just 'similarity' of friends replying to your posts. I believe that you may wish to extend this concept.
Instead of taking all the subset... | Variance of set of subsets | StijnDeVuyst, and repeated by igrinis, provides a good measure and concept for the 'variance among subsets' you were looking for.
In relation to your task to find 'turnover' and not just 'similarity' | Variance of set of subsets
StijnDeVuyst, and repeated by igrinis, provides a good measure and concept for the 'variance among subsets' you were looking for.
In relation to your task to find 'turnover' and not just 'similarity' of friends replying to your posts. I believe that you may wish to extend this concept.
Inste... | Variance of set of subsets
StijnDeVuyst, and repeated by igrinis, provides a good measure and concept for the 'variance among subsets' you were looking for.
In relation to your task to find 'turnover' and not just 'similarity' |
54,920 | Variance of set of subsets | This is simplistic, but I always start there...
Suppose you have 100 friends and 5 posts. And suppose each post gets 20 comments.
At one extreme, 20 of the same people all commented on each post. At the other extreme, 20 different people commented on each post.
In the first case the average number of comments per post... | Variance of set of subsets | This is simplistic, but I always start there...
Suppose you have 100 friends and 5 posts. And suppose each post gets 20 comments.
At one extreme, 20 of the same people all commented on each post. At | Variance of set of subsets
This is simplistic, but I always start there...
Suppose you have 100 friends and 5 posts. And suppose each post gets 20 comments.
At one extreme, 20 of the same people all commented on each post. At the other extreme, 20 different people commented on each post.
In the first case the average ... | Variance of set of subsets
This is simplistic, but I always start there...
Suppose you have 100 friends and 5 posts. And suppose each post gets 20 comments.
At one extreme, 20 of the same people all commented on each post. At |
54,921 | MLE for Poisson distribution is undefined with all-zero observations | The likelihood function of the Poisson given observations $x_1, x_2, \ldots, x_n$ is
$$ l(\lambda; x) = \prod_i e^{-\lambda}\frac{\lambda^{x_i}}{x_i!} = \frac{e^{-n\lambda}}{x_1!x_2!\cdots x_n!}\lambda^{x_1 + x_2 + \cdots + x_n}$$
If $x_1 = x_2 = \cdots = x_n = 0$ then this becomes
$$ l(\lambda; x) = e^{- n \lambda} $$... | MLE for Poisson distribution is undefined with all-zero observations | The likelihood function of the Poisson given observations $x_1, x_2, \ldots, x_n$ is
$$ l(\lambda; x) = \prod_i e^{-\lambda}\frac{\lambda^{x_i}}{x_i!} = \frac{e^{-n\lambda}}{x_1!x_2!\cdots x_n!}\lambd | MLE for Poisson distribution is undefined with all-zero observations
The likelihood function of the Poisson given observations $x_1, x_2, \ldots, x_n$ is
$$ l(\lambda; x) = \prod_i e^{-\lambda}\frac{\lambda^{x_i}}{x_i!} = \frac{e^{-n\lambda}}{x_1!x_2!\cdots x_n!}\lambda^{x_1 + x_2 + \cdots + x_n}$$
If $x_1 = x_2 = \cdo... | MLE for Poisson distribution is undefined with all-zero observations
The likelihood function of the Poisson given observations $x_1, x_2, \ldots, x_n$ is
$$ l(\lambda; x) = \prod_i e^{-\lambda}\frac{\lambda^{x_i}}{x_i!} = \frac{e^{-n\lambda}}{x_1!x_2!\cdots x_n!}\lambd |
54,922 | MLE for Poisson distribution is undefined with all-zero observations | I still keep the opinion that MLE is undefined when all the observations are zero. However, this does not affect on the expectation or variance of this MLE, since the average of all-zero observations is zero, which does not have any effect on these computation, whether MLE is defined or undefined at this point. | MLE for Poisson distribution is undefined with all-zero observations | I still keep the opinion that MLE is undefined when all the observations are zero. However, this does not affect on the expectation or variance of this MLE, since the average of all-zero observations | MLE for Poisson distribution is undefined with all-zero observations
I still keep the opinion that MLE is undefined when all the observations are zero. However, this does not affect on the expectation or variance of this MLE, since the average of all-zero observations is zero, which does not have any effect on these c... | MLE for Poisson distribution is undefined with all-zero observations
I still keep the opinion that MLE is undefined when all the observations are zero. However, this does not affect on the expectation or variance of this MLE, since the average of all-zero observations |
54,923 | Can t test be used for comparing groups with a sample size of 3? | The permutation test will have insufficient power. (There just aren't enough different ways to split six samples into two groups of three.) But If the assumptions of the t-test hold, then its results are valid.
Many thoughtful readers will question whether such a situation could actually arise. Let me share a real s... | Can t test be used for comparing groups with a sample size of 3? | The permutation test will have insufficient power. (There just aren't enough different ways to split six samples into two groups of three.) But If the assumptions of the t-test hold, then its result | Can t test be used for comparing groups with a sample size of 3?
The permutation test will have insufficient power. (There just aren't enough different ways to split six samples into two groups of three.) But If the assumptions of the t-test hold, then its results are valid.
Many thoughtful readers will question whet... | Can t test be used for comparing groups with a sample size of 3?
The permutation test will have insufficient power. (There just aren't enough different ways to split six samples into two groups of three.) But If the assumptions of the t-test hold, then its result |
54,924 | How is the exact permutation test procedure carried out: iterating over permutations or using combinations of one group? | Whether or not you take the combinations or permutations doesn't actually affect your results, as the number of permutations of $n_{A}$ specific objects in $A$ and $n_{B}$ specific objects in $B$ is the same for all combinations of $x_{1} ... x_{n_{A}}$ and $x_{n_{A+1}} ... x_{n_{A} + n_{B}}$ since the size of each set... | How is the exact permutation test procedure carried out: iterating over permutations or using combin | Whether or not you take the combinations or permutations doesn't actually affect your results, as the number of permutations of $n_{A}$ specific objects in $A$ and $n_{B}$ specific objects in $B$ is t | How is the exact permutation test procedure carried out: iterating over permutations or using combinations of one group?
Whether or not you take the combinations or permutations doesn't actually affect your results, as the number of permutations of $n_{A}$ specific objects in $A$ and $n_{B}$ specific objects in $B$ is ... | How is the exact permutation test procedure carried out: iterating over permutations or using combin
Whether or not you take the combinations or permutations doesn't actually affect your results, as the number of permutations of $n_{A}$ specific objects in $A$ and $n_{B}$ specific objects in $B$ is t |
54,925 | Bivariate random vector uniform distribution | The definition of a "uniform distribution" is that the density function is constant for all $x,y$ within the support region. So one must have
$$f_{X,Y}(x,y) = \frac{1}{A}$$
where $A$ is the area of either the square or the circle.
The same formula will hold for the density function of a "uniform distribution" on any ge... | Bivariate random vector uniform distribution | The definition of a "uniform distribution" is that the density function is constant for all $x,y$ within the support region. So one must have
$$f_{X,Y}(x,y) = \frac{1}{A}$$
where $A$ is the area of ei | Bivariate random vector uniform distribution
The definition of a "uniform distribution" is that the density function is constant for all $x,y$ within the support region. So one must have
$$f_{X,Y}(x,y) = \frac{1}{A}$$
where $A$ is the area of either the square or the circle.
The same formula will hold for the density f... | Bivariate random vector uniform distribution
The definition of a "uniform distribution" is that the density function is constant for all $x,y$ within the support region. So one must have
$$f_{X,Y}(x,y) = \frac{1}{A}$$
where $A$ is the area of ei |
54,926 | Bivariate random vector uniform distribution | The volume under fxy(x, y) must be equal to 1, over the x, y support, since fxy(x, y) is a probability density function. The x, y support defines an area A. This area can be any area.
Since the volume equals V = A x fxy(x, y) = 1, then fxy(x, y) = 1/A. Which is constant over all the x, y support. | Bivariate random vector uniform distribution | The volume under fxy(x, y) must be equal to 1, over the x, y support, since fxy(x, y) is a probability density function. The x, y support defines an area A. This area can be any area.
Since the volume | Bivariate random vector uniform distribution
The volume under fxy(x, y) must be equal to 1, over the x, y support, since fxy(x, y) is a probability density function. The x, y support defines an area A. This area can be any area.
Since the volume equals V = A x fxy(x, y) = 1, then fxy(x, y) = 1/A. Which is constant over... | Bivariate random vector uniform distribution
The volume under fxy(x, y) must be equal to 1, over the x, y support, since fxy(x, y) is a probability density function. The x, y support defines an area A. This area can be any area.
Since the volume |
54,927 | Why bother with Benjamini-Hochberg correction? | This is a good question, but you have several concepts confused.
Firstly, to answer your broader question, yes splitting p-values and performing correction on them separately is an often-performed and well known approach when you have prior information about the system you're studying. To see more examples of this and... | Why bother with Benjamini-Hochberg correction? | This is a good question, but you have several concepts confused.
Firstly, to answer your broader question, yes splitting p-values and performing correction on them separately is an often-performed an | Why bother with Benjamini-Hochberg correction?
This is a good question, but you have several concepts confused.
Firstly, to answer your broader question, yes splitting p-values and performing correction on them separately is an often-performed and well known approach when you have prior information about the system yo... | Why bother with Benjamini-Hochberg correction?
This is a good question, but you have several concepts confused.
Firstly, to answer your broader question, yes splitting p-values and performing correction on them separately is an often-performed an |
54,928 | Pairwise independence of sufficient statistics in exponential families | The problem with this "paradox" comes from absorbing $h(x)$ into the
dominating measure and then forgetting about the dominating measure.
The most common definition of a probability density is associated with a measure that is a product measure, like the Lebesgue measure. In this case, it is straightforward to pro... | Pairwise independence of sufficient statistics in exponential families | The problem with this "paradox" comes from absorbing $h(x)$ into the
dominating measure and then forgetting about the dominating measure.
The most common definition of a probability density is asso | Pairwise independence of sufficient statistics in exponential families
The problem with this "paradox" comes from absorbing $h(x)$ into the
dominating measure and then forgetting about the dominating measure.
The most common definition of a probability density is associated with a measure that is a product measure... | Pairwise independence of sufficient statistics in exponential families
The problem with this "paradox" comes from absorbing $h(x)$ into the
dominating measure and then forgetting about the dominating measure.
The most common definition of a probability density is asso |
54,929 | Pairwise independence of sufficient statistics in exponential families | I think it is not true
Consider a sample of $n$ observations from a normal distributed random variable $N(\mu, \sigma^2)$ with unknown mean and variance, which is from an exponential family
$\left (\sum x_i, \sum x_i^2\right)$ is a sufficient statistic
$\sum x_i$ and $\sum x_i^2$ are not independent | Pairwise independence of sufficient statistics in exponential families | I think it is not true
Consider a sample of $n$ observations from a normal distributed random variable $N(\mu, \sigma^2)$ with unknown mean and variance, which is from an exponential family
$\left (\ | Pairwise independence of sufficient statistics in exponential families
I think it is not true
Consider a sample of $n$ observations from a normal distributed random variable $N(\mu, \sigma^2)$ with unknown mean and variance, which is from an exponential family
$\left (\sum x_i, \sum x_i^2\right)$ is a sufficient stati... | Pairwise independence of sufficient statistics in exponential families
I think it is not true
Consider a sample of $n$ observations from a normal distributed random variable $N(\mu, \sigma^2)$ with unknown mean and variance, which is from an exponential family
$\left (\ |
54,930 | Is graduate level probability theory (Durett) used often in ML, DL research? | As a statistics PhD student studying Bayesian deep learning and Gaussian processes, I have found it useful to be familiar with probability. I do not directly use the results for now because I am working on applied problems, but a lot of the theoretical work I look at is based on nonparametric techniques such as Gaussi... | Is graduate level probability theory (Durett) used often in ML, DL research? | As a statistics PhD student studying Bayesian deep learning and Gaussian processes, I have found it useful to be familiar with probability. I do not directly use the results for now because I am work | Is graduate level probability theory (Durett) used often in ML, DL research?
As a statistics PhD student studying Bayesian deep learning and Gaussian processes, I have found it useful to be familiar with probability. I do not directly use the results for now because I am working on applied problems, but a lot of the t... | Is graduate level probability theory (Durett) used often in ML, DL research?
As a statistics PhD student studying Bayesian deep learning and Gaussian processes, I have found it useful to be familiar with probability. I do not directly use the results for now because I am work |
54,931 | Is graduate level probability theory (Durett) used often in ML, DL research? | Should I take a graduate level statistics course in Probability Theory
that follows Durrett's textbook
NO. I have seen exactly zero instances where the sort of measure-theoretic background that is explored in depth in books like Durrett and Klenke is actually used in ML. The theory of probability and random variab... | Is graduate level probability theory (Durett) used often in ML, DL research? | Should I take a graduate level statistics course in Probability Theory
that follows Durrett's textbook
NO. I have seen exactly zero instances where the sort of measure-theoretic background that is | Is graduate level probability theory (Durett) used often in ML, DL research?
Should I take a graduate level statistics course in Probability Theory
that follows Durrett's textbook
NO. I have seen exactly zero instances where the sort of measure-theoretic background that is explored in depth in books like Durrett an... | Is graduate level probability theory (Durett) used often in ML, DL research?
Should I take a graduate level statistics course in Probability Theory
that follows Durrett's textbook
NO. I have seen exactly zero instances where the sort of measure-theoretic background that is |
54,932 | Plotting non-parametric (E)CDEF confidence envelopes for comparison | You can use the Kolmogorov-Smirnov test, and invert it to get a confidence band. Let $X_1, X_2, \dotsc, X_n$ be iid observations from some continuous distribution function $F$. Then the KS test statistic is given by
$$
D_n = \sup_x \mid \hat{F}_ n(x)-F_0(x) \mid =
\max_{i=1,2,\dotsc,n} \max \{\frac{i}{n}-F_0(... | Plotting non-parametric (E)CDEF confidence envelopes for comparison | You can use the Kolmogorov-Smirnov test, and invert it to get a confidence band. Let $X_1, X_2, \dotsc, X_n$ be iid observations from some continuous distribution function $F$. Then the KS test stati | Plotting non-parametric (E)CDEF confidence envelopes for comparison
You can use the Kolmogorov-Smirnov test, and invert it to get a confidence band. Let $X_1, X_2, \dotsc, X_n$ be iid observations from some continuous distribution function $F$. Then the KS test statistic is given by
$$
D_n = \sup_x \mid \hat{F}_ n... | Plotting non-parametric (E)CDEF confidence envelopes for comparison
You can use the Kolmogorov-Smirnov test, and invert it to get a confidence band. Let $X_1, X_2, \dotsc, X_n$ be iid observations from some continuous distribution function $F$. Then the KS test stati |
54,933 | Plotting the typical set of a Gaussian distribution | One of the confusing things about concentration of measure is that we're trying to demonstrate deviations away from our naive, low-dimensional intuition. Here that is demonstrated in how the radial volume changes relative to a uniform distribution over radii. As we move away from a given point the shells of constant ... | Plotting the typical set of a Gaussian distribution | One of the confusing things about concentration of measure is that we're trying to demonstrate deviations away from our naive, low-dimensional intuition. Here that is demonstrated in how the radial v | Plotting the typical set of a Gaussian distribution
One of the confusing things about concentration of measure is that we're trying to demonstrate deviations away from our naive, low-dimensional intuition. Here that is demonstrated in how the radial volume changes relative to a uniform distribution over radii. As we ... | Plotting the typical set of a Gaussian distribution
One of the confusing things about concentration of measure is that we're trying to demonstrate deviations away from our naive, low-dimensional intuition. Here that is demonstrated in how the radial v |
54,934 | Ratio of two centered independent centered chi^2 | If I'm not mistaken, at least for even $k$, this is solvable, but it is very tedious. Following is the outline, in which, for simplicity, I'm omitting constant terms from any integral (i.e., those not involved in the integration).
The ratio distribution of two independent $\chi^2$ RVs is
$$
\sim \int_y |y| (zy)^{\frac{... | Ratio of two centered independent centered chi^2 | If I'm not mistaken, at least for even $k$, this is solvable, but it is very tedious. Following is the outline, in which, for simplicity, I'm omitting constant terms from any integral (i.e., those not | Ratio of two centered independent centered chi^2
If I'm not mistaken, at least for even $k$, this is solvable, but it is very tedious. Following is the outline, in which, for simplicity, I'm omitting constant terms from any integral (i.e., those not involved in the integration).
The ratio distribution of two independen... | Ratio of two centered independent centered chi^2
If I'm not mistaken, at least for even $k$, this is solvable, but it is very tedious. Following is the outline, in which, for simplicity, I'm omitting constant terms from any integral (i.e., those not |
54,935 | Ratio of two centered independent centered chi^2 | The behaviour of the distribution is quite 'wild' for small values of parameter $k$.
Here is a Monte Carlo simulation of the pdf of the ratio when $k = 1$:
... and when $k = 2$:
However, it rapidly stabilises as $k$ increases, and when $k$ is larger, is extremely well approximated by a Cauchy distribution (same as S... | Ratio of two centered independent centered chi^2 | The behaviour of the distribution is quite 'wild' for small values of parameter $k$.
Here is a Monte Carlo simulation of the pdf of the ratio when $k = 1$:
... and when $k = 2$:
However, it rapidly | Ratio of two centered independent centered chi^2
The behaviour of the distribution is quite 'wild' for small values of parameter $k$.
Here is a Monte Carlo simulation of the pdf of the ratio when $k = 1$:
... and when $k = 2$:
However, it rapidly stabilises as $k$ increases, and when $k$ is larger, is extremely well... | Ratio of two centered independent centered chi^2
The behaviour of the distribution is quite 'wild' for small values of parameter $k$.
Here is a Monte Carlo simulation of the pdf of the ratio when $k = 1$:
... and when $k = 2$:
However, it rapidly |
54,936 | z-test for one population proportion hypothesis with a small sample size | To achieve that level of confidence, you would have to satisfy the most stringent critic. They would require you to establish
Your sample truly is a simple random sample.
The respondents answer honestly and correctly.
That if the barest minority, just less than half, of the population actually would answer "yes", you... | z-test for one population proportion hypothesis with a small sample size | To achieve that level of confidence, you would have to satisfy the most stringent critic. They would require you to establish
Your sample truly is a simple random sample.
The respondents answer hone | z-test for one population proportion hypothesis with a small sample size
To achieve that level of confidence, you would have to satisfy the most stringent critic. They would require you to establish
Your sample truly is a simple random sample.
The respondents answer honestly and correctly.
That if the barest minority... | z-test for one population proportion hypothesis with a small sample size
To achieve that level of confidence, you would have to satisfy the most stringent critic. They would require you to establish
Your sample truly is a simple random sample.
The respondents answer hone |
54,937 | Relative importance of predictors in logistic regression | I assume all predictors have been standardized (thus, centered and scaled by the sample standard deviations).
Let $\mathbf{x}$ be the vector of predictors and $y$ the response, conditionally Bernoulli-distributed wrt $\mathbf{x}$. Then if $\mu=\mathbb{E[y|\mathbf{x}]}=p(y=1|\mathbf{x})$, then clearly
$$\frac{\partial... | Relative importance of predictors in logistic regression | I assume all predictors have been standardized (thus, centered and scaled by the sample standard deviations).
Let $\mathbf{x}$ be the vector of predictors and $y$ the response, conditionally Bernoull | Relative importance of predictors in logistic regression
I assume all predictors have been standardized (thus, centered and scaled by the sample standard deviations).
Let $\mathbf{x}$ be the vector of predictors and $y$ the response, conditionally Bernoulli-distributed wrt $\mathbf{x}$. Then if $\mu=\mathbb{E[y|\mathb... | Relative importance of predictors in logistic regression
I assume all predictors have been standardized (thus, centered and scaled by the sample standard deviations).
Let $\mathbf{x}$ be the vector of predictors and $y$ the response, conditionally Bernoull |
54,938 | How many data points to acurately approximate the average of recent values in a time series? | I agree with Carl that fitting a model to the data would be an ideal solution, if it makes sense in your context. But I also want to suggest that the following way of thinking about your problem might be helpful.
Suppose that I have a time-varying process that looks like a random walk (so that the location is autoco... | How many data points to acurately approximate the average of recent values in a time series? | I agree with Carl that fitting a model to the data would be an ideal solution, if it makes sense in your context. But I also want to suggest that the following way of thinking about your problem migh | How many data points to acurately approximate the average of recent values in a time series?
I agree with Carl that fitting a model to the data would be an ideal solution, if it makes sense in your context. But I also want to suggest that the following way of thinking about your problem might be helpful.
Suppose tha... | How many data points to acurately approximate the average of recent values in a time series?
I agree with Carl that fitting a model to the data would be an ideal solution, if it makes sense in your context. But I also want to suggest that the following way of thinking about your problem migh |
54,939 | How many data points to acurately approximate the average of recent values in a time series? | Q1: How many points?
All of them. The best way, is to fit a model to the data. If the model is a good one, i.e., if an accurate $T(t)$ can be found, where $T$ is the temperature as a function of $t$ time, then the problem is solved, just choose a $t$, and $T$ is predicted.
In a temperature time series this may require... | How many data points to acurately approximate the average of recent values in a time series? | Q1: How many points?
All of them. The best way, is to fit a model to the data. If the model is a good one, i.e., if an accurate $T(t)$ can be found, where $T$ is the temperature as a function of $t$ t | How many data points to acurately approximate the average of recent values in a time series?
Q1: How many points?
All of them. The best way, is to fit a model to the data. If the model is a good one, i.e., if an accurate $T(t)$ can be found, where $T$ is the temperature as a function of $t$ time, then the problem is so... | How many data points to acurately approximate the average of recent values in a time series?
Q1: How many points?
All of them. The best way, is to fit a model to the data. If the model is a good one, i.e., if an accurate $T(t)$ can be found, where $T$ is the temperature as a function of $t$ t |
54,940 | How many data points to acurately approximate the average of recent values in a time series? | This is more a suggestion than a complete answer, but maybe you could use the median instead of the average so that outliers affect less the result. | How many data points to acurately approximate the average of recent values in a time series? | This is more a suggestion than a complete answer, but maybe you could use the median instead of the average so that outliers affect less the result. | How many data points to acurately approximate the average of recent values in a time series?
This is more a suggestion than a complete answer, but maybe you could use the median instead of the average so that outliers affect less the result. | How many data points to acurately approximate the average of recent values in a time series?
This is more a suggestion than a complete answer, but maybe you could use the median instead of the average so that outliers affect less the result. |
54,941 | What's the intuition of variance, quadratic variation and total variation of Brownian Motion in practice? | Aside from the heavily technical definitions of Brownian motion, the simplest is that if you run Brownian motion from a starting point $B_0=x$, the resulting distribution $B_t$ at time $t$ is Gaussian, with mean $x$ and variance $t$. This is useful because it gives you a sense of how spread out Brownian motion will be ... | What's the intuition of variance, quadratic variation and total variation of Brownian Motion in prac | Aside from the heavily technical definitions of Brownian motion, the simplest is that if you run Brownian motion from a starting point $B_0=x$, the resulting distribution $B_t$ at time $t$ is Gaussian | What's the intuition of variance, quadratic variation and total variation of Brownian Motion in practice?
Aside from the heavily technical definitions of Brownian motion, the simplest is that if you run Brownian motion from a starting point $B_0=x$, the resulting distribution $B_t$ at time $t$ is Gaussian, with mean $x... | What's the intuition of variance, quadratic variation and total variation of Brownian Motion in prac
Aside from the heavily technical definitions of Brownian motion, the simplest is that if you run Brownian motion from a starting point $B_0=x$, the resulting distribution $B_t$ at time $t$ is Gaussian |
54,942 | meaning of metric vs. statistic vs. parameter | As already mentioned by Kodiologist, metric is rather informal name for e way of measuring something, e.g. this is how it is used by Google Analytics
Metrics are quantitative measurements. The metric Sessions is the
total number of sessions. The metric Pages/Session is the average
number of pages viewed per sessio... | meaning of metric vs. statistic vs. parameter | As already mentioned by Kodiologist, metric is rather informal name for e way of measuring something, e.g. this is how it is used by Google Analytics
Metrics are quantitative measurements. The metric | meaning of metric vs. statistic vs. parameter
As already mentioned by Kodiologist, metric is rather informal name for e way of measuring something, e.g. this is how it is used by Google Analytics
Metrics are quantitative measurements. The metric Sessions is the
total number of sessions. The metric Pages/Session is t... | meaning of metric vs. statistic vs. parameter
As already mentioned by Kodiologist, metric is rather informal name for e way of measuring something, e.g. this is how it is used by Google Analytics
Metrics are quantitative measurements. The metric |
54,943 | meaning of metric vs. statistic vs. parameter | This sense of the word "metric" is informal. It means a way to measure or quantify something.
There's an unrelated formal sense of the word "metric" that arises in analysis. There, a metric is a real-valued binary function that is nonnegative, returns 0 iff its arguments are equal, is symmetric, and satisfies the trian... | meaning of metric vs. statistic vs. parameter | This sense of the word "metric" is informal. It means a way to measure or quantify something.
There's an unrelated formal sense of the word "metric" that arises in analysis. There, a metric is a real- | meaning of metric vs. statistic vs. parameter
This sense of the word "metric" is informal. It means a way to measure or quantify something.
There's an unrelated formal sense of the word "metric" that arises in analysis. There, a metric is a real-valued binary function that is nonnegative, returns 0 iff its arguments ar... | meaning of metric vs. statistic vs. parameter
This sense of the word "metric" is informal. It means a way to measure or quantify something.
There's an unrelated formal sense of the word "metric" that arises in analysis. There, a metric is a real- |
54,944 | meaning of metric vs. statistic vs. parameter | What is the appropriate way to use the term "metric," and how is its meaning different from "statistic" and different from "parameter"?
... was the question first asked. It has not been answered.
I believe the term parameter is the original, traditional expression used to describe a range of defining limits, and also ... | meaning of metric vs. statistic vs. parameter | What is the appropriate way to use the term "metric," and how is its meaning different from "statistic" and different from "parameter"?
... was the question first asked. It has not been answered.
I b | meaning of metric vs. statistic vs. parameter
What is the appropriate way to use the term "metric," and how is its meaning different from "statistic" and different from "parameter"?
... was the question first asked. It has not been answered.
I believe the term parameter is the original, traditional expression used to ... | meaning of metric vs. statistic vs. parameter
What is the appropriate way to use the term "metric," and how is its meaning different from "statistic" and different from "parameter"?
... was the question first asked. It has not been answered.
I b |
54,945 | meaning of metric vs. statistic vs. parameter | A metric is a measurement and therefore has units: a parameter may not. For example a mole in chemistry is the amount if stuff that has 6*10^23 molecules is atoms or whatever, and is a dimensionless number - a parameter, not a metric - that has no units.
A metric space is any set of data where distance between two poi... | meaning of metric vs. statistic vs. parameter | A metric is a measurement and therefore has units: a parameter may not. For example a mole in chemistry is the amount if stuff that has 6*10^23 molecules is atoms or whatever, and is a dimensionless n | meaning of metric vs. statistic vs. parameter
A metric is a measurement and therefore has units: a parameter may not. For example a mole in chemistry is the amount if stuff that has 6*10^23 molecules is atoms or whatever, and is a dimensionless number - a parameter, not a metric - that has no units.
A metric space is ... | meaning of metric vs. statistic vs. parameter
A metric is a measurement and therefore has units: a parameter may not. For example a mole in chemistry is the amount if stuff that has 6*10^23 molecules is atoms or whatever, and is a dimensionless n |
54,946 | Hypothesis Test: Bound for number of observations from Y that exceed max(X) if X=Y in distribution | Let us reason as follows.
If the null hypothesis is true, then in a combined sample, any of the $n_X+n_Y$ observations has the same chance to be labelled with $Y$ as any other observation.
Counting how many $Y$s stick out one end is like we have a deck of $n_X$ red cards and $n_Y$ white cards, and we deal cards off th... | Hypothesis Test: Bound for number of observations from Y that exceed max(X) if X=Y in distribution | Let us reason as follows.
If the null hypothesis is true, then in a combined sample, any of the $n_X+n_Y$ observations has the same chance to be labelled with $Y$ as any other observation.
Counting h | Hypothesis Test: Bound for number of observations from Y that exceed max(X) if X=Y in distribution
Let us reason as follows.
If the null hypothesis is true, then in a combined sample, any of the $n_X+n_Y$ observations has the same chance to be labelled with $Y$ as any other observation.
Counting how many $Y$s stick ou... | Hypothesis Test: Bound for number of observations from Y that exceed max(X) if X=Y in distribution
Let us reason as follows.
If the null hypothesis is true, then in a combined sample, any of the $n_X+n_Y$ observations has the same chance to be labelled with $Y$ as any other observation.
Counting h |
54,947 | How are whiskers in a Boxplot of different lengths? [duplicate] | Not necessarily. The whiskers actually end at the highest point within $Q3+1.5R$ and at the lowest point above $Q1-1.5R$. So for instance if $Q3+1.5R=100$ and the highest value in your sample is $90$ then the whisker will end at $90$. You must be observing something like this. | How are whiskers in a Boxplot of different lengths? [duplicate] | Not necessarily. The whiskers actually end at the highest point within $Q3+1.5R$ and at the lowest point above $Q1-1.5R$. So for instance if $Q3+1.5R=100$ and the highest value in your sample is $90$ | How are whiskers in a Boxplot of different lengths? [duplicate]
Not necessarily. The whiskers actually end at the highest point within $Q3+1.5R$ and at the lowest point above $Q1-1.5R$. So for instance if $Q3+1.5R=100$ and the highest value in your sample is $90$ then the whisker will end at $90$. You must be observing... | How are whiskers in a Boxplot of different lengths? [duplicate]
Not necessarily. The whiskers actually end at the highest point within $Q3+1.5R$ and at the lowest point above $Q1-1.5R$. So for instance if $Q3+1.5R=100$ and the highest value in your sample is $90$ |
54,948 | Calculate Kappa statistic in R [closed] | Your reference and class1 are correctly defined, but using a wrong function.
The function kappa in R base is not calculating Cohen's Kappa but "Compute or Estimate the Condition Number of a Matrix". See ?kappa.
In stead you can try
caret::confusionMatrix(reference,class1)
Confusion Matrix and Statistics
Reference
Pre... | Calculate Kappa statistic in R [closed] | Your reference and class1 are correctly defined, but using a wrong function.
The function kappa in R base is not calculating Cohen's Kappa but "Compute or Estimate the Condition Number of a Matrix". S | Calculate Kappa statistic in R [closed]
Your reference and class1 are correctly defined, but using a wrong function.
The function kappa in R base is not calculating Cohen's Kappa but "Compute or Estimate the Condition Number of a Matrix". See ?kappa.
In stead you can try
caret::confusionMatrix(reference,class1)
Confus... | Calculate Kappa statistic in R [closed]
Your reference and class1 are correctly defined, but using a wrong function.
The function kappa in R base is not calculating Cohen's Kappa but "Compute or Estimate the Condition Number of a Matrix". S |
54,949 | Proper name for "modified Bland–Altman plot" | On acceptance: Acceptance of names depends on who you want them to be accepted by. Bland-Altman plots are simply Tukey mean-difference plots (and Tukey was there much earlier), so if you want statisticians to accept the name you possibly wouldn't name it after Bland and Altman. On the other hand, in some application ar... | Proper name for "modified Bland–Altman plot" | On acceptance: Acceptance of names depends on who you want them to be accepted by. Bland-Altman plots are simply Tukey mean-difference plots (and Tukey was there much earlier), so if you want statisti | Proper name for "modified Bland–Altman plot"
On acceptance: Acceptance of names depends on who you want them to be accepted by. Bland-Altman plots are simply Tukey mean-difference plots (and Tukey was there much earlier), so if you want statisticians to accept the name you possibly wouldn't name it after Bland and Altm... | Proper name for "modified Bland–Altman plot"
On acceptance: Acceptance of names depends on who you want them to be accepted by. Bland-Altman plots are simply Tukey mean-difference plots (and Tukey was there much earlier), so if you want statisti |
54,950 | Stationarity of AR(1) process, stable filter | A stable filter is a filter which exists, and is causal. Causal means that your current observation is a function of past or contemporaneous noise, not future noise. Why do they use the word stable? Well, intuitively, you can see what happens when you simulate data from the model if $|\phi| > 1$. You will see the proce... | Stationarity of AR(1) process, stable filter | A stable filter is a filter which exists, and is causal. Causal means that your current observation is a function of past or contemporaneous noise, not future noise. Why do they use the word stable? W | Stationarity of AR(1) process, stable filter
A stable filter is a filter which exists, and is causal. Causal means that your current observation is a function of past or contemporaneous noise, not future noise. Why do they use the word stable? Well, intuitively, you can see what happens when you simulate data from the ... | Stationarity of AR(1) process, stable filter
A stable filter is a filter which exists, and is causal. Causal means that your current observation is a function of past or contemporaneous noise, not future noise. Why do they use the word stable? W |
54,951 | Stationarity of AR(1) process, stable filter | This is a somewhat simple answer:
The "Definition" section of the same Wiki article says:
An autoregressive model can thus be viewed as the output of an all-pole infinite impulse response filter whose input is white noise.
In this case, the stability is a consequence of the so called filter having its poles inside th... | Stationarity of AR(1) process, stable filter | This is a somewhat simple answer:
The "Definition" section of the same Wiki article says:
An autoregressive model can thus be viewed as the output of an all-pole infinite impulse response filter whos | Stationarity of AR(1) process, stable filter
This is a somewhat simple answer:
The "Definition" section of the same Wiki article says:
An autoregressive model can thus be viewed as the output of an all-pole infinite impulse response filter whose input is white noise.
In this case, the stability is a consequence of th... | Stationarity of AR(1) process, stable filter
This is a somewhat simple answer:
The "Definition" section of the same Wiki article says:
An autoregressive model can thus be viewed as the output of an all-pole infinite impulse response filter whos |
54,952 | What F-test is performed by $\texttt{lm()}$ function in R, at the end of the output? | The $F$ test always tests against the intercept-only model (y ~ 1) unless the model has not intercept, then a zero-mean model is used (y ~ 0). In your case, this means that the null hypothesis $\beta_1 = \dots = \beta_5 = 0$ is tested. | What F-test is performed by $\texttt{lm()}$ function in R, at the end of the output? | The $F$ test always tests against the intercept-only model (y ~ 1) unless the model has not intercept, then a zero-mean model is used (y ~ 0). In your case, this means that the null hypothesis $\beta_ | What F-test is performed by $\texttt{lm()}$ function in R, at the end of the output?
The $F$ test always tests against the intercept-only model (y ~ 1) unless the model has not intercept, then a zero-mean model is used (y ~ 0). In your case, this means that the null hypothesis $\beta_1 = \dots = \beta_5 = 0$ is tested. | What F-test is performed by $\texttt{lm()}$ function in R, at the end of the output?
The $F$ test always tests against the intercept-only model (y ~ 1) unless the model has not intercept, then a zero-mean model is used (y ~ 0). In your case, this means that the null hypothesis $\beta_ |
54,953 | Testing whether two data sets are statistically different | It depends on the type of statistical diffrences you are looking. It also depends upon the data distribution.
A great small table summarizing the statistical test are here with the use cases :
https://cyfar.org/types-statistical-tests | Testing whether two data sets are statistically different | It depends on the type of statistical diffrences you are looking. It also depends upon the data distribution.
A great small table summarizing the statistical test are here with the use cases :
https: | Testing whether two data sets are statistically different
It depends on the type of statistical diffrences you are looking. It also depends upon the data distribution.
A great small table summarizing the statistical test are here with the use cases :
https://cyfar.org/types-statistical-tests | Testing whether two data sets are statistically different
It depends on the type of statistical diffrences you are looking. It also depends upon the data distribution.
A great small table summarizing the statistical test are here with the use cases :
https: |
54,954 | Interpretation of a spline | The only difference is in an intercept term. This is standard with smooth terms in models of this kind.
Taking your two plots and resizing the red one to be on the same scale as the other one, then shifting the y-axis to align the two:
we can see that they are otherwise identical -- one is just a shift of the other (w... | Interpretation of a spline | The only difference is in an intercept term. This is standard with smooth terms in models of this kind.
Taking your two plots and resizing the red one to be on the same scale as the other one, then sh | Interpretation of a spline
The only difference is in an intercept term. This is standard with smooth terms in models of this kind.
Taking your two plots and resizing the red one to be on the same scale as the other one, then shifting the y-axis to align the two:
we can see that they are otherwise identical -- one is j... | Interpretation of a spline
The only difference is in an intercept term. This is standard with smooth terms in models of this kind.
Taking your two plots and resizing the red one to be on the same scale as the other one, then sh |
54,955 | Interpretation of a spline | To add a little to @Glen_b's answer, the standard splines in mgcv are subject to constraints to enable their identification as they are confounded with the model intercept term.
The constraint mgcv uses is
$$\sum_i f_j(x_{ij}) = 0 ~~ \forall ~ j$$
This is the sum-to-zero constraint, where $f_j$ is a spline function and... | Interpretation of a spline | To add a little to @Glen_b's answer, the standard splines in mgcv are subject to constraints to enable their identification as they are confounded with the model intercept term.
The constraint mgcv us | Interpretation of a spline
To add a little to @Glen_b's answer, the standard splines in mgcv are subject to constraints to enable their identification as they are confounded with the model intercept term.
The constraint mgcv uses is
$$\sum_i f_j(x_{ij}) = 0 ~~ \forall ~ j$$
This is the sum-to-zero constraint, where $f_... | Interpretation of a spline
To add a little to @Glen_b's answer, the standard splines in mgcv are subject to constraints to enable their identification as they are confounded with the model intercept term.
The constraint mgcv us |
54,956 | Degrees freedom reported by the lmer model don't seem plausible | Are you using the lmerTest package to get your p-values to output for the summary of an lmer object? If so, you are estimating degrees of freedom using the Satterthwaite approximation. The top of your output should say something like:
t-tests use Satterthwaite approximations to degrees of freedom
I assume you are ask... | Degrees freedom reported by the lmer model don't seem plausible | Are you using the lmerTest package to get your p-values to output for the summary of an lmer object? If so, you are estimating degrees of freedom using the Satterthwaite approximation. The top of your | Degrees freedom reported by the lmer model don't seem plausible
Are you using the lmerTest package to get your p-values to output for the summary of an lmer object? If so, you are estimating degrees of freedom using the Satterthwaite approximation. The top of your output should say something like:
t-tests use Satterth... | Degrees freedom reported by the lmer model don't seem plausible
Are you using the lmerTest package to get your p-values to output for the summary of an lmer object? If so, you are estimating degrees of freedom using the Satterthwaite approximation. The top of your |
54,957 | Degrees freedom reported by the lmer model don't seem plausible | How do you define "plausible" degrees of freedom?
Simply speaking, calculating degrees of freedom for GLMMs is complicated and there is no simple formula for calculating them. Let me quote the r-sig-mixed-models FAQ:
(There is an R FAQ entry on this topic, which links to a mailing list
post by Doug Bates (there is ... | Degrees freedom reported by the lmer model don't seem plausible | How do you define "plausible" degrees of freedom?
Simply speaking, calculating degrees of freedom for GLMMs is complicated and there is no simple formula for calculating them. Let me quote the r-sig- | Degrees freedom reported by the lmer model don't seem plausible
How do you define "plausible" degrees of freedom?
Simply speaking, calculating degrees of freedom for GLMMs is complicated and there is no simple formula for calculating them. Let me quote the r-sig-mixed-models FAQ:
(There is an R FAQ entry on this topi... | Degrees freedom reported by the lmer model don't seem plausible
How do you define "plausible" degrees of freedom?
Simply speaking, calculating degrees of freedom for GLMMs is complicated and there is no simple formula for calculating them. Let me quote the r-sig- |
54,958 | lme4_fixed-effect model matrix is rank deficient so dropping 1 column / coefficient | In the data you link to, Language and useOfIntrinsic encode the exact same information. Think about it this way: Language gives the anova flexibility to estimate the mean for each language independently. Once this has been done, there is no additional among-language variation floating around to estimate the effect of... | lme4_fixed-effect model matrix is rank deficient so dropping 1 column / coefficient | In the data you link to, Language and useOfIntrinsic encode the exact same information. Think about it this way: Language gives the anova flexibility to estimate the mean for each language independen | lme4_fixed-effect model matrix is rank deficient so dropping 1 column / coefficient
In the data you link to, Language and useOfIntrinsic encode the exact same information. Think about it this way: Language gives the anova flexibility to estimate the mean for each language independently. Once this has been done, there... | lme4_fixed-effect model matrix is rank deficient so dropping 1 column / coefficient
In the data you link to, Language and useOfIntrinsic encode the exact same information. Think about it this way: Language gives the anova flexibility to estimate the mean for each language independen |
54,959 | What's the use of the embedding matrix in a char-rnn seq2seq model? | Embeddings are dense vector representations of the characters. The rationale behind using it is to convert an arbitrary discrete id, to a continuous representation.
The main advantage is that back-propagation is possible over continuous representations while it is not over discrete representations. A second advantage ... | What's the use of the embedding matrix in a char-rnn seq2seq model? | Embeddings are dense vector representations of the characters. The rationale behind using it is to convert an arbitrary discrete id, to a continuous representation.
The main advantage is that back-pr | What's the use of the embedding matrix in a char-rnn seq2seq model?
Embeddings are dense vector representations of the characters. The rationale behind using it is to convert an arbitrary discrete id, to a continuous representation.
The main advantage is that back-propagation is possible over continuous representation... | What's the use of the embedding matrix in a char-rnn seq2seq model?
Embeddings are dense vector representations of the characters. The rationale behind using it is to convert an arbitrary discrete id, to a continuous representation.
The main advantage is that back-pr |
54,960 | At what level are covariates held constant in multiple logistic regression? | This is mostly addressed at What does “all else equal” mean in multiple regression? Namely, that they can be held constant at any value or level of the covariates. In some sense, it is easiest to explain them (or conceive of them) as being held at the means of the other continuous variables and the reference levels o... | At what level are covariates held constant in multiple logistic regression? | This is mostly addressed at What does “all else equal” mean in multiple regression? Namely, that they can be held constant at any value or level of the covariates. In some sense, it is easiest to ex | At what level are covariates held constant in multiple logistic regression?
This is mostly addressed at What does “all else equal” mean in multiple regression? Namely, that they can be held constant at any value or level of the covariates. In some sense, it is easiest to explain them (or conceive of them) as being he... | At what level are covariates held constant in multiple logistic regression?
This is mostly addressed at What does “all else equal” mean in multiple regression? Namely, that they can be held constant at any value or level of the covariates. In some sense, it is easiest to ex |
54,961 | At what level are covariates held constant in multiple logistic regression? | Coding really doesn't matter, because when it comes down to it, regression coefficients are always based on slope, i.e., $\Delta y/\Delta x$. Categorical factors are always broken down to either $k-1$ dummy indicators for each $k$-level factor (corner point coding, level-1's $\Delta y/\Delta x$ goes to constant term) ... | At what level are covariates held constant in multiple logistic regression? | Coding really doesn't matter, because when it comes down to it, regression coefficients are always based on slope, i.e., $\Delta y/\Delta x$. Categorical factors are always broken down to either $k-1 | At what level are covariates held constant in multiple logistic regression?
Coding really doesn't matter, because when it comes down to it, regression coefficients are always based on slope, i.e., $\Delta y/\Delta x$. Categorical factors are always broken down to either $k-1$ dummy indicators for each $k$-level factor... | At what level are covariates held constant in multiple logistic regression?
Coding really doesn't matter, because when it comes down to it, regression coefficients are always based on slope, i.e., $\Delta y/\Delta x$. Categorical factors are always broken down to either $k-1 |
54,962 | Can one truly fight outliers with more data? | As with most questions about outliers, I don't think there's an easy answer. It will depend on your situation.
For instance, if you are modeling the relationship between race and income, and, just by chance, Michael Jordan answers your survey, then more data can help because it can clarify the situation, but, since ver... | Can one truly fight outliers with more data? | As with most questions about outliers, I don't think there's an easy answer. It will depend on your situation.
For instance, if you are modeling the relationship between race and income, and, just by | Can one truly fight outliers with more data?
As with most questions about outliers, I don't think there's an easy answer. It will depend on your situation.
For instance, if you are modeling the relationship between race and income, and, just by chance, Michael Jordan answers your survey, then more data can help because... | Can one truly fight outliers with more data?
As with most questions about outliers, I don't think there's an easy answer. It will depend on your situation.
For instance, if you are modeling the relationship between race and income, and, just by |
54,963 | Can one truly fight outliers with more data? | If your outliers occur because of natural outliers in the distribution, then yes, your estimations will become more stable with more data. Let's say you're using a logistic regression, in a theoretical case where the outcome depends on an observed variable with some normally distributed noise. Outliers will come in the... | Can one truly fight outliers with more data? | If your outliers occur because of natural outliers in the distribution, then yes, your estimations will become more stable with more data. Let's say you're using a logistic regression, in a theoretica | Can one truly fight outliers with more data?
If your outliers occur because of natural outliers in the distribution, then yes, your estimations will become more stable with more data. Let's say you're using a logistic regression, in a theoretical case where the outcome depends on an observed variable with some normally... | Can one truly fight outliers with more data?
If your outliers occur because of natural outliers in the distribution, then yes, your estimations will become more stable with more data. Let's say you're using a logistic regression, in a theoretica |
54,964 | Can one truly fight outliers with more data? | Outliers are those samples that deviate from the pattern(s) of most data. Usually, the number of outliers are far less than normal samples. So, for each new sample, it is more likely that it is a normal sample than outlier. Thus I think, gathering more data can help fight outliers. | Can one truly fight outliers with more data? | Outliers are those samples that deviate from the pattern(s) of most data. Usually, the number of outliers are far less than normal samples. So, for each new sample, it is more likely that it is a norm | Can one truly fight outliers with more data?
Outliers are those samples that deviate from the pattern(s) of most data. Usually, the number of outliers are far less than normal samples. So, for each new sample, it is more likely that it is a normal sample than outlier. Thus I think, gathering more data can help fight ou... | Can one truly fight outliers with more data?
Outliers are those samples that deviate from the pattern(s) of most data. Usually, the number of outliers are far less than normal samples. So, for each new sample, it is more likely that it is a norm |
54,965 | How to normalize if MAD equals zero? | If at least 50% of your observations are identical then yes, this normalisation operation wouldn’t make sense mathematically as well as intuitively.
I would probably consider binning the observations as suggested before. For instance, all observations with the same value will be labelled group 1 and everything else gr... | How to normalize if MAD equals zero? | If at least 50% of your observations are identical then yes, this normalisation operation wouldn’t make sense mathematically as well as intuitively.
I would probably consider binning the observations | How to normalize if MAD equals zero?
If at least 50% of your observations are identical then yes, this normalisation operation wouldn’t make sense mathematically as well as intuitively.
I would probably consider binning the observations as suggested before. For instance, all observations with the same value will be la... | How to normalize if MAD equals zero?
If at least 50% of your observations are identical then yes, this normalisation operation wouldn’t make sense mathematically as well as intuitively.
I would probably consider binning the observations |
54,966 | How to normalize if MAD equals zero? | Normalization is not at all straightforward, as this question indicates. Consider small numbers of large outliers. Even though they don't contribute to MAD, their final values normalized by MAD/median will be very high in absolute values, probably higher than their final values would be had you normalized by SD/mean. I... | How to normalize if MAD equals zero? | Normalization is not at all straightforward, as this question indicates. Consider small numbers of large outliers. Even though they don't contribute to MAD, their final values normalized by MAD/median | How to normalize if MAD equals zero?
Normalization is not at all straightforward, as this question indicates. Consider small numbers of large outliers. Even though they don't contribute to MAD, their final values normalized by MAD/median will be very high in absolute values, probably higher than their final values woul... | How to normalize if MAD equals zero?
Normalization is not at all straightforward, as this question indicates. Consider small numbers of large outliers. Even though they don't contribute to MAD, their final values normalized by MAD/median |
54,967 | How to normalize if MAD equals zero? | Another way might be to induce some deviance on the 50% constant values. For example, if 50% of the values are 1, generate random values with range from 0.9999 to 1.0001 for constant values | How to normalize if MAD equals zero? | Another way might be to induce some deviance on the 50% constant values. For example, if 50% of the values are 1, generate random values with range from 0.9999 to 1.0001 for constant values | How to normalize if MAD equals zero?
Another way might be to induce some deviance on the 50% constant values. For example, if 50% of the values are 1, generate random values with range from 0.9999 to 1.0001 for constant values | How to normalize if MAD equals zero?
Another way might be to induce some deviance on the 50% constant values. For example, if 50% of the values are 1, generate random values with range from 0.9999 to 1.0001 for constant values |
54,968 | How much is overfitting? | There are no hard-and-fast rules about what constitutes "over-fitting".
When using regression, heuristics are sometimes given in terms of the ratio of the sample size to the number of parameters, rather than the difference in predictive accuracy in-sample versus out-of-sample. E.g., in a regression context, I recall r... | How much is overfitting? | There are no hard-and-fast rules about what constitutes "over-fitting".
When using regression, heuristics are sometimes given in terms of the ratio of the sample size to the number of parameters, rat | How much is overfitting?
There are no hard-and-fast rules about what constitutes "over-fitting".
When using regression, heuristics are sometimes given in terms of the ratio of the sample size to the number of parameters, rather than the difference in predictive accuracy in-sample versus out-of-sample. E.g., in a regre... | How much is overfitting?
There are no hard-and-fast rules about what constitutes "over-fitting".
When using regression, heuristics are sometimes given in terms of the ratio of the sample size to the number of parameters, rat |
54,969 | How much is overfitting? | Another suggestion: You could also take a look at the OOB error in Random Forest. This OOB error should actually be worse on the training data then the error on the test data (since on the training data only trees are used which haven't been trained on the observation and therefor these are less trees). | How much is overfitting? | Another suggestion: You could also take a look at the OOB error in Random Forest. This OOB error should actually be worse on the training data then the error on the test data (since on the training da | How much is overfitting?
Another suggestion: You could also take a look at the OOB error in Random Forest. This OOB error should actually be worse on the training data then the error on the test data (since on the training data only trees are used which haven't been trained on the observation and therefor these are les... | How much is overfitting?
Another suggestion: You could also take a look at the OOB error in Random Forest. This OOB error should actually be worse on the training data then the error on the test data (since on the training da |
54,970 | How much is overfitting? | Interesting question. I'm not familiar with such a definition.
You can evaluate that using cross validation.
Do cross validation for X times
1.1 In each time measure the accuracy on both the training set and test set
Test whether the train accuracy and test accuracy are likely to come from the same distribution (e.g.... | How much is overfitting? | Interesting question. I'm not familiar with such a definition.
You can evaluate that using cross validation.
Do cross validation for X times
1.1 In each time measure the accuracy on both the trainin | How much is overfitting?
Interesting question. I'm not familiar with such a definition.
You can evaluate that using cross validation.
Do cross validation for X times
1.1 In each time measure the accuracy on both the training set and test set
Test whether the train accuracy and test accuracy are likely to come from th... | How much is overfitting?
Interesting question. I'm not familiar with such a definition.
You can evaluate that using cross validation.
Do cross validation for X times
1.1 In each time measure the accuracy on both the trainin |
54,971 | What evaluation metric to use for high class imbalance where i want to capture most of the positive (ones) in the dataset | Neither seems appropriate. Rather, assign whatever penalty scores you want to the two kinds of errors (mistaking a 0 for a 1, and mistaking a 1 for a 0) and sum the errors. This allows you to precisely control the tradeoff. | What evaluation metric to use for high class imbalance where i want to capture most of the positive | Neither seems appropriate. Rather, assign whatever penalty scores you want to the two kinds of errors (mistaking a 0 for a 1, and mistaking a 1 for a 0) and sum the errors. This allows you to precisel | What evaluation metric to use for high class imbalance where i want to capture most of the positive (ones) in the dataset
Neither seems appropriate. Rather, assign whatever penalty scores you want to the two kinds of errors (mistaking a 0 for a 1, and mistaking a 1 for a 0) and sum the errors. This allows you to precis... | What evaluation metric to use for high class imbalance where i want to capture most of the positive
Neither seems appropriate. Rather, assign whatever penalty scores you want to the two kinds of errors (mistaking a 0 for a 1, and mistaking a 1 for a 0) and sum the errors. This allows you to precisel |
54,972 | What evaluation metric to use for high class imbalance where i want to capture most of the positive (ones) in the dataset | You can look at the Precision,Recall and the F1 score which is nothing but the harmonic mean of the Precision and Recall. | What evaluation metric to use for high class imbalance where i want to capture most of the positive | You can look at the Precision,Recall and the F1 score which is nothing but the harmonic mean of the Precision and Recall. | What evaluation metric to use for high class imbalance where i want to capture most of the positive (ones) in the dataset
You can look at the Precision,Recall and the F1 score which is nothing but the harmonic mean of the Precision and Recall. | What evaluation metric to use for high class imbalance where i want to capture most of the positive
You can look at the Precision,Recall and the F1 score which is nothing but the harmonic mean of the Precision and Recall. |
54,973 | What evaluation metric to use for high class imbalance where i want to capture most of the positive (ones) in the dataset | Your reading is correct in the sense that AUC-PRC is a better metric for imbalanced classification compared to AUC-ROC. I disagree with Kodi in sense that AUC could be useful in these scenarios. Like Santanu said you could look for precision, recall and F1. I would want to add Sensitivity and Kappa.
However, choice of... | What evaluation metric to use for high class imbalance where i want to capture most of the positive | Your reading is correct in the sense that AUC-PRC is a better metric for imbalanced classification compared to AUC-ROC. I disagree with Kodi in sense that AUC could be useful in these scenarios. Like | What evaluation metric to use for high class imbalance where i want to capture most of the positive (ones) in the dataset
Your reading is correct in the sense that AUC-PRC is a better metric for imbalanced classification compared to AUC-ROC. I disagree with Kodi in sense that AUC could be useful in these scenarios. Lik... | What evaluation metric to use for high class imbalance where i want to capture most of the positive
Your reading is correct in the sense that AUC-PRC is a better metric for imbalanced classification compared to AUC-ROC. I disagree with Kodi in sense that AUC could be useful in these scenarios. Like |
54,974 | Modeling Correlated Outputs in Multi-Output Neural Networks | The question is, if the likelihood function you specified does so. E.g. if you model 2 variables $y_1, y_2$, you will often use a likelihood function of the form
$$
p(y_1, y_2 | x) = p(y_1|x) p(y_2|x).
$$
For example, this is the same as summing up the log-likelihoods of two Bernoulli variables if you do two classifici... | Modeling Correlated Outputs in Multi-Output Neural Networks | The question is, if the likelihood function you specified does so. E.g. if you model 2 variables $y_1, y_2$, you will often use a likelihood function of the form
$$
p(y_1, y_2 | x) = p(y_1|x) p(y_2|x) | Modeling Correlated Outputs in Multi-Output Neural Networks
The question is, if the likelihood function you specified does so. E.g. if you model 2 variables $y_1, y_2$, you will often use a likelihood function of the form
$$
p(y_1, y_2 | x) = p(y_1|x) p(y_2|x).
$$
For example, this is the same as summing up the log-lik... | Modeling Correlated Outputs in Multi-Output Neural Networks
The question is, if the likelihood function you specified does so. E.g. if you model 2 variables $y_1, y_2$, you will often use a likelihood function of the form
$$
p(y_1, y_2 | x) = p(y_1|x) p(y_2|x) |
54,975 | Should I use the logits or the scaled probabilities from them to extract my predictions? | It is not exactly clear what kind of model you are referring to, but in case of logistic regression, multinomial logistic regression and similar models, they output probabilities.
As about predictions, notice that if you pass the logits through softmax function then it does not change the relations between values, so ... | Should I use the logits or the scaled probabilities from them to extract my predictions? | It is not exactly clear what kind of model you are referring to, but in case of logistic regression, multinomial logistic regression and similar models, they output probabilities.
As about prediction | Should I use the logits or the scaled probabilities from them to extract my predictions?
It is not exactly clear what kind of model you are referring to, but in case of logistic regression, multinomial logistic regression and similar models, they output probabilities.
As about predictions, notice that if you pass the ... | Should I use the logits or the scaled probabilities from them to extract my predictions?
It is not exactly clear what kind of model you are referring to, but in case of logistic regression, multinomial logistic regression and similar models, they output probabilities.
As about prediction |
54,976 | Fisher R-to-Z transform for group correlation stats | You are right: it's not necessary to perform Fisher's transform. Do the t-test. It uses an exact null distribution, whereas comparing Fisher z-transform to a normal distribution would be an approximation.
Trying to do both the z-transform and the transformation to t-distribution would be complete nonsense. The formula ... | Fisher R-to-Z transform for group correlation stats | You are right: it's not necessary to perform Fisher's transform. Do the t-test. It uses an exact null distribution, whereas comparing Fisher z-transform to a normal distribution would be an approximat | Fisher R-to-Z transform for group correlation stats
You are right: it's not necessary to perform Fisher's transform. Do the t-test. It uses an exact null distribution, whereas comparing Fisher z-transform to a normal distribution would be an approximation.
Trying to do both the z-transform and the transformation to t-d... | Fisher R-to-Z transform for group correlation stats
You are right: it's not necessary to perform Fisher's transform. Do the t-test. It uses an exact null distribution, whereas comparing Fisher z-transform to a normal distribution would be an approximat |
54,977 | Fisher R-to-Z transform for group correlation stats | If you analyse the $r$ values directly you are assuming they all have the same precision which is only likely to be true if they are (a) all based on the same $n$ (b) all more or less the same. You could compute the standard errors and then do your analysis weighting each by the inverse of its sampling variance. It wou... | Fisher R-to-Z transform for group correlation stats | If you analyse the $r$ values directly you are assuming they all have the same precision which is only likely to be true if they are (a) all based on the same $n$ (b) all more or less the same. You co | Fisher R-to-Z transform for group correlation stats
If you analyse the $r$ values directly you are assuming they all have the same precision which is only likely to be true if they are (a) all based on the same $n$ (b) all more or less the same. You could compute the standard errors and then do your analysis weighting ... | Fisher R-to-Z transform for group correlation stats
If you analyse the $r$ values directly you are assuming they all have the same precision which is only likely to be true if they are (a) all based on the same $n$ (b) all more or less the same. You co |
54,978 | Fisher R-to-Z transform for group correlation stats | If I am reading you correctly, you are comparing the mean r values of two groups. In general, even though the t test is robust to violations of normality, you have greater power with normal distributions. Therefore, if some of your r's are high (over .6 or so) it would be a good idea to transform them. Naturally, the t... | Fisher R-to-Z transform for group correlation stats | If I am reading you correctly, you are comparing the mean r values of two groups. In general, even though the t test is robust to violations of normality, you have greater power with normal distributi | Fisher R-to-Z transform for group correlation stats
If I am reading you correctly, you are comparing the mean r values of two groups. In general, even though the t test is robust to violations of normality, you have greater power with normal distributions. Therefore, if some of your r's are high (over .6 or so) it woul... | Fisher R-to-Z transform for group correlation stats
If I am reading you correctly, you are comparing the mean r values of two groups. In general, even though the t test is robust to violations of normality, you have greater power with normal distributi |
54,979 | Automated forecasting of 1000 weekly time series (food product retail) | Learn R, at least well enough to program for loops to loop over your time series. Plus, learn enough R to read and write your data (e.g., using the read.table() and write.table() commands). There are tons of introductions to R around, pick almost any one.
Read Hyndman & Athanasopoulos "Forecasting: principles and pract... | Automated forecasting of 1000 weekly time series (food product retail) | Learn R, at least well enough to program for loops to loop over your time series. Plus, learn enough R to read and write your data (e.g., using the read.table() and write.table() commands). There are | Automated forecasting of 1000 weekly time series (food product retail)
Learn R, at least well enough to program for loops to loop over your time series. Plus, learn enough R to read and write your data (e.g., using the read.table() and write.table() commands). There are tons of introductions to R around, pick almost an... | Automated forecasting of 1000 weekly time series (food product retail)
Learn R, at least well enough to program for loops to loop over your time series. Plus, learn enough R to read and write your data (e.g., using the read.table() and write.table() commands). There are |
54,980 | Automated forecasting of 1000 weekly time series (food product retail) | AUTOBOX ( a piece of software that I had helped develop) has an R version that you can try out . It will detect not only the ARIMA structure but the week of the year structure and changes in the week-of-the-year structure along with level shifts and local time trends while incorporating the lead and lag effects of us... | Automated forecasting of 1000 weekly time series (food product retail) | AUTOBOX ( a piece of software that I had helped develop) has an R version that you can try out . It will detect not only the ARIMA structure but the week of the year structure and changes in the wee | Automated forecasting of 1000 weekly time series (food product retail)
AUTOBOX ( a piece of software that I had helped develop) has an R version that you can try out . It will detect not only the ARIMA structure but the week of the year structure and changes in the week-of-the-year structure along with level shifts a... | Automated forecasting of 1000 weekly time series (food product retail)
AUTOBOX ( a piece of software that I had helped develop) has an R version that you can try out . It will detect not only the ARIMA structure but the week of the year structure and changes in the wee |
54,981 | price elasticity and time series modelling | The most important question here is 'Is the observed variation in the price exogenous?'. Unless you did pricing experiment, the answer is usually no for any observational data and there is no hope of recovering price elasticity just from observing sales and price. That is, the price in your equation has to be correlate... | price elasticity and time series modelling | The most important question here is 'Is the observed variation in the price exogenous?'. Unless you did pricing experiment, the answer is usually no for any observational data and there is no hope of | price elasticity and time series modelling
The most important question here is 'Is the observed variation in the price exogenous?'. Unless you did pricing experiment, the answer is usually no for any observational data and there is no hope of recovering price elasticity just from observing sales and price. That is, the... | price elasticity and time series modelling
The most important question here is 'Is the observed variation in the price exogenous?'. Unless you did pricing experiment, the answer is usually no for any observational data and there is no hope of |
54,982 | How do I compute the correlation between two features and their output class? | Correlation is used as a method for feature selection and is usually calculated between a feature and the output class (filter methods for feature selection). It roughly translates to how much will the change be reflected on the output class for a small change in the current feature. If the change is proportional and v... | How do I compute the correlation between two features and their output class? | Correlation is used as a method for feature selection and is usually calculated between a feature and the output class (filter methods for feature selection). It roughly translates to how much will th | How do I compute the correlation between two features and their output class?
Correlation is used as a method for feature selection and is usually calculated between a feature and the output class (filter methods for feature selection). It roughly translates to how much will the change be reflected on the output class ... | How do I compute the correlation between two features and their output class?
Correlation is used as a method for feature selection and is usually calculated between a feature and the output class (filter methods for feature selection). It roughly translates to how much will th |
54,983 | How do I compute the correlation between two features and their output class? | This is called correlation filter. If you are using R, You can have a look at FSelector package's linear.correlation and rank.correlation functions. When class labels are categorical, you can use Point-Biserial Correlation, polyserial or polychloric correlation.
The idea is if feature 1 is highly correlated with class ... | How do I compute the correlation between two features and their output class? | This is called correlation filter. If you are using R, You can have a look at FSelector package's linear.correlation and rank.correlation functions. When class labels are categorical, you can use Poin | How do I compute the correlation between two features and their output class?
This is called correlation filter. If you are using R, You can have a look at FSelector package's linear.correlation and rank.correlation functions. When class labels are categorical, you can use Point-Biserial Correlation, polyserial or poly... | How do I compute the correlation between two features and their output class?
This is called correlation filter. If you are using R, You can have a look at FSelector package's linear.correlation and rank.correlation functions. When class labels are categorical, you can use Poin |
54,984 | Survival bias in survival analysis | Survival bias occurs in retrospective studies where inclusion is in some sense outcome dependent (through outcomes or their moderators) but is treated as representative of a population at-risk at baseline. Your description does not give any details suggesting survival bias is an issue here.
Censoring leads to a differe... | Survival bias in survival analysis | Survival bias occurs in retrospective studies where inclusion is in some sense outcome dependent (through outcomes or their moderators) but is treated as representative of a population at-risk at base | Survival bias in survival analysis
Survival bias occurs in retrospective studies where inclusion is in some sense outcome dependent (through outcomes or their moderators) but is treated as representative of a population at-risk at baseline. Your description does not give any details suggesting survival bias is an issue... | Survival bias in survival analysis
Survival bias occurs in retrospective studies where inclusion is in some sense outcome dependent (through outcomes or their moderators) but is treated as representative of a population at-risk at base |
54,985 | Relationship between standard error of the mean and standard deviation | The samples are 'not normally disributed'. Don't they have to be to use pnorm?
The question is asking about the distribution of sample means, not the distribution of the original variable.
Under mild conditions, sample means will tend to be closer to normally distributed than the original variable was. See what happen... | Relationship between standard error of the mean and standard deviation | The samples are 'not normally disributed'. Don't they have to be to use pnorm?
The question is asking about the distribution of sample means, not the distribution of the original variable.
Under mild | Relationship between standard error of the mean and standard deviation
The samples are 'not normally disributed'. Don't they have to be to use pnorm?
The question is asking about the distribution of sample means, not the distribution of the original variable.
Under mild conditions, sample means will tend to be closer ... | Relationship between standard error of the mean and standard deviation
The samples are 'not normally disributed'. Don't they have to be to use pnorm?
The question is asking about the distribution of sample means, not the distribution of the original variable.
Under mild |
54,986 | Can someone please explain the truncated back propagation through time algorithm? | I am sure you have found your answer by now, but for others. The truncated part of Truncated Backpropagation through Time simply refers to at which point in time to stop calculating the gradients for the backpropagation phase.
Lets say you truncate after $k$ steps then the difference is you calculate the below instead.... | Can someone please explain the truncated back propagation through time algorithm? | I am sure you have found your answer by now, but for others. The truncated part of Truncated Backpropagation through Time simply refers to at which point in time to stop calculating the gradients for | Can someone please explain the truncated back propagation through time algorithm?
I am sure you have found your answer by now, but for others. The truncated part of Truncated Backpropagation through Time simply refers to at which point in time to stop calculating the gradients for the backpropagation phase.
Lets say yo... | Can someone please explain the truncated back propagation through time algorithm?
I am sure you have found your answer by now, but for others. The truncated part of Truncated Backpropagation through Time simply refers to at which point in time to stop calculating the gradients for |
54,987 | On real-world use of gamma distributions | According to Wikipedia, "the negative binomial distribution is sometimes considered the discrete analogue of the Gamma distribution". (See also comment by Scortchi.)
It has similar interpretations to the Gamma distribution in terms of "waiting times".
Note that for a Gamma distribution with shape parameter $\alpha$ an... | On real-world use of gamma distributions | According to Wikipedia, "the negative binomial distribution is sometimes considered the discrete analogue of the Gamma distribution". (See also comment by Scortchi.)
It has similar interpretations to | On real-world use of gamma distributions
According to Wikipedia, "the negative binomial distribution is sometimes considered the discrete analogue of the Gamma distribution". (See also comment by Scortchi.)
It has similar interpretations to the Gamma distribution in terms of "waiting times".
Note that for a Gamma dist... | On real-world use of gamma distributions
According to Wikipedia, "the negative binomial distribution is sometimes considered the discrete analogue of the Gamma distribution". (See also comment by Scortchi.)
It has similar interpretations to |
54,988 | Kappa Statistic for Variable Number of Raters | You can do this using a "generalized formula." The intuition here is to use the following formula for observed agreement, which uses the number of raters rather than conditionals for specific raters.
$$p_o=\frac{1}{n'}\sum_{i=1}^{n'}\sum_{k=1}^q\frac{r_{ik}(r_{ik}^\star-1)}{r_i(r_i-1)}$$
where $n'$ is the number of ite... | Kappa Statistic for Variable Number of Raters | You can do this using a "generalized formula." The intuition here is to use the following formula for observed agreement, which uses the number of raters rather than conditionals for specific raters.
| Kappa Statistic for Variable Number of Raters
You can do this using a "generalized formula." The intuition here is to use the following formula for observed agreement, which uses the number of raters rather than conditionals for specific raters.
$$p_o=\frac{1}{n'}\sum_{i=1}^{n'}\sum_{k=1}^q\frac{r_{ik}(r_{ik}^\star-1)}... | Kappa Statistic for Variable Number of Raters
You can do this using a "generalized formula." The intuition here is to use the following formula for observed agreement, which uses the number of raters rather than conditionals for specific raters.
|
54,989 | How can I need to de-transformation from diff(log(data),1)? | Say your original series is $y_t$ and you define the transformed series:
$$\tilde{y}_t = \log(y_t)-\log(y_{t-1})$$
You then forecast the value of $\tilde{y}_{t+1}$ by using your ARIMA(1,0,2) model, giving you $\hat{\tilde{y}}_{t+1}$, but you want a forecast of $y_{t+1}$. You can compute it like this:
$$\hat{y}_{t+1} = ... | How can I need to de-transformation from diff(log(data),1)? | Say your original series is $y_t$ and you define the transformed series:
$$\tilde{y}_t = \log(y_t)-\log(y_{t-1})$$
You then forecast the value of $\tilde{y}_{t+1}$ by using your ARIMA(1,0,2) model, gi | How can I need to de-transformation from diff(log(data),1)?
Say your original series is $y_t$ and you define the transformed series:
$$\tilde{y}_t = \log(y_t)-\log(y_{t-1})$$
You then forecast the value of $\tilde{y}_{t+1}$ by using your ARIMA(1,0,2) model, giving you $\hat{\tilde{y}}_{t+1}$, but you want a forecast of... | How can I need to de-transformation from diff(log(data),1)?
Say your original series is $y_t$ and you define the transformed series:
$$\tilde{y}_t = \log(y_t)-\log(y_{t-1})$$
You then forecast the value of $\tilde{y}_{t+1}$ by using your ARIMA(1,0,2) model, gi |
54,990 | Logistic Regression-Linear Features | I think the term they used may not be standard term. I guess it means the decision boundary can be roughly approximated by a heyperplane. (a line in 2D space). Here are two examples for "linear feature" (A) or not (B) in 2 dimensional sapce.
Here is my answer to a very related question, which may be helpful for you.
D... | Logistic Regression-Linear Features | I think the term they used may not be standard term. I guess it means the decision boundary can be roughly approximated by a heyperplane. (a line in 2D space). Here are two examples for "linear featur | Logistic Regression-Linear Features
I think the term they used may not be standard term. I guess it means the decision boundary can be roughly approximated by a heyperplane. (a line in 2D space). Here are two examples for "linear feature" (A) or not (B) in 2 dimensional sapce.
Here is my answer to a very related quest... | Logistic Regression-Linear Features
I think the term they used may not be standard term. I guess it means the decision boundary can be roughly approximated by a heyperplane. (a line in 2D space). Here are two examples for "linear featur |
54,991 | Logistic Regression-Linear Features | For another view of linear separability (assuming that's what linear features means) imagine you have a simple dataset with sex as a binary, categorical covariate and results as a binary outcome of some experiment.
sex outcome
m 1
m 1
m 0
f 0
f 0
f 0
For binary response data (i.e. like this... | Logistic Regression-Linear Features | For another view of linear separability (assuming that's what linear features means) imagine you have a simple dataset with sex as a binary, categorical covariate and results as a binary outcome of so | Logistic Regression-Linear Features
For another view of linear separability (assuming that's what linear features means) imagine you have a simple dataset with sex as a binary, categorical covariate and results as a binary outcome of some experiment.
sex outcome
m 1
m 1
m 0
f 0
f 0
f 0
For ... | Logistic Regression-Linear Features
For another view of linear separability (assuming that's what linear features means) imagine you have a simple dataset with sex as a binary, categorical covariate and results as a binary outcome of so |
54,992 | Sufficiency of Sample Mean for Laplace Distribution | For on observation, the Laplace pdf is
$$f_X(x) = \dfrac 1 {2b} \exp(-\dfrac {|x-\mu|} b)$$
For multiple iid observations, the pdf is
$$f_\boldsymbol X(\boldsymbol x) = \dfrac 1 {(2b)^n} \exp(- \dfrac 1 b \sum_{i=1}^n {|x_i-\mu|})$$
The easiest way to determine what statistics are sufficient for $\boldsymbol X$ is to t... | Sufficiency of Sample Mean for Laplace Distribution | For on observation, the Laplace pdf is
$$f_X(x) = \dfrac 1 {2b} \exp(-\dfrac {|x-\mu|} b)$$
For multiple iid observations, the pdf is
$$f_\boldsymbol X(\boldsymbol x) = \dfrac 1 {(2b)^n} \exp(- \dfrac | Sufficiency of Sample Mean for Laplace Distribution
For on observation, the Laplace pdf is
$$f_X(x) = \dfrac 1 {2b} \exp(-\dfrac {|x-\mu|} b)$$
For multiple iid observations, the pdf is
$$f_\boldsymbol X(\boldsymbol x) = \dfrac 1 {(2b)^n} \exp(- \dfrac 1 b \sum_{i=1}^n {|x_i-\mu|})$$
The easiest way to determine what s... | Sufficiency of Sample Mean for Laplace Distribution
For on observation, the Laplace pdf is
$$f_X(x) = \dfrac 1 {2b} \exp(-\dfrac {|x-\mu|} b)$$
For multiple iid observations, the pdf is
$$f_\boldsymbol X(\boldsymbol x) = \dfrac 1 {(2b)^n} \exp(- \dfrac |
54,993 | Sufficiency of Sample Mean for Laplace Distribution | The sample median is the maximum likelihood estimator of the mean if the scale is known, but it is not the sufficient statistics. I agree that the order statistics is the sufficient statistics. This can be seen using the factorization theorem and examining the dependence of the RN derivative, upon the examination of th... | Sufficiency of Sample Mean for Laplace Distribution | The sample median is the maximum likelihood estimator of the mean if the scale is known, but it is not the sufficient statistics. I agree that the order statistics is the sufficient statistics. This c | Sufficiency of Sample Mean for Laplace Distribution
The sample median is the maximum likelihood estimator of the mean if the scale is known, but it is not the sufficient statistics. I agree that the order statistics is the sufficient statistics. This can be seen using the factorization theorem and examining the depende... | Sufficiency of Sample Mean for Laplace Distribution
The sample median is the maximum likelihood estimator of the mean if the scale is known, but it is not the sufficient statistics. I agree that the order statistics is the sufficient statistics. This c |
54,994 | Is it possible to use two offsets? | An offset is generally just a coefficient set to a specific value. To get more than one offset, in general you just need to combine the different variables in a way that is consistent to get that fixed value.
In a Poisson equation if you set $Z$ as the offset (or exposure its sometimes called):
$$\log(\mathbb{E}[Y]) = ... | Is it possible to use two offsets? | An offset is generally just a coefficient set to a specific value. To get more than one offset, in general you just need to combine the different variables in a way that is consistent to get that fixe | Is it possible to use two offsets?
An offset is generally just a coefficient set to a specific value. To get more than one offset, in general you just need to combine the different variables in a way that is consistent to get that fixed value.
In a Poisson equation if you set $Z$ as the offset (or exposure its sometime... | Is it possible to use two offsets?
An offset is generally just a coefficient set to a specific value. To get more than one offset, in general you just need to combine the different variables in a way that is consistent to get that fixe |
54,995 | Can Dickey-Fuller be used if the residuals are non-normal? | Yes, that is not a necessary condition. Recall that all we know about the null distribution of the Dickey-Fuller test is its asymptotic representation (although the literature of course considers many refinements).
As is often the case, we do not need distributional assumptions on the error terms when considering asymp... | Can Dickey-Fuller be used if the residuals are non-normal? | Yes, that is not a necessary condition. Recall that all we know about the null distribution of the Dickey-Fuller test is its asymptotic representation (although the literature of course considers many | Can Dickey-Fuller be used if the residuals are non-normal?
Yes, that is not a necessary condition. Recall that all we know about the null distribution of the Dickey-Fuller test is its asymptotic representation (although the literature of course considers many refinements).
As is often the case, we do not need distribut... | Can Dickey-Fuller be used if the residuals are non-normal?
Yes, that is not a necessary condition. Recall that all we know about the null distribution of the Dickey-Fuller test is its asymptotic representation (although the literature of course considers many |
54,996 | Can Dickey-Fuller be used if the residuals are non-normal? | Yes, the innovations need not be normal, not at all.
The underlying mathematical fact that gives rise to the asymptotic null distribution of the DF statistic is Functional Central Limit Theorem, or Invariance Principle.
The FCLT, if you'd like, is an infinite dimensional generalization of the CLT. The CLT holds for dep... | Can Dickey-Fuller be used if the residuals are non-normal? | Yes, the innovations need not be normal, not at all.
The underlying mathematical fact that gives rise to the asymptotic null distribution of the DF statistic is Functional Central Limit Theorem, or In | Can Dickey-Fuller be used if the residuals are non-normal?
Yes, the innovations need not be normal, not at all.
The underlying mathematical fact that gives rise to the asymptotic null distribution of the DF statistic is Functional Central Limit Theorem, or Invariance Principle.
The FCLT, if you'd like, is an infinite d... | Can Dickey-Fuller be used if the residuals are non-normal?
Yes, the innovations need not be normal, not at all.
The underlying mathematical fact that gives rise to the asymptotic null distribution of the DF statistic is Functional Central Limit Theorem, or In |
54,997 | Spherical symmetry: a generalization of exchangeability? | Spherical symmetry is a special case of exchangeability.
The invariance property for spherically symmetric sequences that you describe is indeed the standard definition of spherical symmetry e.g. see On Ali's Characterization of the Spherical Normal Distribution,
Steven F. Arnold and James Lynch,
Journal of the Royal ... | Spherical symmetry: a generalization of exchangeability? | Spherical symmetry is a special case of exchangeability.
The invariance property for spherically symmetric sequences that you describe is indeed the standard definition of spherical symmetry e.g. see | Spherical symmetry: a generalization of exchangeability?
Spherical symmetry is a special case of exchangeability.
The invariance property for spherically symmetric sequences that you describe is indeed the standard definition of spherical symmetry e.g. see On Ali's Characterization of the Spherical Normal Distribution... | Spherical symmetry: a generalization of exchangeability?
Spherical symmetry is a special case of exchangeability.
The invariance property for spherically symmetric sequences that you describe is indeed the standard definition of spherical symmetry e.g. see |
54,998 | What is the relationship between classification and regression in Neural Network? | The difference between a classification and regression is that a classification outputs a prediction probability for class/classes and regression provides a value. We can make a neural network to output a value by simply changing the activation function in the final layer to output the values.
By changing the activatio... | What is the relationship between classification and regression in Neural Network? | The difference between a classification and regression is that a classification outputs a prediction probability for class/classes and regression provides a value. We can make a neural network to outp | What is the relationship between classification and regression in Neural Network?
The difference between a classification and regression is that a classification outputs a prediction probability for class/classes and regression provides a value. We can make a neural network to output a value by simply changing the acti... | What is the relationship between classification and regression in Neural Network?
The difference between a classification and regression is that a classification outputs a prediction probability for class/classes and regression provides a value. We can make a neural network to outp |
54,999 | Estimating error from a 1% sample | Clearly a good (unbiased) estimate of the number of people in the population with the condition is $X/(1\%)=100X$.
$X$ has a Binomial distribution--but we don't know its parameters, because we lack information on the population size (except to know it is at least $800/(1\%)=800\times100=80000$). If we assume the prop... | Estimating error from a 1% sample | Clearly a good (unbiased) estimate of the number of people in the population with the condition is $X/(1\%)=100X$.
$X$ has a Binomial distribution--but we don't know its parameters, because we lack | Estimating error from a 1% sample
Clearly a good (unbiased) estimate of the number of people in the population with the condition is $X/(1\%)=100X$.
$X$ has a Binomial distribution--but we don't know its parameters, because we lack information on the population size (except to know it is at least $800/(1\%)=800\times... | Estimating error from a 1% sample
Clearly a good (unbiased) estimate of the number of people in the population with the condition is $X/(1\%)=100X$.
$X$ has a Binomial distribution--but we don't know its parameters, because we lack |
55,000 | Estimating error from a 1% sample | Suppose we have a population of $N$ Bernoulli trials, but $N$ is unknown. Suppose $α ∈ [0, 1]$ (.01 in the example) is known and we draw a simple random sample of size $αN$ (unknown). We observe $X$ successes (known) in the $αN$ trials. We want to estimate $K$, the number of successes among the $N$ trials in the popula... | Estimating error from a 1% sample | Suppose we have a population of $N$ Bernoulli trials, but $N$ is unknown. Suppose $α ∈ [0, 1]$ (.01 in the example) is known and we draw a simple random sample of size $αN$ (unknown). We observe $X$ s | Estimating error from a 1% sample
Suppose we have a population of $N$ Bernoulli trials, but $N$ is unknown. Suppose $α ∈ [0, 1]$ (.01 in the example) is known and we draw a simple random sample of size $αN$ (unknown). We observe $X$ successes (known) in the $αN$ trials. We want to estimate $K$, the number of successes ... | Estimating error from a 1% sample
Suppose we have a population of $N$ Bernoulli trials, but $N$ is unknown. Suppose $α ∈ [0, 1]$ (.01 in the example) is known and we draw a simple random sample of size $αN$ (unknown). We observe $X$ s |
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