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 |
|---|---|---|---|---|---|---|
53,201 | Do propensity scores reflect the probability of treatment or outcome? | The propensity is for treatment assigned, not outcome.
While there are natural situations where propensity strongly mimics randomization, there are more scenarios where treatment is determined in the most non-random ways possible. Given a sufficiently large sample, searches for the probability of treatment assignment ... | Do propensity scores reflect the probability of treatment or outcome? | The propensity is for treatment assigned, not outcome.
While there are natural situations where propensity strongly mimics randomization, there are more scenarios where treatment is determined in the | Do propensity scores reflect the probability of treatment or outcome?
The propensity is for treatment assigned, not outcome.
While there are natural situations where propensity strongly mimics randomization, there are more scenarios where treatment is determined in the most non-random ways possible. Given a sufficient... | Do propensity scores reflect the probability of treatment or outcome?
The propensity is for treatment assigned, not outcome.
While there are natural situations where propensity strongly mimics randomization, there are more scenarios where treatment is determined in the |
53,202 | Do propensity scores reflect the probability of treatment or outcome? | The propensity score was developed for the most part by Donald Rubin. Here's the abstract to his 1983 paper with Rosenbaum from Biometrika.
The propensity score is the conditional probability of assignment to a particular treatment given a vector of observed covariates. Both large and small sample theory show that adj... | Do propensity scores reflect the probability of treatment or outcome? | The propensity score was developed for the most part by Donald Rubin. Here's the abstract to his 1983 paper with Rosenbaum from Biometrika.
The propensity score is the conditional probability of assi | Do propensity scores reflect the probability of treatment or outcome?
The propensity score was developed for the most part by Donald Rubin. Here's the abstract to his 1983 paper with Rosenbaum from Biometrika.
The propensity score is the conditional probability of assignment to a particular treatment given a vector of... | Do propensity scores reflect the probability of treatment or outcome?
The propensity score was developed for the most part by Donald Rubin. Here's the abstract to his 1983 paper with Rosenbaum from Biometrika.
The propensity score is the conditional probability of assi |
53,203 | Do propensity scores reflect the probability of treatment or outcome? | As both others have said, propensity scores represent the probability of receiving treatment. From the Stata manual for its native propensity score matching command (emphasis mine):
Propensity-score matching uses an average of the outcomes of similar
subjects who get the other treatment level to impute the missing
... | Do propensity scores reflect the probability of treatment or outcome? | As both others have said, propensity scores represent the probability of receiving treatment. From the Stata manual for its native propensity score matching command (emphasis mine):
Propensity-score | Do propensity scores reflect the probability of treatment or outcome?
As both others have said, propensity scores represent the probability of receiving treatment. From the Stata manual for its native propensity score matching command (emphasis mine):
Propensity-score matching uses an average of the outcomes of simila... | Do propensity scores reflect the probability of treatment or outcome?
As both others have said, propensity scores represent the probability of receiving treatment. From the Stata manual for its native propensity score matching command (emphasis mine):
Propensity-score |
53,204 | Gradient in Gradient Boosting | In short answer, the gradient here refers to the gradient of loss function, and it is the target value for each new tree to predict.
Suppose you have a true value $y$ and a predicted value $\hat{y}$. The predicted value is constructed from some existing trees. Then you are trying to construct the next tree which gives ... | Gradient in Gradient Boosting | In short answer, the gradient here refers to the gradient of loss function, and it is the target value for each new tree to predict.
Suppose you have a true value $y$ and a predicted value $\hat{y}$. | Gradient in Gradient Boosting
In short answer, the gradient here refers to the gradient of loss function, and it is the target value for each new tree to predict.
Suppose you have a true value $y$ and a predicted value $\hat{y}$. The predicted value is constructed from some existing trees. Then you are trying to constr... | Gradient in Gradient Boosting
In short answer, the gradient here refers to the gradient of loss function, and it is the target value for each new tree to predict.
Suppose you have a true value $y$ and a predicted value $\hat{y}$. |
53,205 | Lagrangian dual of SVM: derivation | First, let's calculate the norm $||w||^2$.
$$||w||^2 = \sum_i \alpha_iy_i\big(\sum_j\alpha_jy_j\langle x_i,x_j\rangle\big)$$
which evidently can be rearranged to $\sum_i\sum_j\alpha_i\alpha_jy_iy_j\langle x_i,x_j\rangle$.
The $\langle x_i, x_j\rangle$ construct is present because it's assumed that the norm is defined ... | Lagrangian dual of SVM: derivation | First, let's calculate the norm $||w||^2$.
$$||w||^2 = \sum_i \alpha_iy_i\big(\sum_j\alpha_jy_j\langle x_i,x_j\rangle\big)$$
which evidently can be rearranged to $\sum_i\sum_j\alpha_i\alpha_jy_iy_j\la | Lagrangian dual of SVM: derivation
First, let's calculate the norm $||w||^2$.
$$||w||^2 = \sum_i \alpha_iy_i\big(\sum_j\alpha_jy_j\langle x_i,x_j\rangle\big)$$
which evidently can be rearranged to $\sum_i\sum_j\alpha_i\alpha_jy_iy_j\langle x_i,x_j\rangle$.
The $\langle x_i, x_j\rangle$ construct is present because it'... | Lagrangian dual of SVM: derivation
First, let's calculate the norm $||w||^2$.
$$||w||^2 = \sum_i \alpha_iy_i\big(\sum_j\alpha_jy_j\langle x_i,x_j\rangle\big)$$
which evidently can be rearranged to $\sum_i\sum_j\alpha_i\alpha_jy_iy_j\la |
53,206 | Is the sample mean always an unbiased estimator of the expected value? | Answered in comments: The first question is answered immediately using the linearity of expectation. The second conclusion is true only when the underlying distribution has finite variance, in which case it follows with a simple computation of the variance. – whuber
The second conclusion even follows without assumi... | Is the sample mean always an unbiased estimator of the expected value? | Answered in comments: The first question is answered immediately using the linearity of expectation. The second conclusion is true only when the underlying distribution has finite variance, in whi | Is the sample mean always an unbiased estimator of the expected value?
Answered in comments: The first question is answered immediately using the linearity of expectation. The second conclusion is true only when the underlying distribution has finite variance, in which case it follows with a simple computation of t... | Is the sample mean always an unbiased estimator of the expected value?
Answered in comments: The first question is answered immediately using the linearity of expectation. The second conclusion is true only when the underlying distribution has finite variance, in whi |
53,207 | Is the sample mean always an unbiased estimator of the expected value? | One case in which $\hat \mu$ may be a biased estimator of $\mu$: the samples $x_1,..., x_n$ are not uniformly randomly sampled from the population of interest. This is really two problems:
(1) Some values in the population are more likely to be sampled than others. A classic example of this is when we are looking at a... | Is the sample mean always an unbiased estimator of the expected value? | One case in which $\hat \mu$ may be a biased estimator of $\mu$: the samples $x_1,..., x_n$ are not uniformly randomly sampled from the population of interest. This is really two problems:
(1) Some v | Is the sample mean always an unbiased estimator of the expected value?
One case in which $\hat \mu$ may be a biased estimator of $\mu$: the samples $x_1,..., x_n$ are not uniformly randomly sampled from the population of interest. This is really two problems:
(1) Some values in the population are more likely to be sam... | Is the sample mean always an unbiased estimator of the expected value?
One case in which $\hat \mu$ may be a biased estimator of $\mu$: the samples $x_1,..., x_n$ are not uniformly randomly sampled from the population of interest. This is really two problems:
(1) Some v |
53,208 | Proving OLS unbiasedness without conditional zero error expectation? | You can't, because the statement is not true under the weaker assumption.
Consider for example the autoregressive model
\begin{equation*}
y_{t}=\beta y_{t-1}+\epsilon _{t},
\end{equation*}
in which the strict exogeneity $E(\epsilon|X)$ is violated even under the assumption $E(\epsilon_{t}y_{t-1})=0$:
we have that
\beg... | Proving OLS unbiasedness without conditional zero error expectation? | You can't, because the statement is not true under the weaker assumption.
Consider for example the autoregressive model
\begin{equation*}
y_{t}=\beta y_{t-1}+\epsilon _{t},
\end{equation*}
in which th | Proving OLS unbiasedness without conditional zero error expectation?
You can't, because the statement is not true under the weaker assumption.
Consider for example the autoregressive model
\begin{equation*}
y_{t}=\beta y_{t-1}+\epsilon _{t},
\end{equation*}
in which the strict exogeneity $E(\epsilon|X)$ is violated eve... | Proving OLS unbiasedness without conditional zero error expectation?
You can't, because the statement is not true under the weaker assumption.
Consider for example the autoregressive model
\begin{equation*}
y_{t}=\beta y_{t-1}+\epsilon _{t},
\end{equation*}
in which th |
53,209 | Proving OLS unbiasedness without conditional zero error expectation? | For this question we can make use of a simple decomposition of the OLS estimator:
$$\begin{equation} \begin{aligned}
\hat{\boldsymbol{\beta}} = (\mathbf{X}^\text{T} \mathbf{X})^{-1} \mathbf{X}^\text{T} \mathbf{Y}
&= (\mathbf{X}^\text{T} \mathbf{X})^{-1} \mathbf{X}^\text{T} (\mathbf{X} \boldsymbol{\beta} + \mathbf{\eps... | Proving OLS unbiasedness without conditional zero error expectation? | For this question we can make use of a simple decomposition of the OLS estimator:
$$\begin{equation} \begin{aligned}
\hat{\boldsymbol{\beta}} = (\mathbf{X}^\text{T} \mathbf{X})^{-1} \mathbf{X}^\text{T | Proving OLS unbiasedness without conditional zero error expectation?
For this question we can make use of a simple decomposition of the OLS estimator:
$$\begin{equation} \begin{aligned}
\hat{\boldsymbol{\beta}} = (\mathbf{X}^\text{T} \mathbf{X})^{-1} \mathbf{X}^\text{T} \mathbf{Y}
&= (\mathbf{X}^\text{T} \mathbf{X})^{... | Proving OLS unbiasedness without conditional zero error expectation?
For this question we can make use of a simple decomposition of the OLS estimator:
$$\begin{equation} \begin{aligned}
\hat{\boldsymbol{\beta}} = (\mathbf{X}^\text{T} \mathbf{X})^{-1} \mathbf{X}^\text{T |
53,210 | Why decision boundary is of (D-1) dimensions? | The line is a 1-D boundary in 2-D space. If you think of yourself as a point on the decision boundary, the number of (non-parallel nor anti-parallel) directions you could travel on the boundary will be its dimensions. With a line you can go forward or backward (which is anti-parallel to forward), so there is only one d... | Why decision boundary is of (D-1) dimensions? | The line is a 1-D boundary in 2-D space. If you think of yourself as a point on the decision boundary, the number of (non-parallel nor anti-parallel) directions you could travel on the boundary will b | Why decision boundary is of (D-1) dimensions?
The line is a 1-D boundary in 2-D space. If you think of yourself as a point on the decision boundary, the number of (non-parallel nor anti-parallel) directions you could travel on the boundary will be its dimensions. With a line you can go forward or backward (which is ant... | Why decision boundary is of (D-1) dimensions?
The line is a 1-D boundary in 2-D space. If you think of yourself as a point on the decision boundary, the number of (non-parallel nor anti-parallel) directions you could travel on the boundary will b |
53,211 | Why decision boundary is of (D-1) dimensions? | I think the answer of @Dan is sufficient, but for someone who have basic Linear Algebra, this is another explanation. It is obvious the discriminant function f is a linear transformation, and vector in the boundary decision form the null-space. It is known that dim(V) = dim(null-space) + dim(f(V)), with V is the input ... | Why decision boundary is of (D-1) dimensions? | I think the answer of @Dan is sufficient, but for someone who have basic Linear Algebra, this is another explanation. It is obvious the discriminant function f is a linear transformation, and vector i | Why decision boundary is of (D-1) dimensions?
I think the answer of @Dan is sufficient, but for someone who have basic Linear Algebra, this is another explanation. It is obvious the discriminant function f is a linear transformation, and vector in the boundary decision form the null-space. It is known that dim(V) = dim... | Why decision boundary is of (D-1) dimensions?
I think the answer of @Dan is sufficient, but for someone who have basic Linear Algebra, this is another explanation. It is obvious the discriminant function f is a linear transformation, and vector i |
53,212 | What is the probability that a best of seven series goes to the seventh game with negative binomial | Summary: the negative-binomial based approach in the question ignores that either team can win Game 7. After correcting for this the results agree.
Assumption
Not explicitly stated in the question, but it seems we are assuming the games are iid. with probability 0.5 for either team to win (a sequence of fair coin flip... | What is the probability that a best of seven series goes to the seventh game with negative binomial | Summary: the negative-binomial based approach in the question ignores that either team can win Game 7. After correcting for this the results agree.
Assumption
Not explicitly stated in the question, b | What is the probability that a best of seven series goes to the seventh game with negative binomial
Summary: the negative-binomial based approach in the question ignores that either team can win Game 7. After correcting for this the results agree.
Assumption
Not explicitly stated in the question, but it seems we are a... | What is the probability that a best of seven series goes to the seventh game with negative binomial
Summary: the negative-binomial based approach in the question ignores that either team can win Game 7. After correcting for this the results agree.
Assumption
Not explicitly stated in the question, b |
53,213 | What is the probability that a best of seven series goes to the seventh game with negative binomial | The negative binomial would be appropriate if you wanted to know how many games it would take before team A won 4 games. However, that might be, say, 104 games, in which case team B would have won 100 games. Obviously that's not the way an actual seven game series works!
Your calculation - $P(X=7 | r=4)$ - using the ... | What is the probability that a best of seven series goes to the seventh game with negative binomial | The negative binomial would be appropriate if you wanted to know how many games it would take before team A won 4 games. However, that might be, say, 104 games, in which case team B would have won 10 | What is the probability that a best of seven series goes to the seventh game with negative binomial
The negative binomial would be appropriate if you wanted to know how many games it would take before team A won 4 games. However, that might be, say, 104 games, in which case team B would have won 100 games. Obviously ... | What is the probability that a best of seven series goes to the seventh game with negative binomial
The negative binomial would be appropriate if you wanted to know how many games it would take before team A won 4 games. However, that might be, say, 104 games, in which case team B would have won 10 |
53,214 | Why is a GARCH model useful? | GARCH can be used for what you call predictions. The question is: predictions of what? Predictions of volatility.
The reason why GARCH is useful is because it may better explain the volatility of certain series, particularly in finance. For instance, look at the graph below. It shows daily log differences of S&P 500 se... | Why is a GARCH model useful? | GARCH can be used for what you call predictions. The question is: predictions of what? Predictions of volatility.
The reason why GARCH is useful is because it may better explain the volatility of cert | Why is a GARCH model useful?
GARCH can be used for what you call predictions. The question is: predictions of what? Predictions of volatility.
The reason why GARCH is useful is because it may better explain the volatility of certain series, particularly in finance. For instance, look at the graph below. It shows daily ... | Why is a GARCH model useful?
GARCH can be used for what you call predictions. The question is: predictions of what? Predictions of volatility.
The reason why GARCH is useful is because it may better explain the volatility of cert |
53,215 | If X and Y are perfectly correlated, what is the correlation of X+Y and X-Y? | Hint: In general, \begin{align}
\rho_{A,B} &= \frac{\operatorname{cov}(A,B)}{\sqrt{\operatorname{var}(A)\operatorname{var}(B)}},\\
\operatorname{var}(X\pm Y)&= \operatorname{var}(X)+\operatorname{var}(Y)
\pm 2\operatorname{cov}(X,Y),\\
\text{and}\qquad\operatorname{cov}(X+Y,X-Y)&=\operatorname{var}(X)-\operatorname{var... | If X and Y are perfectly correlated, what is the correlation of X+Y and X-Y? | Hint: In general, \begin{align}
\rho_{A,B} &= \frac{\operatorname{cov}(A,B)}{\sqrt{\operatorname{var}(A)\operatorname{var}(B)}},\\
\operatorname{var}(X\pm Y)&= \operatorname{var}(X)+\operatorname{var} | If X and Y are perfectly correlated, what is the correlation of X+Y and X-Y?
Hint: In general, \begin{align}
\rho_{A,B} &= \frac{\operatorname{cov}(A,B)}{\sqrt{\operatorname{var}(A)\operatorname{var}(B)}},\\
\operatorname{var}(X\pm Y)&= \operatorname{var}(X)+\operatorname{var}(Y)
\pm 2\operatorname{cov}(X,Y),\\
\text{a... | If X and Y are perfectly correlated, what is the correlation of X+Y and X-Y?
Hint: In general, \begin{align}
\rho_{A,B} &= \frac{\operatorname{cov}(A,B)}{\sqrt{\operatorname{var}(A)\operatorname{var}(B)}},\\
\operatorname{var}(X\pm Y)&= \operatorname{var}(X)+\operatorname{var} |
53,216 | If X and Y are perfectly correlated, what is the correlation of X+Y and X-Y? | I'll treat this as self-study, and I'd encourage you to read its wiki and add the tag.
Your argument is already very good. Here are a few pointers. Feel free to write a comment so we can discuss and work towards a good answer.
I assume you are looking at Pearson's correlation, right? (Does your argument work for other... | If X and Y are perfectly correlated, what is the correlation of X+Y and X-Y? | I'll treat this as self-study, and I'd encourage you to read its wiki and add the tag.
Your argument is already very good. Here are a few pointers. Feel free to write a comment so we can discuss and w | If X and Y are perfectly correlated, what is the correlation of X+Y and X-Y?
I'll treat this as self-study, and I'd encourage you to read its wiki and add the tag.
Your argument is already very good. Here are a few pointers. Feel free to write a comment so we can discuss and work towards a good answer.
I assume you ar... | If X and Y are perfectly correlated, what is the correlation of X+Y and X-Y?
I'll treat this as self-study, and I'd encourage you to read its wiki and add the tag.
Your argument is already very good. Here are a few pointers. Feel free to write a comment so we can discuss and w |
53,217 | If X and Y are perfectly correlated, what is the correlation of X+Y and X-Y? | I see this already has an accepted answer, but I've always liked simulations more than equations, and this seemed like a fun question. I generated a variable $x$ from a distribution $N(0, 1)$ whose sample size $n$ was drawn from $U(100, 10000)$. To make $y$, I simply added a constant—drawn from $U(1, 100)$—to $x$. I th... | If X and Y are perfectly correlated, what is the correlation of X+Y and X-Y? | I see this already has an accepted answer, but I've always liked simulations more than equations, and this seemed like a fun question. I generated a variable $x$ from a distribution $N(0, 1)$ whose sa | If X and Y are perfectly correlated, what is the correlation of X+Y and X-Y?
I see this already has an accepted answer, but I've always liked simulations more than equations, and this seemed like a fun question. I generated a variable $x$ from a distribution $N(0, 1)$ whose sample size $n$ was drawn from $U(100, 10000)... | If X and Y are perfectly correlated, what is the correlation of X+Y and X-Y?
I see this already has an accepted answer, but I've always liked simulations more than equations, and this seemed like a fun question. I generated a variable $x$ from a distribution $N(0, 1)$ whose sa |
53,218 | If X and Y are perfectly correlated, what is the correlation of X+Y and X-Y? | If $X$ is a linear function of $Y$ (definition of perfect correlation), then both $X-Y$ and $X+Y$ will be linear functions of $Y$, and therefore are linear functions of each other.
So, $X-Y$ and $X+Y$ are perfectly correlated. | If X and Y are perfectly correlated, what is the correlation of X+Y and X-Y? | If $X$ is a linear function of $Y$ (definition of perfect correlation), then both $X-Y$ and $X+Y$ will be linear functions of $Y$, and therefore are linear functions of each other.
So, $X-Y$ and $X+Y | If X and Y are perfectly correlated, what is the correlation of X+Y and X-Y?
If $X$ is a linear function of $Y$ (definition of perfect correlation), then both $X-Y$ and $X+Y$ will be linear functions of $Y$, and therefore are linear functions of each other.
So, $X-Y$ and $X+Y$ are perfectly correlated. | If X and Y are perfectly correlated, what is the correlation of X+Y and X-Y?
If $X$ is a linear function of $Y$ (definition of perfect correlation), then both $X-Y$ and $X+Y$ will be linear functions of $Y$, and therefore are linear functions of each other.
So, $X-Y$ and $X+Y |
53,219 | If X and Y are perfectly correlated, what is the correlation of X+Y and X-Y? | $X,Y$ perfectly correlate $\implies Cov(X,Y)=\sqrt{Var(X)Var(Y)}$
$Cov(X+Y,X-Y)=Cov(X,X)-Cov(X,Y)+Cov(Y,X)-Cov(Y,Y)=Var(X)-Var(Y)$
$Var(X+Y)Var(X-Y)=[Var(X)+Var(Y)+2Cov(X,Y)][Var(X)+Var(Y)-2Cov(X,Y)]=[Var(X)+Var(Y)]^2-4Cov(X,Y)Cov(X,Y)=_{\rho_{X,Y}=1}=[Var(X)+Var(Y)]^2-4Var(X)Var(Y)=[Var(X)-Var(Y)]^2$
Hence, $\rho_{X+Y... | If X and Y are perfectly correlated, what is the correlation of X+Y and X-Y? | $X,Y$ perfectly correlate $\implies Cov(X,Y)=\sqrt{Var(X)Var(Y)}$
$Cov(X+Y,X-Y)=Cov(X,X)-Cov(X,Y)+Cov(Y,X)-Cov(Y,Y)=Var(X)-Var(Y)$
$Var(X+Y)Var(X-Y)=[Var(X)+Var(Y)+2Cov(X,Y)][Var(X)+Var(Y)-2Cov(X,Y)]= | If X and Y are perfectly correlated, what is the correlation of X+Y and X-Y?
$X,Y$ perfectly correlate $\implies Cov(X,Y)=\sqrt{Var(X)Var(Y)}$
$Cov(X+Y,X-Y)=Cov(X,X)-Cov(X,Y)+Cov(Y,X)-Cov(Y,Y)=Var(X)-Var(Y)$
$Var(X+Y)Var(X-Y)=[Var(X)+Var(Y)+2Cov(X,Y)][Var(X)+Var(Y)-2Cov(X,Y)]=[Var(X)+Var(Y)]^2-4Cov(X,Y)Cov(X,Y)=_{\rho_... | If X and Y are perfectly correlated, what is the correlation of X+Y and X-Y?
$X,Y$ perfectly correlate $\implies Cov(X,Y)=\sqrt{Var(X)Var(Y)}$
$Cov(X+Y,X-Y)=Cov(X,X)-Cov(X,Y)+Cov(Y,X)-Cov(Y,Y)=Var(X)-Var(Y)$
$Var(X+Y)Var(X-Y)=[Var(X)+Var(Y)+2Cov(X,Y)][Var(X)+Var(Y)-2Cov(X,Y)]= |
53,220 | Does the likelihood function for the Poisson distribution integrate to 1 | Besides my comment, the claim is true if you replace the sum with an integral (which makes more sense). Indeed, one can show that for all $k \in \mathbb{N}$: $$\int_0^\infty P(X=k|\lambda)\,d\lambda = \int_0^\infty \frac{\lambda^kexp(-\lambda)}{k!}\,d\lambda = \frac{\Gamma(k+1)}{k!} = \frac{k!}{k!} =1.$$
In fact, the... | Does the likelihood function for the Poisson distribution integrate to 1 | Besides my comment, the claim is true if you replace the sum with an integral (which makes more sense). Indeed, one can show that for all $k \in \mathbb{N}$: $$\int_0^\infty P(X=k|\lambda)\,d\lambda | Does the likelihood function for the Poisson distribution integrate to 1
Besides my comment, the claim is true if you replace the sum with an integral (which makes more sense). Indeed, one can show that for all $k \in \mathbb{N}$: $$\int_0^\infty P(X=k|\lambda)\,d\lambda = \int_0^\infty \frac{\lambda^kexp(-\lambda)}{... | Does the likelihood function for the Poisson distribution integrate to 1
Besides my comment, the claim is true if you replace the sum with an integral (which makes more sense). Indeed, one can show that for all $k \in \mathbb{N}$: $$\int_0^\infty P(X=k|\lambda)\,d\lambda |
53,221 | Explain non-uniform p-values for small sample t-tests in R | This isn't a bug in R.
Welch-Satterthwaite type t-tests (the default two sample t-test in R) don't actually have a t-distribution.
The t-with-fractional-d.f. you get is an approximation to the null distribution.
The Welch-Satterthwaite tests work well in a variety of situations, but even when all the assumptions hol... | Explain non-uniform p-values for small sample t-tests in R | This isn't a bug in R.
Welch-Satterthwaite type t-tests (the default two sample t-test in R) don't actually have a t-distribution.
The t-with-fractional-d.f. you get is an approximation to the null | Explain non-uniform p-values for small sample t-tests in R
This isn't a bug in R.
Welch-Satterthwaite type t-tests (the default two sample t-test in R) don't actually have a t-distribution.
The t-with-fractional-d.f. you get is an approximation to the null distribution.
The Welch-Satterthwaite tests work well in a v... | Explain non-uniform p-values for small sample t-tests in R
This isn't a bug in R.
Welch-Satterthwaite type t-tests (the default two sample t-test in R) don't actually have a t-distribution.
The t-with-fractional-d.f. you get is an approximation to the null |
53,222 | Unbiased Estimator of the Variance of the Sample Variance | The question is to find an unbiased estimator of:
$$\text{Var}(S^2)=\frac{\mu_4}{n}-\frac{(n-3)}{n(n-1)} {\mu_2^2}$$
... where $\mu_r$ denotes the $r^\text{th}$ central moment of the population. This requires finding unbiased estimators of $\mu_4$ and of $\mu_2^2$.
An unbiased estimator of $\mu_4$
By defn, an unbiase... | Unbiased Estimator of the Variance of the Sample Variance | The question is to find an unbiased estimator of:
$$\text{Var}(S^2)=\frac{\mu_4}{n}-\frac{(n-3)}{n(n-1)} {\mu_2^2}$$
... where $\mu_r$ denotes the $r^\text{th}$ central moment of the population. Thi | Unbiased Estimator of the Variance of the Sample Variance
The question is to find an unbiased estimator of:
$$\text{Var}(S^2)=\frac{\mu_4}{n}-\frac{(n-3)}{n(n-1)} {\mu_2^2}$$
... where $\mu_r$ denotes the $r^\text{th}$ central moment of the population. This requires finding unbiased estimators of $\mu_4$ and of $\mu_... | Unbiased Estimator of the Variance of the Sample Variance
The question is to find an unbiased estimator of:
$$\text{Var}(S^2)=\frac{\mu_4}{n}-\frac{(n-3)}{n(n-1)} {\mu_2^2}$$
... where $\mu_r$ denotes the $r^\text{th}$ central moment of the population. Thi |
53,223 | What is the difference between Universe and Population? | I just took stats last year. Population is, as you described, a complete set of elements (persons or objects) that possess some common characteristic defined by the sampling criteria established by the researcher.
In statistics, Universe is a synonym of Population.
Source:
population. (n.d.) Collins English Dictio... | What is the difference between Universe and Population? | I just took stats last year. Population is, as you described, a complete set of elements (persons or objects) that possess some common characteristic defined by the sampling criteria established by t | What is the difference between Universe and Population?
I just took stats last year. Population is, as you described, a complete set of elements (persons or objects) that possess some common characteristic defined by the sampling criteria established by the researcher.
In statistics, Universe is a synonym of Populat... | What is the difference between Universe and Population?
I just took stats last year. Population is, as you described, a complete set of elements (persons or objects) that possess some common characteristic defined by the sampling criteria established by t |
53,224 | What is the difference between Universe and Population? | The term 'universe', while it has a well-established meaning in set theory and other related mathematical fields, in my experience is rarely used in statistics as a synonym of the term 'population'.
Indeed, all classical statistics textbooks, exclusively use the term 'population', usually defined as
entire group of in... | What is the difference between Universe and Population? | The term 'universe', while it has a well-established meaning in set theory and other related mathematical fields, in my experience is rarely used in statistics as a synonym of the term 'population'.
I | What is the difference between Universe and Population?
The term 'universe', while it has a well-established meaning in set theory and other related mathematical fields, in my experience is rarely used in statistics as a synonym of the term 'population'.
Indeed, all classical statistics textbooks, exclusively use the t... | What is the difference between Universe and Population?
The term 'universe', while it has a well-established meaning in set theory and other related mathematical fields, in my experience is rarely used in statistics as a synonym of the term 'population'.
I |
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The collection of all elements possessing common characteristics that comprise universe is known as the popula... | What is the difference between Universe and Population? | Want to improve this post? Add citations from reputable sources by editing the post. Posts with unsourced content may be edited or deleted.
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The collection of all elements possessing common chara... | What is the difference between Universe and Population?
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53,226 | What is the difference between Universe and Population? | Want to improve this post? Add citations from reputable sources by editing the post. Posts with unsourced content may be edited or deleted.
Universe is the set all experimental units, from which a sample is to be drawn. Population is the set of all v... | What is the difference between Universe and Population? | Want to improve this post? Add citations from reputable sources by editing the post. Posts with unsourced content may be edited or deleted.
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Universe is the set all experimental units, from which... | What is the difference between Universe and Population?
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53,227 | What is the difference between Universe and Population? | Want to improve this post? Add citations from reputable sources by editing the post. Posts with unsourced content may be edited or deleted.
The collection of all elements possessing common characteristic that comprise (Univers) is known as the popula... | What is the difference between Universe and Population? | Want to improve this post? Add citations from reputable sources by editing the post. Posts with unsourced content may be edited or deleted.
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53,228 | What is the difference between Universe and Population? | Universe, population and sample must be understood together. Universe and population can refer to same thing and can be considered as synonym if only the population you use while choosing your samples includes all the members of universe. If you have data for all the members of universe then your population is universe... | What is the difference between Universe and Population? | Universe, population and sample must be understood together. Universe and population can refer to same thing and can be considered as synonym if only the population you use while choosing your samples | What is the difference between Universe and Population?
Universe, population and sample must be understood together. Universe and population can refer to same thing and can be considered as synonym if only the population you use while choosing your samples includes all the members of universe. If you have data for all ... | What is the difference between Universe and Population?
Universe, population and sample must be understood together. Universe and population can refer to same thing and can be considered as synonym if only the population you use while choosing your samples |
53,229 | What is the difference between Universe and Population? | Want to improve this post? Add citations from reputable sources by editing the post. Posts with unsourced content may be edited or deleted.
The universe is broad in its nature. The universe in research is the area of your study while the population i... | What is the difference between Universe and Population? | Want to improve this post? Add citations from reputable sources by editing the post. Posts with unsourced content may be edited or deleted.
| What is the difference between Universe and Population?
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The universe is broad in its nature. The universe in r... | What is the difference between Universe and Population?
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53,230 | Distribution like hypergeometric distribution, but with false replacements | Suppose an urn of $n$ balls begins with $s$ successes. What are the chances it will end up with $t$ successes ($0 \le t \le s$) after $d$ draws?
Ignoring the trivial case $s=0$, this is a Markov chain on the numbers of successes $s$. The chance of a transition from $s$ to $s-1$ is $p(s,s-1)=s/n$; otherwise, the sta... | Distribution like hypergeometric distribution, but with false replacements | Suppose an urn of $n$ balls begins with $s$ successes. What are the chances it will end up with $t$ successes ($0 \le t \le s$) after $d$ draws?
Ignoring the trivial case $s=0$, this is a Markov ch | Distribution like hypergeometric distribution, but with false replacements
Suppose an urn of $n$ balls begins with $s$ successes. What are the chances it will end up with $t$ successes ($0 \le t \le s$) after $d$ draws?
Ignoring the trivial case $s=0$, this is a Markov chain on the numbers of successes $s$. The cha... | Distribution like hypergeometric distribution, but with false replacements
Suppose an urn of $n$ balls begins with $s$ successes. What are the chances it will end up with $t$ successes ($0 \le t \le s$) after $d$ draws?
Ignoring the trivial case $s=0$, this is a Markov ch |
53,231 | Distribution like hypergeometric distribution, but with false replacements | There will be a recursion. If $S_{n,g,b}$ is the number of green balls successfully drawn with $n$ attempts starting with $g$ green balls and $b−g$ white balls then
$$\mathbb P (S_{n,g,b} = s)= \frac{g}{b} \mathbb P (S_{n-1,g-1,b} = s-1) + \frac{b-g}{b} \mathbb P (S_{n-1,g,b} = s)$$
starting with $\mathbb P (S_{0... | Distribution like hypergeometric distribution, but with false replacements | There will be a recursion. If $S_{n,g,b}$ is the number of green balls successfully drawn with $n$ attempts starting with $g$ green balls and $b−g$ white balls then
$$\mathbb P (S_{n,g,b} = s)= \frac | Distribution like hypergeometric distribution, but with false replacements
There will be a recursion. If $S_{n,g,b}$ is the number of green balls successfully drawn with $n$ attempts starting with $g$ green balls and $b−g$ white balls then
$$\mathbb P (S_{n,g,b} = s)= \frac{g}{b} \mathbb P (S_{n-1,g-1,b} = s-1) + \f... | Distribution like hypergeometric distribution, but with false replacements
There will be a recursion. If $S_{n,g,b}$ is the number of green balls successfully drawn with $n$ attempts starting with $g$ green balls and $b−g$ white balls then
$$\mathbb P (S_{n,g,b} = s)= \frac |
53,232 | Number of distinct scatterplots among $p$ variables | Assuming you don't count a plot of $X_3$ vs $X_6$ as distinct from a plot of $X_6$ vs $X_3$ and further assuming you don't care to plot a variable vs itself, then you want the number of distinct pairs $i,j$ for $i<j$ and $i$ and $j$ integers between $1$ and $p$ exclusive.
There's $p \times p$ pairs $(i,j)$. We remove ... | Number of distinct scatterplots among $p$ variables | Assuming you don't count a plot of $X_3$ vs $X_6$ as distinct from a plot of $X_6$ vs $X_3$ and further assuming you don't care to plot a variable vs itself, then you want the number of distinct pairs | Number of distinct scatterplots among $p$ variables
Assuming you don't count a plot of $X_3$ vs $X_6$ as distinct from a plot of $X_6$ vs $X_3$ and further assuming you don't care to plot a variable vs itself, then you want the number of distinct pairs $i,j$ for $i<j$ and $i$ and $j$ integers between $1$ and $p$ exclus... | Number of distinct scatterplots among $p$ variables
Assuming you don't count a plot of $X_3$ vs $X_6$ as distinct from a plot of $X_6$ vs $X_3$ and further assuming you don't care to plot a variable vs itself, then you want the number of distinct pairs |
53,233 | Meaning of Min/Max Accuracy of a regression model | Let's break down the code:
apply(actuals_preds, 1, min)
Takes, for each row, the minimum of the prediction and the result. Similarly,
apply(actuals_preds, 1, max)
takes the maximum.
Suppose the test outcomes are $y_1, \ldots, y_n$, and the predictions are $\hat{y}_1, \ldots, \hat{y}_n$. For any $i$, there are two ca... | Meaning of Min/Max Accuracy of a regression model | Let's break down the code:
apply(actuals_preds, 1, min)
Takes, for each row, the minimum of the prediction and the result. Similarly,
apply(actuals_preds, 1, max)
takes the maximum.
Suppose the tes | Meaning of Min/Max Accuracy of a regression model
Let's break down the code:
apply(actuals_preds, 1, min)
Takes, for each row, the minimum of the prediction and the result. Similarly,
apply(actuals_preds, 1, max)
takes the maximum.
Suppose the test outcomes are $y_1, \ldots, y_n$, and the predictions are $\hat{y}_1,... | Meaning of Min/Max Accuracy of a regression model
Let's break down the code:
apply(actuals_preds, 1, min)
Takes, for each row, the minimum of the prediction and the result. Similarly,
apply(actuals_preds, 1, max)
takes the maximum.
Suppose the tes |
53,234 | Meaning of Min/Max Accuracy of a regression model | MinMax tells you how far the model's prediction is off. For a perfect model, this measure is 1.0. The lower the measure, the worse the model, based on out-of-sample performance.
Just look at the formula and how it's implemented in R. If predict (the column predicteds in your data frame) exactly equals actual (actuals... | Meaning of Min/Max Accuracy of a regression model | MinMax tells you how far the model's prediction is off. For a perfect model, this measure is 1.0. The lower the measure, the worse the model, based on out-of-sample performance.
Just look at the form | Meaning of Min/Max Accuracy of a regression model
MinMax tells you how far the model's prediction is off. For a perfect model, this measure is 1.0. The lower the measure, the worse the model, based on out-of-sample performance.
Just look at the formula and how it's implemented in R. If predict (the column predicteds ... | Meaning of Min/Max Accuracy of a regression model
MinMax tells you how far the model's prediction is off. For a perfect model, this measure is 1.0. The lower the measure, the worse the model, based on out-of-sample performance.
Just look at the form |
53,235 | Meaning of Min/Max Accuracy of a regression model | Actuals and predict both are in same dataset. Min_Max_accuracy will find out accuracy rate of each row. it can be considered accuracy rate of the model. it would less than zero like .69034, then accuracy percentage is 69%. | Meaning of Min/Max Accuracy of a regression model | Actuals and predict both are in same dataset. Min_Max_accuracy will find out accuracy rate of each row. it can be considered accuracy rate of the model. it would less than zero like .69034, then accur | Meaning of Min/Max Accuracy of a regression model
Actuals and predict both are in same dataset. Min_Max_accuracy will find out accuracy rate of each row. it can be considered accuracy rate of the model. it would less than zero like .69034, then accuracy percentage is 69%. | Meaning of Min/Max Accuracy of a regression model
Actuals and predict both are in same dataset. Min_Max_accuracy will find out accuracy rate of each row. it can be considered accuracy rate of the model. it would less than zero like .69034, then accur |
53,236 | Classification accuracy based on probability | Classifier metrics that compare the predicted probabilities to the true classes go by the name of proper scoring rules. The two most popular are the log-loss
$$ L = \sum_i y_i \log(p_i) + (1 - y_i) \log(1 - p_i) $$
and the brier score
$$ L = \sum_i (y_i - p_i)^2 $$
The log-loss is used more in practice, as it is the l... | Classification accuracy based on probability | Classifier metrics that compare the predicted probabilities to the true classes go by the name of proper scoring rules. The two most popular are the log-loss
$$ L = \sum_i y_i \log(p_i) + (1 - y_i) \ | Classification accuracy based on probability
Classifier metrics that compare the predicted probabilities to the true classes go by the name of proper scoring rules. The two most popular are the log-loss
$$ L = \sum_i y_i \log(p_i) + (1 - y_i) \log(1 - p_i) $$
and the brier score
$$ L = \sum_i (y_i - p_i)^2 $$
The log-... | Classification accuracy based on probability
Classifier metrics that compare the predicted probabilities to the true classes go by the name of proper scoring rules. The two most popular are the log-loss
$$ L = \sum_i y_i \log(p_i) + (1 - y_i) \ |
53,237 | Classification accuracy based on probability | It might be the case that one model (say M1 on your case) leads to more extreme predictions compared to the other (M2), meaning that "certainty" (I think this concept is misleading) will be also higher for correctly predicted/classified events. Instead of reporting % of correctly classified events, you could simply com... | Classification accuracy based on probability | It might be the case that one model (say M1 on your case) leads to more extreme predictions compared to the other (M2), meaning that "certainty" (I think this concept is misleading) will be also highe | Classification accuracy based on probability
It might be the case that one model (say M1 on your case) leads to more extreme predictions compared to the other (M2), meaning that "certainty" (I think this concept is misleading) will be also higher for correctly predicted/classified events. Instead of reporting % of corr... | Classification accuracy based on probability
It might be the case that one model (say M1 on your case) leads to more extreme predictions compared to the other (M2), meaning that "certainty" (I think this concept is misleading) will be also highe |
53,238 | How to make sense of this PCA plot with logistic regression decision boundary (breast cancer data)? | What does the 2-d PCA data/plot mean?
The 2-d PCA data/plot represent two "compound features" which PCA created to capture as much of the variance in your original 13 features as possible.
Assuming your 13 features are linearly independent (e.g. one feature is not just another feature times 2, for every row in your da... | How to make sense of this PCA plot with logistic regression decision boundary (breast cancer data)? | What does the 2-d PCA data/plot mean?
The 2-d PCA data/plot represent two "compound features" which PCA created to capture as much of the variance in your original 13 features as possible.
Assuming y | How to make sense of this PCA plot with logistic regression decision boundary (breast cancer data)?
What does the 2-d PCA data/plot mean?
The 2-d PCA data/plot represent two "compound features" which PCA created to capture as much of the variance in your original 13 features as possible.
Assuming your 13 features are ... | How to make sense of this PCA plot with logistic regression decision boundary (breast cancer data)?
What does the 2-d PCA data/plot mean?
The 2-d PCA data/plot represent two "compound features" which PCA created to capture as much of the variance in your original 13 features as possible.
Assuming y |
53,239 | How to make sense of this PCA plot with logistic regression decision boundary (breast cancer data)? | From your question:
I train the logistic regression model on the 2-d data from the PCA. I
plot the decision boundary using the intercept and coefficient and it
does linearly separate the data.
Logistic regresssion is not a classifier. Its coefficients certainly do not represent a "decision boundary." You have a m... | How to make sense of this PCA plot with logistic regression decision boundary (breast cancer data)? | From your question:
I train the logistic regression model on the 2-d data from the PCA. I
plot the decision boundary using the intercept and coefficient and it
does linearly separate the data.
L | How to make sense of this PCA plot with logistic regression decision boundary (breast cancer data)?
From your question:
I train the logistic regression model on the 2-d data from the PCA. I
plot the decision boundary using the intercept and coefficient and it
does linearly separate the data.
Logistic regresssion ... | How to make sense of this PCA plot with logistic regression decision boundary (breast cancer data)?
From your question:
I train the logistic regression model on the 2-d data from the PCA. I
plot the decision boundary using the intercept and coefficient and it
does linearly separate the data.
L |
53,240 | How to make sense of this PCA plot with logistic regression decision boundary (breast cancer data)? | @MaxPower has a good answer, and I want to elaborate on his point A) in his comment:
This means either one of two things: either A) your 2 PCA dimensions
don't capture enough of the information contained in your raw 13
features, or B) your problem is very hard to predict, even with all
the information from your 13 fea... | How to make sense of this PCA plot with logistic regression decision boundary (breast cancer data)? | @MaxPower has a good answer, and I want to elaborate on his point A) in his comment:
This means either one of two things: either A) your 2 PCA dimensions
don't capture enough of the information conta | How to make sense of this PCA plot with logistic regression decision boundary (breast cancer data)?
@MaxPower has a good answer, and I want to elaborate on his point A) in his comment:
This means either one of two things: either A) your 2 PCA dimensions
don't capture enough of the information contained in your raw 13
... | How to make sense of this PCA plot with logistic regression decision boundary (breast cancer data)?
@MaxPower has a good answer, and I want to elaborate on his point A) in his comment:
This means either one of two things: either A) your 2 PCA dimensions
don't capture enough of the information conta |
53,241 | Does uniform conditional distribution imply independence? | Independence would mean that knowing the value of $Y$ gives no information on the value of $X$.
So here $X$ will be independent of $Y$ only if $X$ has a uniform marginal distribution on $[0,1]$, and the conditional distribution $X|Y$ is uniform on $[0,1]$ independent of the value of $Y$.
An example be a uniform (joint)... | Does uniform conditional distribution imply independence? | Independence would mean that knowing the value of $Y$ gives no information on the value of $X$.
So here $X$ will be independent of $Y$ only if $X$ has a uniform marginal distribution on $[0,1]$, and t | Does uniform conditional distribution imply independence?
Independence would mean that knowing the value of $Y$ gives no information on the value of $X$.
So here $X$ will be independent of $Y$ only if $X$ has a uniform marginal distribution on $[0,1]$, and the conditional distribution $X|Y$ is uniform on $[0,1]$ indepe... | Does uniform conditional distribution imply independence?
Independence would mean that knowing the value of $Y$ gives no information on the value of $X$.
So here $X$ will be independent of $Y$ only if $X$ has a uniform marginal distribution on $[0,1]$, and t |
53,242 | Does uniform conditional distribution imply independence? | If the conditional pdf of $X$ given $Y$ is the same density function for all values of $Y$ (in the support of $f_Y(y)$), that is, $f_{X\mid Y}(x\mid y)$ equals $g(x)$ where the value of $g$ does not depend on $y$ at all, then
$$f_X(x) = \int f_{X,Y}(x,y) \mathrm dy = \int f_{X\mid Y}(x\mid y)\cdot f_Y(y)\mathrm dy = g... | Does uniform conditional distribution imply independence? | If the conditional pdf of $X$ given $Y$ is the same density function for all values of $Y$ (in the support of $f_Y(y)$), that is, $f_{X\mid Y}(x\mid y)$ equals $g(x)$ where the value of $g$ does not d | Does uniform conditional distribution imply independence?
If the conditional pdf of $X$ given $Y$ is the same density function for all values of $Y$ (in the support of $f_Y(y)$), that is, $f_{X\mid Y}(x\mid y)$ equals $g(x)$ where the value of $g$ does not depend on $y$ at all, then
$$f_X(x) = \int f_{X,Y}(x,y) \mathrm... | Does uniform conditional distribution imply independence?
If the conditional pdf of $X$ given $Y$ is the same density function for all values of $Y$ (in the support of $f_Y(y)$), that is, $f_{X\mid Y}(x\mid y)$ equals $g(x)$ where the value of $g$ does not d |
53,243 | What is the heaviest tail possible for a continuous normalizable distribution? | There is no distribution which is more heavy-tailed than any other distribution.
Proof:
Assume $f$ is any PDF, and its CDF is $F$. We can always construct another distribution
$$G(x) = 1 - \sqrt{1 - F(x)}, \quad g(x) = \frac{f(x)}{2\sqrt{1 - F(x)}}$$
which has havier tails, since:
$$\int_x^\infty f(t)\, dt = 1 - F(x) <... | What is the heaviest tail possible for a continuous normalizable distribution? | There is no distribution which is more heavy-tailed than any other distribution.
Proof:
Assume $f$ is any PDF, and its CDF is $F$. We can always construct another distribution
$$G(x) = 1 - \sqrt{1 - F | What is the heaviest tail possible for a continuous normalizable distribution?
There is no distribution which is more heavy-tailed than any other distribution.
Proof:
Assume $f$ is any PDF, and its CDF is $F$. We can always construct another distribution
$$G(x) = 1 - \sqrt{1 - F(x)}, \quad g(x) = \frac{f(x)}{2\sqrt{1 -... | What is the heaviest tail possible for a continuous normalizable distribution?
There is no distribution which is more heavy-tailed than any other distribution.
Proof:
Assume $f$ is any PDF, and its CDF is $F$. We can always construct another distribution
$$G(x) = 1 - \sqrt{1 - F |
53,244 | What is the heaviest tail possible for a continuous normalizable distribution? | Great question! As you point out, Cauchy has a power-law tail. So on a log-log scale, the complementary cdf is linear.
But the only constraint on the function is that it never increases and goes to $-\infty$ in the limit. So you could swap the linear function out for a negative log, or even cook up an extreme example b... | What is the heaviest tail possible for a continuous normalizable distribution? | Great question! As you point out, Cauchy has a power-law tail. So on a log-log scale, the complementary cdf is linear.
But the only constraint on the function is that it never increases and goes to $- | What is the heaviest tail possible for a continuous normalizable distribution?
Great question! As you point out, Cauchy has a power-law tail. So on a log-log scale, the complementary cdf is linear.
But the only constraint on the function is that it never increases and goes to $-\infty$ in the limit. So you could swap t... | What is the heaviest tail possible for a continuous normalizable distribution?
Great question! As you point out, Cauchy has a power-law tail. So on a log-log scale, the complementary cdf is linear.
But the only constraint on the function is that it never increases and goes to $- |
53,245 | Meaning of model calibration | Let's suppose you have a set of training data and you have created a model that predicts the probability that a team will win a game. You did this e.g. by training a binary (win/loss) target on a set of input parameters. The model outputs a prediction, which is just the probability that the team will win the game.
You... | Meaning of model calibration | Let's suppose you have a set of training data and you have created a model that predicts the probability that a team will win a game. You did this e.g. by training a binary (win/loss) target on a set | Meaning of model calibration
Let's suppose you have a set of training data and you have created a model that predicts the probability that a team will win a game. You did this e.g. by training a binary (win/loss) target on a set of input parameters. The model outputs a prediction, which is just the probability that the... | Meaning of model calibration
Let's suppose you have a set of training data and you have created a model that predicts the probability that a team will win a game. You did this e.g. by training a binary (win/loss) target on a set |
53,246 | Meaning of model calibration | If the model is well-calibrated the points will appear along the main diagonal on the diagnostic reliability diagrams(or calibration curves). The closer the more reliable the model.
If the points are below the diagonal, that indicates that the model has over-forecast; the probabilities are too large. And if the points ... | Meaning of model calibration | If the model is well-calibrated the points will appear along the main diagonal on the diagnostic reliability diagrams(or calibration curves). The closer the more reliable the model.
If the points are | Meaning of model calibration
If the model is well-calibrated the points will appear along the main diagonal on the diagnostic reliability diagrams(or calibration curves). The closer the more reliable the model.
If the points are below the diagonal, that indicates that the model has over-forecast; the probabilities are ... | Meaning of model calibration
If the model is well-calibrated the points will appear along the main diagonal on the diagnostic reliability diagrams(or calibration curves). The closer the more reliable the model.
If the points are |
53,247 | Significance in simple regression but not multiple regression | First, multiple regression does not necessarily have more power, particularly when there are so many interaction terms as you have specified. Each extra variable, each extra factor level, and each extra interaction uses up degrees of freedom, so you might decrease your ability to detect a true difference if the extra v... | Significance in simple regression but not multiple regression | First, multiple regression does not necessarily have more power, particularly when there are so many interaction terms as you have specified. Each extra variable, each extra factor level, and each ext | Significance in simple regression but not multiple regression
First, multiple regression does not necessarily have more power, particularly when there are so many interaction terms as you have specified. Each extra variable, each extra factor level, and each extra interaction uses up degrees of freedom, so you might de... | Significance in simple regression but not multiple regression
First, multiple regression does not necessarily have more power, particularly when there are so many interaction terms as you have specified. Each extra variable, each extra factor level, and each ext |
53,248 | Fat tail? Short tail? Long tail? Where do I go from here? | Growth rates must be distributed as some variation of the Cauchy distribution. I have written a series of papers on this. The Cauchy distribution has no mean so it has no variance or covariance. You can find my author page at https://papers.ssrn.com/sol3/cf_dev/AbsByAuth.cfm?per_id=1541471
Start with the paper title... | Fat tail? Short tail? Long tail? Where do I go from here? | Growth rates must be distributed as some variation of the Cauchy distribution. I have written a series of papers on this. The Cauchy distribution has no mean so it has no variance or covariance. Yo | Fat tail? Short tail? Long tail? Where do I go from here?
Growth rates must be distributed as some variation of the Cauchy distribution. I have written a series of papers on this. The Cauchy distribution has no mean so it has no variance or covariance. You can find my author page at https://papers.ssrn.com/sol3/cf_d... | Fat tail? Short tail? Long tail? Where do I go from here?
Growth rates must be distributed as some variation of the Cauchy distribution. I have written a series of papers on this. The Cauchy distribution has no mean so it has no variance or covariance. Yo |
53,249 | Fat tail? Short tail? Long tail? Where do I go from here? | Your Q-Q plot doesn't look like it has a fat tail. I'll show you how a fat tail looks like:
Your tail is like a Victoria Secret's model compared to the above. I wish some of my model residuals had tails like yours has. | Fat tail? Short tail? Long tail? Where do I go from here? | Your Q-Q plot doesn't look like it has a fat tail. I'll show you how a fat tail looks like:
Your tail is like a Victoria Secret's model compared to the above. I wish some of my model residuals had ta | Fat tail? Short tail? Long tail? Where do I go from here?
Your Q-Q plot doesn't look like it has a fat tail. I'll show you how a fat tail looks like:
Your tail is like a Victoria Secret's model compared to the above. I wish some of my model residuals had tails like yours has. | Fat tail? Short tail? Long tail? Where do I go from here?
Your Q-Q plot doesn't look like it has a fat tail. I'll show you how a fat tail looks like:
Your tail is like a Victoria Secret's model compared to the above. I wish some of my model residuals had ta |
53,250 | Fat tail? Short tail? Long tail? Where do I go from here? | It seems that bootstrapping, as suggested by @Tim in comments, might be a good way to proceed. Even if your statistical software doesn't directly support bootstrapping it's not to hard to roll your own. For example, say you have all data for each individual in a single row (species; 3 treatment types; starting and endi... | Fat tail? Short tail? Long tail? Where do I go from here? | It seems that bootstrapping, as suggested by @Tim in comments, might be a good way to proceed. Even if your statistical software doesn't directly support bootstrapping it's not to hard to roll your ow | Fat tail? Short tail? Long tail? Where do I go from here?
It seems that bootstrapping, as suggested by @Tim in comments, might be a good way to proceed. Even if your statistical software doesn't directly support bootstrapping it's not to hard to roll your own. For example, say you have all data for each individual in a... | Fat tail? Short tail? Long tail? Where do I go from here?
It seems that bootstrapping, as suggested by @Tim in comments, might be a good way to proceed. Even if your statistical software doesn't directly support bootstrapping it's not to hard to roll your ow |
53,251 | Characteristic of good binning for weight of evidence algorithm | The 5% condition is a rule of thumb for Weight of Evidence (WOE) binning. In general, a good WOE binning of a variable should also have the following characteristics:
1. Monotonous increase/decrease in WOE for consecutive bins. This is because the WOE is used primarily for logistic/linear regression models which assume... | Characteristic of good binning for weight of evidence algorithm | The 5% condition is a rule of thumb for Weight of Evidence (WOE) binning. In general, a good WOE binning of a variable should also have the following characteristics:
1. Monotonous increase/decrease i | Characteristic of good binning for weight of evidence algorithm
The 5% condition is a rule of thumb for Weight of Evidence (WOE) binning. In general, a good WOE binning of a variable should also have the following characteristics:
1. Monotonous increase/decrease in WOE for consecutive bins. This is because the WOE is u... | Characteristic of good binning for weight of evidence algorithm
The 5% condition is a rule of thumb for Weight of Evidence (WOE) binning. In general, a good WOE binning of a variable should also have the following characteristics:
1. Monotonous increase/decrease i |
53,252 | What is the deeper intuition behind the symmetric proposal distribution in the Metropolis-Hastings Algorithm? | 1) the Normal and Uniform are symmetric probability density functions
themselves, is this notion of "symmetry" the same as the "symmetry"
above?
Both distributions are symmetric around their mean. But the symmetry in Metropolis-Hastings is that $q(x|y)=q(y|x)$ which makes the ratio cancel in the Metropolis-Hasting... | What is the deeper intuition behind the symmetric proposal distribution in the Metropolis-Hastings A | 1) the Normal and Uniform are symmetric probability density functions
themselves, is this notion of "symmetry" the same as the "symmetry"
above?
Both distributions are symmetric around their mean | What is the deeper intuition behind the symmetric proposal distribution in the Metropolis-Hastings Algorithm?
1) the Normal and Uniform are symmetric probability density functions
themselves, is this notion of "symmetry" the same as the "symmetry"
above?
Both distributions are symmetric around their mean. But the ... | What is the deeper intuition behind the symmetric proposal distribution in the Metropolis-Hastings A
1) the Normal and Uniform are symmetric probability density functions
themselves, is this notion of "symmetry" the same as the "symmetry"
above?
Both distributions are symmetric around their mean |
53,253 | Is Levene's test necessary? | Regardless of the good points made in the comments above about whether you condition your testing procedure on the results of preliminary investigation (e.g. choosing Welch vs. standard t-tests based on the outcome of Levene's test) I suspect that the reason for this difference between ANOVA/t-test (i.e., linear models... | Is Levene's test necessary? | Regardless of the good points made in the comments above about whether you condition your testing procedure on the results of preliminary investigation (e.g. choosing Welch vs. standard t-tests based | Is Levene's test necessary?
Regardless of the good points made in the comments above about whether you condition your testing procedure on the results of preliminary investigation (e.g. choosing Welch vs. standard t-tests based on the outcome of Levene's test) I suspect that the reason for this difference between ANOVA... | Is Levene's test necessary?
Regardless of the good points made in the comments above about whether you condition your testing procedure on the results of preliminary investigation (e.g. choosing Welch vs. standard t-tests based |
53,254 | What is the difference between accuracy and precision? | (Just for reference, I am posting my comments as an answer. Note that the first version of the question did not include the formula.)
"Accuracy" and "precision" are general terms throughout science. A good way to internalize the difference are the common "bullseye diagrams". In machine learning/statistics as a whole, a... | What is the difference between accuracy and precision? | (Just for reference, I am posting my comments as an answer. Note that the first version of the question did not include the formula.)
"Accuracy" and "precision" are general terms throughout science. A | What is the difference between accuracy and precision?
(Just for reference, I am posting my comments as an answer. Note that the first version of the question did not include the formula.)
"Accuracy" and "precision" are general terms throughout science. A good way to internalize the difference are the common "bullseye ... | What is the difference between accuracy and precision?
(Just for reference, I am posting my comments as an answer. Note that the first version of the question did not include the formula.)
"Accuracy" and "precision" are general terms throughout science. A |
53,255 | Why do Statistics, Machine learning and Operations research stand out as separate entities | In machine learning "programming" = coding up an algorithm, in operations research "programming" = optimization?
More serious answer, I think the differences are more historical lineage and application area than techniques per se. One perspective on the cultures of (academic) statistics vs. machine learning I found int... | Why do Statistics, Machine learning and Operations research stand out as separate entities | In machine learning "programming" = coding up an algorithm, in operations research "programming" = optimization?
More serious answer, I think the differences are more historical lineage and applicatio | Why do Statistics, Machine learning and Operations research stand out as separate entities
In machine learning "programming" = coding up an algorithm, in operations research "programming" = optimization?
More serious answer, I think the differences are more historical lineage and application area than techniques per se... | Why do Statistics, Machine learning and Operations research stand out as separate entities
In machine learning "programming" = coding up an algorithm, in operations research "programming" = optimization?
More serious answer, I think the differences are more historical lineage and applicatio |
53,256 | Why do Statistics, Machine learning and Operations research stand out as separate entities | In my view, the differences are more cultural than methodological. All three share a common mathematical foundation in probability theory, optimization, and linear algebra. I disagree that any one of these is more "rigorous" than any other. Each field has its PhD's who do mind-bendingly rigorous and difficult research.... | Why do Statistics, Machine learning and Operations research stand out as separate entities | In my view, the differences are more cultural than methodological. All three share a common mathematical foundation in probability theory, optimization, and linear algebra. I disagree that any one of | Why do Statistics, Machine learning and Operations research stand out as separate entities
In my view, the differences are more cultural than methodological. All three share a common mathematical foundation in probability theory, optimization, and linear algebra. I disagree that any one of these is more "rigorous" than... | Why do Statistics, Machine learning and Operations research stand out as separate entities
In my view, the differences are more cultural than methodological. All three share a common mathematical foundation in probability theory, optimization, and linear algebra. I disagree that any one of |
53,257 | P-value for point biserial correlation in R | The point-biserial correlation is equivalent to calculating the Pearson correlation between a continuous and a dichotomous variable (the latter needs to be encoded with 0 and 1). Therefore, you can just use the standard cor.test function in R, which will output the correlation, a 95% confidence interval, and an indepen... | P-value for point biserial correlation in R | The point-biserial correlation is equivalent to calculating the Pearson correlation between a continuous and a dichotomous variable (the latter needs to be encoded with 0 and 1). Therefore, you can ju | P-value for point biserial correlation in R
The point-biserial correlation is equivalent to calculating the Pearson correlation between a continuous and a dichotomous variable (the latter needs to be encoded with 0 and 1). Therefore, you can just use the standard cor.test function in R, which will output the correlatio... | P-value for point biserial correlation in R
The point-biserial correlation is equivalent to calculating the Pearson correlation between a continuous and a dichotomous variable (the latter needs to be encoded with 0 and 1). Therefore, you can ju |
53,258 | P-value for point biserial correlation in R | In response to @user9413061,
I think I discovered the source of the problem.
In the standard definition of biserial correlation, the population standard deviation is used.
ltm::biserial.cor uses the sample standard deviation.
In the following, a function is defined to calculate the population standard deviation. The f... | P-value for point biserial correlation in R | In response to @user9413061,
I think I discovered the source of the problem.
In the standard definition of biserial correlation, the population standard deviation is used.
ltm::biserial.cor uses the s | P-value for point biserial correlation in R
In response to @user9413061,
I think I discovered the source of the problem.
In the standard definition of biserial correlation, the population standard deviation is used.
ltm::biserial.cor uses the sample standard deviation.
In the following, a function is defined to calcula... | P-value for point biserial correlation in R
In response to @user9413061,
I think I discovered the source of the problem.
In the standard definition of biserial correlation, the population standard deviation is used.
ltm::biserial.cor uses the s |
53,259 | P-value for point biserial correlation in R | For my understanding you don't have to code the dichotome variable with 0 and 1. Therefore using other values results in exactly the same output. Try for example:
x <- 1:100
y <- rep(c(0,1), 50)
y2 <- rep(c(-786,345), 50)
cor.test(x, y)
cor.test(x, y2)
Both gives you an r of 0.01732137. The only thing that can happen ... | P-value for point biserial correlation in R | For my understanding you don't have to code the dichotome variable with 0 and 1. Therefore using other values results in exactly the same output. Try for example:
x <- 1:100
y <- rep(c(0,1), 50)
y2 <- | P-value for point biserial correlation in R
For my understanding you don't have to code the dichotome variable with 0 and 1. Therefore using other values results in exactly the same output. Try for example:
x <- 1:100
y <- rep(c(0,1), 50)
y2 <- rep(c(-786,345), 50)
cor.test(x, y)
cor.test(x, y2)
Both gives you an r of... | P-value for point biserial correlation in R
For my understanding you don't have to code the dichotome variable with 0 and 1. Therefore using other values results in exactly the same output. Try for example:
x <- 1:100
y <- rep(c(0,1), 50)
y2 <- |
53,260 | Is there a 3D neural network and how to code it in R? | A '3d network' might commonly be described as a network with 2d layers. It's not fundamentally different from any other network because the principles of activation are the same. The activation of each unit is a linear combination of its inputs, passed through a (typically nonlinear) activation function. In one sense, ... | Is there a 3D neural network and how to code it in R? | A '3d network' might commonly be described as a network with 2d layers. It's not fundamentally different from any other network because the principles of activation are the same. The activation of eac | Is there a 3D neural network and how to code it in R?
A '3d network' might commonly be described as a network with 2d layers. It's not fundamentally different from any other network because the principles of activation are the same. The activation of each unit is a linear combination of its inputs, passed through a (ty... | Is there a 3D neural network and how to code it in R?
A '3d network' might commonly be described as a network with 2d layers. It's not fundamentally different from any other network because the principles of activation are the same. The activation of eac |
53,261 | Is there a 3D neural network and how to code it in R? | For artificial neural networks (the kind employed in machine learning) there is no "dimensionality". As @user20160 notes, convolution nets are often presented in 2D to help us understand the operations of the network, but there is no position in space for any of the units, just connections to different parts of an imag... | Is there a 3D neural network and how to code it in R? | For artificial neural networks (the kind employed in machine learning) there is no "dimensionality". As @user20160 notes, convolution nets are often presented in 2D to help us understand the operation | Is there a 3D neural network and how to code it in R?
For artificial neural networks (the kind employed in machine learning) there is no "dimensionality". As @user20160 notes, convolution nets are often presented in 2D to help us understand the operations of the network, but there is no position in space for any of the... | Is there a 3D neural network and how to code it in R?
For artificial neural networks (the kind employed in machine learning) there is no "dimensionality". As @user20160 notes, convolution nets are often presented in 2D to help us understand the operation |
53,262 | Simulating random variables from a discrete distribution | This answer develops a simple procedure to generate values from this distribution. It illustrates the procedure, analyzes its scope of application (that is, for which $p$ it might be considered a practical method), and provides executable code.
The Idea
Because
$$x^2 = 2\binom{x}{2} + \binom{x}{1},$$
consider the dist... | Simulating random variables from a discrete distribution | This answer develops a simple procedure to generate values from this distribution. It illustrates the procedure, analyzes its scope of application (that is, for which $p$ it might be considered a pra | Simulating random variables from a discrete distribution
This answer develops a simple procedure to generate values from this distribution. It illustrates the procedure, analyzes its scope of application (that is, for which $p$ it might be considered a practical method), and provides executable code.
The Idea
Because
... | Simulating random variables from a discrete distribution
This answer develops a simple procedure to generate values from this distribution. It illustrates the procedure, analyzes its scope of application (that is, for which $p$ it might be considered a pra |
53,263 | Simulating random variables from a discrete distribution | @dsaxton's approach is known as inverse transform sampling and is probably the way to go for a problem like this. To be a bit more explicit, the approach is:
Draw $u$ from uniform distribution on (0,1).
Compute $x = F^{-1}(u)$ where $F^{-1}$ is the inverse of the cumulative distribution function.
Computing $x = F^{-1... | Simulating random variables from a discrete distribution | @dsaxton's approach is known as inverse transform sampling and is probably the way to go for a problem like this. To be a bit more explicit, the approach is:
Draw $u$ from uniform distribution on (0, | Simulating random variables from a discrete distribution
@dsaxton's approach is known as inverse transform sampling and is probably the way to go for a problem like this. To be a bit more explicit, the approach is:
Draw $u$ from uniform distribution on (0,1).
Compute $x = F^{-1}(u)$ where $F^{-1}$ is the inverse of th... | Simulating random variables from a discrete distribution
@dsaxton's approach is known as inverse transform sampling and is probably the way to go for a problem like this. To be a bit more explicit, the approach is:
Draw $u$ from uniform distribution on (0, |
53,264 | Simulating random variables from a discrete distribution | Draw $u$ from a uniform$(0, 1)$ distribution and let $x$ be the smallest value of $k$ for which $\sum_{j=0}^{k} \frac{(1 - p)^3}{p (1 + p)} j^2 p^j > u$. Then $x$ will be a realization from the desired distribution. | Simulating random variables from a discrete distribution | Draw $u$ from a uniform$(0, 1)$ distribution and let $x$ be the smallest value of $k$ for which $\sum_{j=0}^{k} \frac{(1 - p)^3}{p (1 + p)} j^2 p^j > u$. Then $x$ will be a realization from the desir | Simulating random variables from a discrete distribution
Draw $u$ from a uniform$(0, 1)$ distribution and let $x$ be the smallest value of $k$ for which $\sum_{j=0}^{k} \frac{(1 - p)^3}{p (1 + p)} j^2 p^j > u$. Then $x$ will be a realization from the desired distribution. | Simulating random variables from a discrete distribution
Draw $u$ from a uniform$(0, 1)$ distribution and let $x$ be the smallest value of $k$ for which $\sum_{j=0}^{k} \frac{(1 - p)^3}{p (1 + p)} j^2 p^j > u$. Then $x$ will be a realization from the desir |
53,265 | Convergence in distribution of the following sequence of random variables | The MGF of a Beta Distribution is:
$$1+\sum_{k=1}^{\infty}\left(\prod_{r=0}^{k-1} \frac{\alpha+r}{\alpha+\beta+r}\right)\frac{t^k}{k!}$$
As $n\to \infty$, we see that
$$r,\alpha,\beta>0 \implies\frac{\alpha/n+r}{\alpha/n+\beta/n+r} \to 1$$
For $r=0$ we get:
$$\lim_{n\to \infty} \frac{\alpha/n}{\alpha/n+\beta/n} = \fra... | Convergence in distribution of the following sequence of random variables | The MGF of a Beta Distribution is:
$$1+\sum_{k=1}^{\infty}\left(\prod_{r=0}^{k-1} \frac{\alpha+r}{\alpha+\beta+r}\right)\frac{t^k}{k!}$$
As $n\to \infty$, we see that
$$r,\alpha,\beta>0 \implies\frac | Convergence in distribution of the following sequence of random variables
The MGF of a Beta Distribution is:
$$1+\sum_{k=1}^{\infty}\left(\prod_{r=0}^{k-1} \frac{\alpha+r}{\alpha+\beta+r}\right)\frac{t^k}{k!}$$
As $n\to \infty$, we see that
$$r,\alpha,\beta>0 \implies\frac{\alpha/n+r}{\alpha/n+\beta/n+r} \to 1$$
For $... | Convergence in distribution of the following sequence of random variables
The MGF of a Beta Distribution is:
$$1+\sum_{k=1}^{\infty}\left(\prod_{r=0}^{k-1} \frac{\alpha+r}{\alpha+\beta+r}\right)\frac{t^k}{k!}$$
As $n\to \infty$, we see that
$$r,\alpha,\beta>0 \implies\frac |
53,266 | Convergence in distribution of the following sequence of random variables | It converges in distribution to a Bernoulli variable with parameter $\alpha/(\alpha+\beta)$.
This figure shows the Beta distributions in the case $\alpha=2,\beta=1$ for $n=1,4,16,64,$ and $\infty$. They settle down to a distribution with a jump of $\beta/(\alpha+\beta)=1/3$ at $0$ and another jump of $\alpha/(\alpha+... | Convergence in distribution of the following sequence of random variables | It converges in distribution to a Bernoulli variable with parameter $\alpha/(\alpha+\beta)$.
This figure shows the Beta distributions in the case $\alpha=2,\beta=1$ for $n=1,4,16,64,$ and $\infty$. | Convergence in distribution of the following sequence of random variables
It converges in distribution to a Bernoulli variable with parameter $\alpha/(\alpha+\beta)$.
This figure shows the Beta distributions in the case $\alpha=2,\beta=1$ for $n=1,4,16,64,$ and $\infty$. They settle down to a distribution with a jump... | Convergence in distribution of the following sequence of random variables
It converges in distribution to a Bernoulli variable with parameter $\alpha/(\alpha+\beta)$.
This figure shows the Beta distributions in the case $\alpha=2,\beta=1$ for $n=1,4,16,64,$ and $\infty$. |
53,267 | What is the perplexity of a mini-language of numbers [0-9] where 0 has prob 10 times the other numbers? | The reason why you get the wrong answer is because the way the calculation has been described in the book is a little confusing. The book says "imagine a string of digits of length $N$". This means a long string of digits, not just a string of $10$ digits.
Imagine a long string of digits from the new language. On aver... | What is the perplexity of a mini-language of numbers [0-9] where 0 has prob 10 times the other numbe | The reason why you get the wrong answer is because the way the calculation has been described in the book is a little confusing. The book says "imagine a string of digits of length $N$". This means a | What is the perplexity of a mini-language of numbers [0-9] where 0 has prob 10 times the other numbers?
The reason why you get the wrong answer is because the way the calculation has been described in the book is a little confusing. The book says "imagine a string of digits of length $N$". This means a long string of d... | What is the perplexity of a mini-language of numbers [0-9] where 0 has prob 10 times the other numbe
The reason why you get the wrong answer is because the way the calculation has been described in the book is a little confusing. The book says "imagine a string of digits of length $N$". This means a |
53,268 | Why would I ever use a linear autoencoder for dimensionality reduction? | Using a linear autoencoder instead of PCA could also be useful in a large-scale learning scenario. Since you can use Stochastic Gradient Descent (SGD) to train the AE, there is no neeed to load all the training samples in the main memory at once, which can be problematic with large-scale problems.
The linear AE may als... | Why would I ever use a linear autoencoder for dimensionality reduction? | Using a linear autoencoder instead of PCA could also be useful in a large-scale learning scenario. Since you can use Stochastic Gradient Descent (SGD) to train the AE, there is no neeed to load all th | Why would I ever use a linear autoencoder for dimensionality reduction?
Using a linear autoencoder instead of PCA could also be useful in a large-scale learning scenario. Since you can use Stochastic Gradient Descent (SGD) to train the AE, there is no neeed to load all the training samples in the main memory at once, w... | Why would I ever use a linear autoencoder for dimensionality reduction?
Using a linear autoencoder instead of PCA could also be useful in a large-scale learning scenario. Since you can use Stochastic Gradient Descent (SGD) to train the AE, there is no neeed to load all th |
53,269 | Deep Neural Network weight initialization [duplicate] | As far as I know the two formulas you gave are pretty much the standard initialization. I did a literature review a while ago, please see my linked answer. | Deep Neural Network weight initialization [duplicate] | As far as I know the two formulas you gave are pretty much the standard initialization. I did a literature review a while ago, please see my linked answer. | Deep Neural Network weight initialization [duplicate]
As far as I know the two formulas you gave are pretty much the standard initialization. I did a literature review a while ago, please see my linked answer. | Deep Neural Network weight initialization [duplicate]
As far as I know the two formulas you gave are pretty much the standard initialization. I did a literature review a while ago, please see my linked answer. |
53,270 | Deep Neural Network weight initialization [duplicate] | Want to improve this post? Provide detailed answers to this question, including citations and an explanation of why your answer is correct. Answers without enough detail may be edited or deleted.
Recently, Batch Normalization was introduced for this ... | Deep Neural Network weight initialization [duplicate] | Want to improve this post? Provide detailed answers to this question, including citations and an explanation of why your answer is correct. Answers without enough detail may be edited or deleted.
| Deep Neural Network weight initialization [duplicate]
Want to improve this post? Provide detailed answers to this question, including citations and an explanation of why your answer is correct. Answers without enough detail may be edited or deleted.
... | Deep Neural Network weight initialization [duplicate]
Want to improve this post? Provide detailed answers to this question, including citations and an explanation of why your answer is correct. Answers without enough detail may be edited or deleted.
|
53,271 | Deep Neural Network weight initialization [duplicate] | The paper 'all you need is a good init' is a good relatively recent article about inits in deep learning. What I liked about it is that:
it has a short and effective literature survey on init methods, references included.
It achieves very good results without too many bells and whistles on cifar10. | Deep Neural Network weight initialization [duplicate] | The paper 'all you need is a good init' is a good relatively recent article about inits in deep learning. What I liked about it is that:
it has a short and effective literature survey on init methods | Deep Neural Network weight initialization [duplicate]
The paper 'all you need is a good init' is a good relatively recent article about inits in deep learning. What I liked about it is that:
it has a short and effective literature survey on init methods, references included.
It achieves very good results without too m... | Deep Neural Network weight initialization [duplicate]
The paper 'all you need is a good init' is a good relatively recent article about inits in deep learning. What I liked about it is that:
it has a short and effective literature survey on init methods |
53,272 | Deep Neural Network weight initialization [duplicate] | Want to improve this post? Provide detailed answers to this question, including citations and an explanation of why your answer is correct. Answers without enough detail may be edited or deleted.
Weights initialization depend on the activation functi... | Deep Neural Network weight initialization [duplicate] | Want to improve this post? Provide detailed answers to this question, including citations and an explanation of why your answer is correct. Answers without enough detail may be edited or deleted.
| Deep Neural Network weight initialization [duplicate]
Want to improve this post? Provide detailed answers to this question, including citations and an explanation of why your answer is correct. Answers without enough detail may be edited or deleted.
... | Deep Neural Network weight initialization [duplicate]
Want to improve this post? Provide detailed answers to this question, including citations and an explanation of why your answer is correct. Answers without enough detail may be edited or deleted.
|
53,273 | How do I compute/estimate the variance of sequential data? [duplicate] | The proper answer to your question is named online sample variance, and in general online statistics. It's named online because you update the current value of the sample statistic and don't look back at that number.
In order to find an online algorithm to handle that what you need is to break the definition of sample ... | How do I compute/estimate the variance of sequential data? [duplicate] | The proper answer to your question is named online sample variance, and in general online statistics. It's named online because you update the current value of the sample statistic and don't look back | How do I compute/estimate the variance of sequential data? [duplicate]
The proper answer to your question is named online sample variance, and in general online statistics. It's named online because you update the current value of the sample statistic and don't look back at that number.
In order to find an online algor... | How do I compute/estimate the variance of sequential data? [duplicate]
The proper answer to your question is named online sample variance, and in general online statistics. It's named online because you update the current value of the sample statistic and don't look back |
53,274 | How do I compute/estimate the variance of sequential data? [duplicate] | It seems after some looking around, that the algorithms given in this technical report by Chan, Golub, and LeVeque from 1983 are still the state of the art. | How do I compute/estimate the variance of sequential data? [duplicate] | It seems after some looking around, that the algorithms given in this technical report by Chan, Golub, and LeVeque from 1983 are still the state of the art. | How do I compute/estimate the variance of sequential data? [duplicate]
It seems after some looking around, that the algorithms given in this technical report by Chan, Golub, and LeVeque from 1983 are still the state of the art. | How do I compute/estimate the variance of sequential data? [duplicate]
It seems after some looking around, that the algorithms given in this technical report by Chan, Golub, and LeVeque from 1983 are still the state of the art. |
53,275 | How do I compute/estimate the variance of sequential data? [duplicate] | My intuition, might not be correct:
Lets say you divide sequence in 2 groups having same number of elements, calculate there mean (mean1 and mean2) and variances (variance1, variance 2) , For calculating variance 2 you can use combined mean of both the sequences i.e. (mean1 + mean2)/2, Now based on this mean (mean3) yo... | How do I compute/estimate the variance of sequential data? [duplicate] | My intuition, might not be correct:
Lets say you divide sequence in 2 groups having same number of elements, calculate there mean (mean1 and mean2) and variances (variance1, variance 2) , For calculat | How do I compute/estimate the variance of sequential data? [duplicate]
My intuition, might not be correct:
Lets say you divide sequence in 2 groups having same number of elements, calculate there mean (mean1 and mean2) and variances (variance1, variance 2) , For calculating variance 2 you can use combined mean of both ... | How do I compute/estimate the variance of sequential data? [duplicate]
My intuition, might not be correct:
Lets say you divide sequence in 2 groups having same number of elements, calculate there mean (mean1 and mean2) and variances (variance1, variance 2) , For calculat |
53,276 | Repeated CrossValidation, finalModel and ROC curves | For all caret models, the final model is trained on the full dataset. caret::train uses the cross-validation scheme you chose to select model parameters (e.g. mtry for a random forest) and estimate out-of-sample performance of the model. Once the cross-validation is done, caret retrains the model on the full dataset,... | Repeated CrossValidation, finalModel and ROC curves | For all caret models, the final model is trained on the full dataset. caret::train uses the cross-validation scheme you chose to select model parameters (e.g. mtry for a random forest) and estimate o | Repeated CrossValidation, finalModel and ROC curves
For all caret models, the final model is trained on the full dataset. caret::train uses the cross-validation scheme you chose to select model parameters (e.g. mtry for a random forest) and estimate out-of-sample performance of the model. Once the cross-validation is... | Repeated CrossValidation, finalModel and ROC curves
For all caret models, the final model is trained on the full dataset. caret::train uses the cross-validation scheme you chose to select model parameters (e.g. mtry for a random forest) and estimate o |
53,277 | Repeated CrossValidation, finalModel and ROC curves | So finally to summarize :
ctrl = trainControl(method="repeatedcv", number=10, repeats = 300, savePredictions = TRUE, classProbs = TRUE)
mdl = train("Label~.", data=Data, method = "glm", trControl = ctrl)
pred = predict(mdl, newdata = Data, type="prob")
roc.1 = roc(Data$Label, pred$control)
roc.2 = roc(mdl$pred$obs,mdl$... | Repeated CrossValidation, finalModel and ROC curves | So finally to summarize :
ctrl = trainControl(method="repeatedcv", number=10, repeats = 300, savePredictions = TRUE, classProbs = TRUE)
mdl = train("Label~.", data=Data, method = "glm", trControl = ct | Repeated CrossValidation, finalModel and ROC curves
So finally to summarize :
ctrl = trainControl(method="repeatedcv", number=10, repeats = 300, savePredictions = TRUE, classProbs = TRUE)
mdl = train("Label~.", data=Data, method = "glm", trControl = ctrl)
pred = predict(mdl, newdata = Data, type="prob")
roc.1 = roc(Dat... | Repeated CrossValidation, finalModel and ROC curves
So finally to summarize :
ctrl = trainControl(method="repeatedcv", number=10, repeats = 300, savePredictions = TRUE, classProbs = TRUE)
mdl = train("Label~.", data=Data, method = "glm", trControl = ct |
53,278 | Gradient descent: compute partial derivative of arbitrary cost function by hand or through software? | There are several options available to you:
Try to compute the derivatives by hand and then implement them in code.
Use a symbolic computation package like Maple, Mathematica, Wolfram Alpha, etc. to find the derivatives. Some of these packages will translate the resulting formulas directly into code.
Use an automatic... | Gradient descent: compute partial derivative of arbitrary cost function by hand or through software? | There are several options available to you:
Try to compute the derivatives by hand and then implement them in code.
Use a symbolic computation package like Maple, Mathematica, Wolfram Alpha, etc. to | Gradient descent: compute partial derivative of arbitrary cost function by hand or through software?
There are several options available to you:
Try to compute the derivatives by hand and then implement them in code.
Use a symbolic computation package like Maple, Mathematica, Wolfram Alpha, etc. to find the derivative... | Gradient descent: compute partial derivative of arbitrary cost function by hand or through software?
There are several options available to you:
Try to compute the derivatives by hand and then implement them in code.
Use a symbolic computation package like Maple, Mathematica, Wolfram Alpha, etc. to |
53,279 | Gradient descent: compute partial derivative of arbitrary cost function by hand or through software? | You can if there's a nice analytic solution. Otherwise, use numerical techniques or libraries like tensorflow / theano. | Gradient descent: compute partial derivative of arbitrary cost function by hand or through software? | You can if there's a nice analytic solution. Otherwise, use numerical techniques or libraries like tensorflow / theano. | Gradient descent: compute partial derivative of arbitrary cost function by hand or through software?
You can if there's a nice analytic solution. Otherwise, use numerical techniques or libraries like tensorflow / theano. | Gradient descent: compute partial derivative of arbitrary cost function by hand or through software?
You can if there's a nice analytic solution. Otherwise, use numerical techniques or libraries like tensorflow / theano. |
53,280 | Find state space model to compare with Box-Jenkins ARIMA model | State-space models are very flexible; indeed they can encompass ARIMA models.
One class of state space models that has some overlap with ARIMA models but also has a large subset of models that don't overlap with them is the Basic Structural Model (BSM). See Harvey (1989)[1]. There are also numerous papers by Harvey (us... | Find state space model to compare with Box-Jenkins ARIMA model | State-space models are very flexible; indeed they can encompass ARIMA models.
One class of state space models that has some overlap with ARIMA models but also has a large subset of models that don't o | Find state space model to compare with Box-Jenkins ARIMA model
State-space models are very flexible; indeed they can encompass ARIMA models.
One class of state space models that has some overlap with ARIMA models but also has a large subset of models that don't overlap with them is the Basic Structural Model (BSM). See... | Find state space model to compare with Box-Jenkins ARIMA model
State-space models are very flexible; indeed they can encompass ARIMA models.
One class of state space models that has some overlap with ARIMA models but also has a large subset of models that don't o |
53,281 | Use ACF and PACF for irregular time series? | The latter approach is preferred since the time difference must be invariant/constant for an ACF/PACF to be useful for model identification purposes. Intervention Detection can be iteratively used to estimate the missing values while accounting for the auto-correlative structure. One can invert the time series--i.e., ... | Use ACF and PACF for irregular time series? | The latter approach is preferred since the time difference must be invariant/constant for an ACF/PACF to be useful for model identification purposes. Intervention Detection can be iteratively used to | Use ACF and PACF for irregular time series?
The latter approach is preferred since the time difference must be invariant/constant for an ACF/PACF to be useful for model identification purposes. Intervention Detection can be iteratively used to estimate the missing values while accounting for the auto-correlative struc... | Use ACF and PACF for irregular time series?
The latter approach is preferred since the time difference must be invariant/constant for an ACF/PACF to be useful for model identification purposes. Intervention Detection can be iteratively used to |
53,282 | Use ACF and PACF for irregular time series? | Yes, you should definitely use the second approach: if you do the first, you are considering distant observations as close. If auto-correlation is decreasing with the lag (as is usually the case) then this would lead to an under-estimation of the ACF values: indeed, using say lag 5 (low correlation) for estimating lag ... | Use ACF and PACF for irregular time series? | Yes, you should definitely use the second approach: if you do the first, you are considering distant observations as close. If auto-correlation is decreasing with the lag (as is usually the case) then | Use ACF and PACF for irregular time series?
Yes, you should definitely use the second approach: if you do the first, you are considering distant observations as close. If auto-correlation is decreasing with the lag (as is usually the case) then this would lead to an under-estimation of the ACF values: indeed, using say... | Use ACF and PACF for irregular time series?
Yes, you should definitely use the second approach: if you do the first, you are considering distant observations as close. If auto-correlation is decreasing with the lag (as is usually the case) then |
53,283 | Why can't my (auto.)arima-model forecast my time series? | Your both examples concern with deterministic time series, with no noise and no trend. Deterministic time series, with no trend is not really the kind of data that ARIMA was designed for (see this question to learn more on ARIMA assumptions).
Actually to forecast future trend given your data what you could do is simply... | Why can't my (auto.)arima-model forecast my time series? | Your both examples concern with deterministic time series, with no noise and no trend. Deterministic time series, with no trend is not really the kind of data that ARIMA was designed for (see this que | Why can't my (auto.)arima-model forecast my time series?
Your both examples concern with deterministic time series, with no noise and no trend. Deterministic time series, with no trend is not really the kind of data that ARIMA was designed for (see this question to learn more on ARIMA assumptions).
Actually to forecast... | Why can't my (auto.)arima-model forecast my time series?
Your both examples concern with deterministic time series, with no noise and no trend. Deterministic time series, with no trend is not really the kind of data that ARIMA was designed for (see this que |
53,284 | Why can't my (auto.)arima-model forecast my time series? | A bit late, but you can specify your frequency and tell arima that you have seasonality:
library(forecast)
ts<-c(1,1,1,1,1,0,0,1,1,1,1,1,0,0,1,1,1,1,1,0,0,1,1,1,1,1,0,0,1,1,1,1,1,0,0,1,1,1,1,1,0,0,1,1,1,1,1,0,0,1,1,1,1,1,0,0,1,1,1,1,1)
ts <- ts(ts, frequency = 7)
fit <- auto.arima(ts, D = 1)
plot(forecast(fit,h=20))
... | Why can't my (auto.)arima-model forecast my time series? | A bit late, but you can specify your frequency and tell arima that you have seasonality:
library(forecast)
ts<-c(1,1,1,1,1,0,0,1,1,1,1,1,0,0,1,1,1,1,1,0,0,1,1,1,1,1,0,0,1,1,1,1,1,0,0,1,1,1,1,1,0,0,1, | Why can't my (auto.)arima-model forecast my time series?
A bit late, but you can specify your frequency and tell arima that you have seasonality:
library(forecast)
ts<-c(1,1,1,1,1,0,0,1,1,1,1,1,0,0,1,1,1,1,1,0,0,1,1,1,1,1,0,0,1,1,1,1,1,0,0,1,1,1,1,1,0,0,1,1,1,1,1,0,0,1,1,1,1,1,0,0,1,1,1,1,1)
ts <- ts(ts, frequency = ... | Why can't my (auto.)arima-model forecast my time series?
A bit late, but you can specify your frequency and tell arima that you have seasonality:
library(forecast)
ts<-c(1,1,1,1,1,0,0,1,1,1,1,1,0,0,1,1,1,1,1,0,0,1,1,1,1,1,0,0,1,1,1,1,1,0,0,1,1,1,1,1,0,0,1, |
53,285 | Equivalence of the dt and pt function in R | I believe this calculates the probability of P(X>x) occurring (since P(X=x)=0 in a continuous distribution). I would expect pt and 1−dt to be the same.
Your belief (and the consequently the expectation you hold) is wrong.
The $d$ in dt refers to density. You're right to think density is not probability. The d... funct... | Equivalence of the dt and pt function in R | I believe this calculates the probability of P(X>x) occurring (since P(X=x)=0 in a continuous distribution). I would expect pt and 1−dt to be the same.
Your belief (and the consequently the expectati | Equivalence of the dt and pt function in R
I believe this calculates the probability of P(X>x) occurring (since P(X=x)=0 in a continuous distribution). I would expect pt and 1−dt to be the same.
Your belief (and the consequently the expectation you hold) is wrong.
The $d$ in dt refers to density. You're right to think... | Equivalence of the dt and pt function in R
I believe this calculates the probability of P(X>x) occurring (since P(X=x)=0 in a continuous distribution). I would expect pt and 1−dt to be the same.
Your belief (and the consequently the expectati |
53,286 | Strictly positive random variables | A truncated normal distribution might fit the bill. (Or a better statistics book.) The truncated normal is obtained by discarding whatever is below zero, in your situation. The pdf, cdf and the moments are fully described in the linked Wikipedia article. | Strictly positive random variables | A truncated normal distribution might fit the bill. (Or a better statistics book.) The truncated normal is obtained by discarding whatever is below zero, in your situation. The pdf, cdf and the moment | Strictly positive random variables
A truncated normal distribution might fit the bill. (Or a better statistics book.) The truncated normal is obtained by discarding whatever is below zero, in your situation. The pdf, cdf and the moments are fully described in the linked Wikipedia article. | Strictly positive random variables
A truncated normal distribution might fit the bill. (Or a better statistics book.) The truncated normal is obtained by discarding whatever is below zero, in your situation. The pdf, cdf and the moment |
53,287 | Strictly positive random variables | Depending on how "normal-like" you want your variable, you might consider a log-normal distribution, in which the logarithm of the variable has a normal distribution. The variable itself is thus always non-negative, and for the type of distribution you specify (large mean, small variance) the variable might look close ... | Strictly positive random variables | Depending on how "normal-like" you want your variable, you might consider a log-normal distribution, in which the logarithm of the variable has a normal distribution. The variable itself is thus alway | Strictly positive random variables
Depending on how "normal-like" you want your variable, you might consider a log-normal distribution, in which the logarithm of the variable has a normal distribution. The variable itself is thus always non-negative, and for the type of distribution you specify (large mean, small varia... | Strictly positive random variables
Depending on how "normal-like" you want your variable, you might consider a log-normal distribution, in which the logarithm of the variable has a normal distribution. The variable itself is thus alway |
53,288 | What is the expected value of $\frac{X}{X+Y}$? | If $(X,Y)$ is binormal, then so is $(X,Z) = (X,X+Y)$. The ratio $X/Z$ is the tangent of the slope of the line through the origin and the point $(Z,X)$. When $X$ and $Z$ are uncorrelated with zero means, it is well known (and easy to compute) that $X/Z$ has a Cauchy distribution. Cauchy distributions have no expectat... | What is the expected value of $\frac{X}{X+Y}$? | If $(X,Y)$ is binormal, then so is $(X,Z) = (X,X+Y)$. The ratio $X/Z$ is the tangent of the slope of the line through the origin and the point $(Z,X)$. When $X$ and $Z$ are uncorrelated with zero me | What is the expected value of $\frac{X}{X+Y}$?
If $(X,Y)$ is binormal, then so is $(X,Z) = (X,X+Y)$. The ratio $X/Z$ is the tangent of the slope of the line through the origin and the point $(Z,X)$. When $X$ and $Z$ are uncorrelated with zero means, it is well known (and easy to compute) that $X/Z$ has a Cauchy distr... | What is the expected value of $\frac{X}{X+Y}$?
If $(X,Y)$ is binormal, then so is $(X,Z) = (X,X+Y)$. The ratio $X/Z$ is the tangent of the slope of the line through the origin and the point $(Z,X)$. When $X$ and $Z$ are uncorrelated with zero me |
53,289 | What is the expected value of $\frac{X}{X+Y}$? | This is a follow-up to whuber's answer, and posted as a separate answer
because it is too long for a comment.
Lest people think that it is the bivariate normality
of $X$ and $Y$ that is causing the problem, it is worth emphasizing that if $W$ is a continuous random variable whose density is nonzero on an open interval... | What is the expected value of $\frac{X}{X+Y}$? | This is a follow-up to whuber's answer, and posted as a separate answer
because it is too long for a comment.
Lest people think that it is the bivariate normality
of $X$ and $Y$ that is causing the p | What is the expected value of $\frac{X}{X+Y}$?
This is a follow-up to whuber's answer, and posted as a separate answer
because it is too long for a comment.
Lest people think that it is the bivariate normality
of $X$ and $Y$ that is causing the problem, it is worth emphasizing that if $W$ is a continuous random variab... | What is the expected value of $\frac{X}{X+Y}$?
This is a follow-up to whuber's answer, and posted as a separate answer
because it is too long for a comment.
Lest people think that it is the bivariate normality
of $X$ and $Y$ that is causing the p |
53,290 | Estimates of the variance of the variance component of a mixed effects model | Here is the analysis with R-package VCA V1.2:
> library(VCA)
> data(sleepstudy)
> fit <- anovaMM(Reaction~Days*(Subject), sleepstudy)
> inf <- VCAinference(fit, VarVC=TRUE)
> print(inf, what="VCA")
Inference from Mixed Model Fit
------------------------------
> VCA Result:
-------------
[Fixed Effects]
... | Estimates of the variance of the variance component of a mixed effects model | Here is the analysis with R-package VCA V1.2:
> library(VCA)
> data(sleepstudy)
> fit <- anovaMM(Reaction~Days*(Subject), sleepstudy)
> inf <- VCAinference(fit, VarVC=TRUE)
> print(inf, what="VCA")
| Estimates of the variance of the variance component of a mixed effects model
Here is the analysis with R-package VCA V1.2:
> library(VCA)
> data(sleepstudy)
> fit <- anovaMM(Reaction~Days*(Subject), sleepstudy)
> inf <- VCAinference(fit, VarVC=TRUE)
> print(inf, what="VCA")
Inference from Mixed Model Fit
-----------... | Estimates of the variance of the variance component of a mixed effects model
Here is the analysis with R-package VCA V1.2:
> library(VCA)
> data(sleepstudy)
> fit <- anovaMM(Reaction~Days*(Subject), sleepstudy)
> inf <- VCAinference(fit, VarVC=TRUE)
> print(inf, what="VCA")
|
53,291 | Estimates of the variance of the variance component of a mixed effects model | In package VCA V1.3 it is possible to use REML-estimation of linear mixed models besides ANOVA-type estimation.
> library(VCA)
> data(sleepstudy)
> fit <- remlMM(Reaction~Days+(Subject)+Days:(Subject), sleepstudy, cov=TRUE)
> fit
REML-Estimation of Mixed Model:
-------------------------------
[Fixed Effects]... | Estimates of the variance of the variance component of a mixed effects model | In package VCA V1.3 it is possible to use REML-estimation of linear mixed models besides ANOVA-type estimation.
> library(VCA)
> data(sleepstudy)
> fit <- remlMM(Reaction~Days+(Subject)+Days:(Subject) | Estimates of the variance of the variance component of a mixed effects model
In package VCA V1.3 it is possible to use REML-estimation of linear mixed models besides ANOVA-type estimation.
> library(VCA)
> data(sleepstudy)
> fit <- remlMM(Reaction~Days+(Subject)+Days:(Subject), sleepstudy, cov=TRUE)
> fit
REML-Estima... | Estimates of the variance of the variance component of a mixed effects model
In package VCA V1.3 it is possible to use REML-estimation of linear mixed models besides ANOVA-type estimation.
> library(VCA)
> data(sleepstudy)
> fit <- remlMM(Reaction~Days+(Subject)+Days:(Subject) |
53,292 | Estimates of the variance of the variance component of a mixed effects model | (Leaving my previous answer to the wrong question in tact for posterity, hopefully this time I'm answering the question actually being asked...)
A question about the variance of the variance estimates was recently posted on R-SIG-MIXED-MODELS. Ben Bolker, one of the lme4 authors, has already worked out how to do this f... | Estimates of the variance of the variance component of a mixed effects model | (Leaving my previous answer to the wrong question in tact for posterity, hopefully this time I'm answering the question actually being asked...)
A question about the variance of the variance estimates | Estimates of the variance of the variance component of a mixed effects model
(Leaving my previous answer to the wrong question in tact for posterity, hopefully this time I'm answering the question actually being asked...)
A question about the variance of the variance estimates was recently posted on R-SIG-MIXED-MODELS.... | Estimates of the variance of the variance component of a mixed effects model
(Leaving my previous answer to the wrong question in tact for posterity, hopefully this time I'm answering the question actually being asked...)
A question about the variance of the variance estimates |
53,293 | Estimates of the variance of the variance component of a mixed effects model | If you are willing to fit the mixed model using ANOVA Type-1 estimation you can use R-package VCA which has two approaches to estimation of the variance of variance components implemented following Searle et al. (1992) "Variance Components" and alternatively an approximation of Giesbrecht and Burns (1985) Two-Stage Ana... | Estimates of the variance of the variance component of a mixed effects model | If you are willing to fit the mixed model using ANOVA Type-1 estimation you can use R-package VCA which has two approaches to estimation of the variance of variance components implemented following Se | Estimates of the variance of the variance component of a mixed effects model
If you are willing to fit the mixed model using ANOVA Type-1 estimation you can use R-package VCA which has two approaches to estimation of the variance of variance components implemented following Searle et al. (1992) "Variance Components" an... | Estimates of the variance of the variance component of a mixed effects model
If you are willing to fit the mixed model using ANOVA Type-1 estimation you can use R-package VCA which has two approaches to estimation of the variance of variance components implemented following Se |
53,294 | Estimates of the variance of the variance component of a mixed effects model | To find standard errors of random effects for lmer(), use library(merDeriv); sqrt(diag(vcov(lmer(), full = TRUE))). Another mentioned library(arm); se.ranef(lmer()) at https://stackoverflow.com/questions/31694812. If you use nlme::lme() instead, see the answer in https://stackoverflow.com/a/76025033/20653759 for standa... | Estimates of the variance of the variance component of a mixed effects model | To find standard errors of random effects for lmer(), use library(merDeriv); sqrt(diag(vcov(lmer(), full = TRUE))). Another mentioned library(arm); se.ranef(lmer()) at https://stackoverflow.com/questi | Estimates of the variance of the variance component of a mixed effects model
To find standard errors of random effects for lmer(), use library(merDeriv); sqrt(diag(vcov(lmer(), full = TRUE))). Another mentioned library(arm); se.ranef(lmer()) at https://stackoverflow.com/questions/31694812. If you use nlme::lme() instea... | Estimates of the variance of the variance component of a mixed effects model
To find standard errors of random effects for lmer(), use library(merDeriv); sqrt(diag(vcov(lmer(), full = TRUE))). Another mentioned library(arm); se.ranef(lmer()) at https://stackoverflow.com/questi |
53,295 | Estimates of the variance of the variance component of a mixed effects model | The lmer function in lme4 does provide estimates of the variance of the varying slopes/intercepts, both on the variance and the standard deviation scales.
> library(lme4)
Loading required package: Matrix
Loading required package: Rcpp
> m <- lmer(Reaction ~ Days + (Days|Subject),sleepstudy)
> m
Linear mixed model fit ... | Estimates of the variance of the variance component of a mixed effects model | The lmer function in lme4 does provide estimates of the variance of the varying slopes/intercepts, both on the variance and the standard deviation scales.
> library(lme4)
Loading required package: Ma | Estimates of the variance of the variance component of a mixed effects model
The lmer function in lme4 does provide estimates of the variance of the varying slopes/intercepts, both on the variance and the standard deviation scales.
> library(lme4)
Loading required package: Matrix
Loading required package: Rcpp
> m <- ... | Estimates of the variance of the variance component of a mixed effects model
The lmer function in lme4 does provide estimates of the variance of the varying slopes/intercepts, both on the variance and the standard deviation scales.
> library(lme4)
Loading required package: Ma |
53,296 | Adjustable sample size in clinical trial | Ideally that's the point of a Phase II trial. Results from these studies, often single-arm in design, are used for power calculations. Sometimes they experiment with dosing and eligibility criteria, the more moving parts in a Phase II study, the more of a gamble a Phase III study will be.
If a compound is showing to be... | Adjustable sample size in clinical trial | Ideally that's the point of a Phase II trial. Results from these studies, often single-arm in design, are used for power calculations. Sometimes they experiment with dosing and eligibility criteria, t | Adjustable sample size in clinical trial
Ideally that's the point of a Phase II trial. Results from these studies, often single-arm in design, are used for power calculations. Sometimes they experiment with dosing and eligibility criteria, the more moving parts in a Phase II study, the more of a gamble a Phase III stud... | Adjustable sample size in clinical trial
Ideally that's the point of a Phase II trial. Results from these studies, often single-arm in design, are used for power calculations. Sometimes they experiment with dosing and eligibility criteria, t |
53,297 | Adjustable sample size in clinical trial | I think AdamO's answer is great, but I think it's also worth emphasizing out that this adaptive sample size design is how many (maybe even most? I've done theoretical work during internships at pharm companies, but can't say I've ever planned a real study...) clinical trials are run.
That is to say, if a sequential d... | Adjustable sample size in clinical trial | I think AdamO's answer is great, but I think it's also worth emphasizing out that this adaptive sample size design is how many (maybe even most? I've done theoretical work during internships at pharm | Adjustable sample size in clinical trial
I think AdamO's answer is great, but I think it's also worth emphasizing out that this adaptive sample size design is how many (maybe even most? I've done theoretical work during internships at pharm companies, but can't say I've ever planned a real study...) clinical trials ar... | Adjustable sample size in clinical trial
I think AdamO's answer is great, but I think it's also worth emphasizing out that this adaptive sample size design is how many (maybe even most? I've done theoretical work during internships at pharm |
53,298 | Covariance of Categorical variables | Use your crayons!
That's all you need to know. The rest of this answer elaborates on it, for those who have not read the link, and then it supplies a formal demonstration of the claim in that link: coloring rectangles in a scatterplot really does give the correct covariance in all cases.
The figure shows two indicat... | Covariance of Categorical variables | Use your crayons!
That's all you need to know. The rest of this answer elaborates on it, for those who have not read the link, and then it supplies a formal demonstration of the claim in that link: c | Covariance of Categorical variables
Use your crayons!
That's all you need to know. The rest of this answer elaborates on it, for those who have not read the link, and then it supplies a formal demonstration of the claim in that link: coloring rectangles in a scatterplot really does give the correct covariance in all c... | Covariance of Categorical variables
Use your crayons!
That's all you need to know. The rest of this answer elaborates on it, for those who have not read the link, and then it supplies a formal demonstration of the claim in that link: c |
53,299 | Covariance of Categorical variables | Consider a single trial from a multinomial, so $n=1$. This will give a random vector $x$ with $k$ components. The $ith$ and $jth$ coordinates of the covariance matrix is given by
$cov(x_i, x_j) = E[(x_i - u_i)(x_j - u_j)] $
$ = E[x_i x_j - p_i x_j -p_j x_i + p_i p_j]$
$ = E[x_i x_j] - E[x_j]p_i - E[x_i]p_j + p_i p_j$... | Covariance of Categorical variables | Consider a single trial from a multinomial, so $n=1$. This will give a random vector $x$ with $k$ components. The $ith$ and $jth$ coordinates of the covariance matrix is given by
$cov(x_i, x_j) = E[ | Covariance of Categorical variables
Consider a single trial from a multinomial, so $n=1$. This will give a random vector $x$ with $k$ components. The $ith$ and $jth$ coordinates of the covariance matrix is given by
$cov(x_i, x_j) = E[(x_i - u_i)(x_j - u_j)] $
$ = E[x_i x_j - p_i x_j -p_j x_i + p_i p_j]$
$ = E[x_i x_j... | Covariance of Categorical variables
Consider a single trial from a multinomial, so $n=1$. This will give a random vector $x$ with $k$ components. The $ith$ and $jth$ coordinates of the covariance matrix is given by
$cov(x_i, x_j) = E[ |
53,300 | Covariance of Categorical variables | Plz see
https://arxiv.org/abs/1605.05087
This article describes more detail derivation about the covariance of categorical variables.
The derivation show:
Defining the variance of categorical variables = Gini-index
Defining the covariance of categorical variables = Correspondence Analysis
And also It showed application... | Covariance of Categorical variables | Plz see
https://arxiv.org/abs/1605.05087
This article describes more detail derivation about the covariance of categorical variables.
The derivation show:
Defining the variance of categorical variable | Covariance of Categorical variables
Plz see
https://arxiv.org/abs/1605.05087
This article describes more detail derivation about the covariance of categorical variables.
The derivation show:
Defining the variance of categorical variables = Gini-index
Defining the covariance of categorical variables = Correspondence Ana... | Covariance of Categorical variables
Plz see
https://arxiv.org/abs/1605.05087
This article describes more detail derivation about the covariance of categorical variables.
The derivation show:
Defining the variance of categorical variable |
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