idx int64 1 56k | question stringlengths 15 155 | answer stringlengths 2 29.2k ⌀ | question_cut stringlengths 15 100 | answer_cut stringlengths 2 200 ⌀ | conversation stringlengths 47 29.3k | conversation_cut stringlengths 47 301 |
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35,501 | Non-random small sample - What conclusions can I get? | To expand on my comments, here's one approach. Someone more used to the area you're working in (and there are many here) may have a better suggestion for solving the same problems:
1) Assume that confounding variables are of two kinds.
i) The first kind (the main one) are counfounders which are always the same for a g... | Non-random small sample - What conclusions can I get? | To expand on my comments, here's one approach. Someone more used to the area you're working in (and there are many here) may have a better suggestion for solving the same problems:
1) Assume that conf | Non-random small sample - What conclusions can I get?
To expand on my comments, here's one approach. Someone more used to the area you're working in (and there are many here) may have a better suggestion for solving the same problems:
1) Assume that confounding variables are of two kinds.
i) The first kind (the main o... | Non-random small sample - What conclusions can I get?
To expand on my comments, here's one approach. Someone more used to the area you're working in (and there are many here) may have a better suggestion for solving the same problems:
1) Assume that conf |
35,502 | Non-random small sample - What conclusions can I get? | In this case, I would be much more interested in the individual story of the 10 kids than in any kind of statistics.
History: Statistics with small samples. Cite Mark Twain, "History doesn't often repeat itself, but it rhymes."
Roger Koenker, Dictionary of Received Ideas of Statistics | Non-random small sample - What conclusions can I get? | In this case, I would be much more interested in the individual story of the 10 kids than in any kind of statistics.
History: Statistics with small samples. Cite Mark Twain, "History doesn't often re | Non-random small sample - What conclusions can I get?
In this case, I would be much more interested in the individual story of the 10 kids than in any kind of statistics.
History: Statistics with small samples. Cite Mark Twain, "History doesn't often repeat itself, but it rhymes."
Roger Koenker, Dictionary of Received... | Non-random small sample - What conclusions can I get?
In this case, I would be much more interested in the individual story of the 10 kids than in any kind of statistics.
History: Statistics with small samples. Cite Mark Twain, "History doesn't often re |
35,503 | Conditional vs unconditional expectation | As @Whuber said, second calculation should give you a random variable rather than a number.
Now to complete these calculations (and to see @Whubers fact) we calculate the following:
$$E(Y)=\sum_y yf(y)=1(0.25) + 1(0.25) + 2(0.5) = 1.5$$
which is what you correctly calculated before. Now, the second expectation is th... | Conditional vs unconditional expectation | As @Whuber said, second calculation should give you a random variable rather than a number.
Now to complete these calculations (and to see @Whubers fact) we calculate the following:
$$E(Y)=\sum_y yf | Conditional vs unconditional expectation
As @Whuber said, second calculation should give you a random variable rather than a number.
Now to complete these calculations (and to see @Whubers fact) we calculate the following:
$$E(Y)=\sum_y yf(y)=1(0.25) + 1(0.25) + 2(0.5) = 1.5$$
which is what you correctly calculated b... | Conditional vs unconditional expectation
As @Whuber said, second calculation should give you a random variable rather than a number.
Now to complete these calculations (and to see @Whubers fact) we calculate the following:
$$E(Y)=\sum_y yf |
35,504 | Conditional vs unconditional expectation | If $p_{X,Y}(x,y)$ denotes the joint probability mass function of discrete
random variables $X$ and $Y$, then the marginal mass functions are
$$\begin{align}
p_X(x) &= \sum_y p_{X,Y}(x,y)\\
p_Y(y) &= \sum_x p_{X,Y}(x,y)
\end{align}$$
and so we have that
$$E[Y] = \sum_y y\cdot p_{Y}(y) = \sum_y y\cdot \sum_xp_{X,Y}(x,y)
... | Conditional vs unconditional expectation | If $p_{X,Y}(x,y)$ denotes the joint probability mass function of discrete
random variables $X$ and $Y$, then the marginal mass functions are
$$\begin{align}
p_X(x) &= \sum_y p_{X,Y}(x,y)\\
p_Y(y) &= \ | Conditional vs unconditional expectation
If $p_{X,Y}(x,y)$ denotes the joint probability mass function of discrete
random variables $X$ and $Y$, then the marginal mass functions are
$$\begin{align}
p_X(x) &= \sum_y p_{X,Y}(x,y)\\
p_Y(y) &= \sum_x p_{X,Y}(x,y)
\end{align}$$
and so we have that
$$E[Y] = \sum_y y\cdot p_{... | Conditional vs unconditional expectation
If $p_{X,Y}(x,y)$ denotes the joint probability mass function of discrete
random variables $X$ and $Y$, then the marginal mass functions are
$$\begin{align}
p_X(x) &= \sum_y p_{X,Y}(x,y)\\
p_Y(y) &= \ |
35,505 | LASSO in R for variable selection: how to choose the tuning parameter | By calling cv.glmnet with default arguments you're k-fold cross-validating on lambda with k = 10. The fitted model will use the 1-standard-error-from-min value of lambda by default, and you can get the value by calling cv.glmnet.object$lambda.1se. See page 5 of the vignette: http://cran.r-project.org/web/packages/glm... | LASSO in R for variable selection: how to choose the tuning parameter | By calling cv.glmnet with default arguments you're k-fold cross-validating on lambda with k = 10. The fitted model will use the 1-standard-error-from-min value of lambda by default, and you can get t | LASSO in R for variable selection: how to choose the tuning parameter
By calling cv.glmnet with default arguments you're k-fold cross-validating on lambda with k = 10. The fitted model will use the 1-standard-error-from-min value of lambda by default, and you can get the value by calling cv.glmnet.object$lambda.1se. ... | LASSO in R for variable selection: how to choose the tuning parameter
By calling cv.glmnet with default arguments you're k-fold cross-validating on lambda with k = 10. The fitted model will use the 1-standard-error-from-min value of lambda by default, and you can get t |
35,506 | Converting odds ratios to Cohen's d for meta analysis | Hi Erica and welcome to the site. Have a look at this (page 3) document and this paper. The basic formula for the conversion is
$$
d=\mathrm{LogOR}\times \frac{\sqrt{3}}{\pi}
$$
Applying the delta-method, we get the following expression for the the variance of $d$ (the standard error of $d$ is just the square root of... | Converting odds ratios to Cohen's d for meta analysis | Hi Erica and welcome to the site. Have a look at this (page 3) document and this paper. The basic formula for the conversion is
$$
d=\mathrm{LogOR}\times \frac{\sqrt{3}}{\pi}
$$
Applying the delta-m | Converting odds ratios to Cohen's d for meta analysis
Hi Erica and welcome to the site. Have a look at this (page 3) document and this paper. The basic formula for the conversion is
$$
d=\mathrm{LogOR}\times \frac{\sqrt{3}}{\pi}
$$
Applying the delta-method, we get the following expression for the the variance of $d$... | Converting odds ratios to Cohen's d for meta analysis
Hi Erica and welcome to the site. Have a look at this (page 3) document and this paper. The basic formula for the conversion is
$$
d=\mathrm{LogOR}\times \frac{\sqrt{3}}{\pi}
$$
Applying the delta-m |
35,507 | In MCMC, how is burn-in time chosen? | There are several diagnostics, including the Geweke Diagnostic, the Heidelberg and Welch Diagnostic, the Raftery and Lewis Diagnostic, and the Gelman and Rubin Multiple Sequence Diagnostic. Also, visual examination of the trace plot can help. All of these are only indications, not guarantees.
You might check out:
http... | In MCMC, how is burn-in time chosen? | There are several diagnostics, including the Geweke Diagnostic, the Heidelberg and Welch Diagnostic, the Raftery and Lewis Diagnostic, and the Gelman and Rubin Multiple Sequence Diagnostic. Also, visu | In MCMC, how is burn-in time chosen?
There are several diagnostics, including the Geweke Diagnostic, the Heidelberg and Welch Diagnostic, the Raftery and Lewis Diagnostic, and the Gelman and Rubin Multiple Sequence Diagnostic. Also, visual examination of the trace plot can help. All of these are only indications, not g... | In MCMC, how is burn-in time chosen?
There are several diagnostics, including the Geweke Diagnostic, the Heidelberg and Welch Diagnostic, the Raftery and Lewis Diagnostic, and the Gelman and Rubin Multiple Sequence Diagnostic. Also, visu |
35,508 | In MCMC, how is burn-in time chosen? | I would run the MCMC many times (with different starting values) and plot the log-likelihood along with parameter estimates across time (or iteration number). Hopefully you see a trend for what the iteration number is for the chain to enter the stationary distribution. I would then use this value (and add a little mo... | In MCMC, how is burn-in time chosen? | I would run the MCMC many times (with different starting values) and plot the log-likelihood along with parameter estimates across time (or iteration number). Hopefully you see a trend for what the i | In MCMC, how is burn-in time chosen?
I would run the MCMC many times (with different starting values) and plot the log-likelihood along with parameter estimates across time (or iteration number). Hopefully you see a trend for what the iteration number is for the chain to enter the stationary distribution. I would the... | In MCMC, how is burn-in time chosen?
I would run the MCMC many times (with different starting values) and plot the log-likelihood along with parameter estimates across time (or iteration number). Hopefully you see a trend for what the i |
35,509 | How are the convergence conditions / KKT conditions for the soft-margin SVM derived | Unfortunately, I am late a couple of years, but after reading Ng's lecture notes, I was asking myself the same question. The complementarity conditions you have listed follow from the other KKT conditions, namely:
$$
\begin{align}
\alpha_i &\geq 0 \tag{1},\\
g_i(w) &\leq 0 \tag{2},\\
\alpha_i g_i(w) &= 0 \tag{3},\\
r_i... | How are the convergence conditions / KKT conditions for the soft-margin SVM derived | Unfortunately, I am late a couple of years, but after reading Ng's lecture notes, I was asking myself the same question. The complementarity conditions you have listed follow from the other KKT condit | How are the convergence conditions / KKT conditions for the soft-margin SVM derived
Unfortunately, I am late a couple of years, but after reading Ng's lecture notes, I was asking myself the same question. The complementarity conditions you have listed follow from the other KKT conditions, namely:
$$
\begin{align}
\alph... | How are the convergence conditions / KKT conditions for the soft-margin SVM derived
Unfortunately, I am late a couple of years, but after reading Ng's lecture notes, I was asking myself the same question. The complementarity conditions you have listed follow from the other KKT condit |
35,510 | How are the convergence conditions / KKT conditions for the soft-margin SVM derived | Considering a general primal problem:
$$\min_w f(w)$$
subject to
$$g_i(w)\leq 0 \forall i, h_j(w)=0 \forall j$$
This gives us the Lagrangian:
$$ \mathcal{L}(w,\alpha,\beta) = f(w) +\sum_i\alpha_i g_i(w) + \sum_j\beta_j h_j(w) $$
KKT condition says that $\alpha_i^*g_i(w^*) = 0 \forall i$
Now let us state the soft margi... | How are the convergence conditions / KKT conditions for the soft-margin SVM derived | Considering a general primal problem:
$$\min_w f(w)$$
subject to
$$g_i(w)\leq 0 \forall i, h_j(w)=0 \forall j$$
This gives us the Lagrangian:
$$ \mathcal{L}(w,\alpha,\beta) = f(w) +\sum_i\alpha_i g_i | How are the convergence conditions / KKT conditions for the soft-margin SVM derived
Considering a general primal problem:
$$\min_w f(w)$$
subject to
$$g_i(w)\leq 0 \forall i, h_j(w)=0 \forall j$$
This gives us the Lagrangian:
$$ \mathcal{L}(w,\alpha,\beta) = f(w) +\sum_i\alpha_i g_i(w) + \sum_j\beta_j h_j(w) $$
KKT co... | How are the convergence conditions / KKT conditions for the soft-margin SVM derived
Considering a general primal problem:
$$\min_w f(w)$$
subject to
$$g_i(w)\leq 0 \forall i, h_j(w)=0 \forall j$$
This gives us the Lagrangian:
$$ \mathcal{L}(w,\alpha,\beta) = f(w) +\sum_i\alpha_i g_i |
35,511 | How does the generalized linear model generalize the general linear model? | Consider a case where your response variable is a set of 'successes' and 'failures' (also represented as 'yeses' and 'nos', $1$s and $0$s, etc.). If this were true, it cannot be the case that your error term is normally distributed. Instead, your error term would be Bernoulli, by definition. Thus, one of the assumpt... | How does the generalized linear model generalize the general linear model? | Consider a case where your response variable is a set of 'successes' and 'failures' (also represented as 'yeses' and 'nos', $1$s and $0$s, etc.). If this were true, it cannot be the case that your er | How does the generalized linear model generalize the general linear model?
Consider a case where your response variable is a set of 'successes' and 'failures' (also represented as 'yeses' and 'nos', $1$s and $0$s, etc.). If this were true, it cannot be the case that your error term is normally distributed. Instead, y... | How does the generalized linear model generalize the general linear model?
Consider a case where your response variable is a set of 'successes' and 'failures' (also represented as 'yeses' and 'nos', $1$s and $0$s, etc.). If this were true, it cannot be the case that your er |
35,512 | How to interpret odds ratio? | It means that the odds of a case having had exposure #1 are 1.5 times the odds of its having the baseline exposure. This is not the same as being 1.5 times as probable: odds are not the same as probability (odds of 2:1 against means a probability of $\frac{1}{3}$). So it comes down to what you mean by 'likely'. | How to interpret odds ratio? | It means that the odds of a case having had exposure #1 are 1.5 times the odds of its having the baseline exposure. This is not the same as being 1.5 times as probable: odds are not the same as probab | How to interpret odds ratio?
It means that the odds of a case having had exposure #1 are 1.5 times the odds of its having the baseline exposure. This is not the same as being 1.5 times as probable: odds are not the same as probability (odds of 2:1 against means a probability of $\frac{1}{3}$). So it comes down to what... | How to interpret odds ratio?
It means that the odds of a case having had exposure #1 are 1.5 times the odds of its having the baseline exposure. This is not the same as being 1.5 times as probable: odds are not the same as probab |
35,513 | How to interpret odds ratio? | In answer to the second part of your question, what you say is correct (assuming that by "likely" you mean in terms of odds not probability). Both odds ratios should be relative to the controls.
However, you should check carefully the definition of the exposures - it is possible that having the second exposure is only... | How to interpret odds ratio? | In answer to the second part of your question, what you say is correct (assuming that by "likely" you mean in terms of odds not probability). Both odds ratios should be relative to the controls.
Howe | How to interpret odds ratio?
In answer to the second part of your question, what you say is correct (assuming that by "likely" you mean in terms of odds not probability). Both odds ratios should be relative to the controls.
However, you should check carefully the definition of the exposures - it is possible that havin... | How to interpret odds ratio?
In answer to the second part of your question, what you say is correct (assuming that by "likely" you mean in terms of odds not probability). Both odds ratios should be relative to the controls.
Howe |
35,514 | How to interpret odds ratio? | Your language, "cases are 1.5 times as likely to have exposure 1 than the controls" is a fine description of the interpretation of an odds ratio. As some have noted "likely" is something of an ambiguous phrase, though I doubt anyone in epidemiology is going to raise an eyebrow at your language.
You might consider eithe... | How to interpret odds ratio? | Your language, "cases are 1.5 times as likely to have exposure 1 than the controls" is a fine description of the interpretation of an odds ratio. As some have noted "likely" is something of an ambiguo | How to interpret odds ratio?
Your language, "cases are 1.5 times as likely to have exposure 1 than the controls" is a fine description of the interpretation of an odds ratio. As some have noted "likely" is something of an ambiguous phrase, though I doubt anyone in epidemiology is going to raise an eyebrow at your langu... | How to interpret odds ratio?
Your language, "cases are 1.5 times as likely to have exposure 1 than the controls" is a fine description of the interpretation of an odds ratio. As some have noted "likely" is something of an ambiguo |
35,515 | Homework: Bayesian Data Analysis: Priors on both binomial parameters | I did all of the questions from the first four chapters six years ago. Here's what I have:
$p(\mu,\theta)\propto\left|\frac{\partial \lambda}{\partial \mu}\right|p(\lambda,\theta)=\mu^{-1}.$
So
$\begin{array}{lrl}p\left(N,\theta\right) & = & \int_{0}^{\infty}p\left(\mu,N,\theta\right)\mathrm{d}\mu\\ & = & \int_{0}^{\in... | Homework: Bayesian Data Analysis: Priors on both binomial parameters | I did all of the questions from the first four chapters six years ago. Here's what I have:
$p(\mu,\theta)\propto\left|\frac{\partial \lambda}{\partial \mu}\right|p(\lambda,\theta)=\mu^{-1}.$
So
$\begi | Homework: Bayesian Data Analysis: Priors on both binomial parameters
I did all of the questions from the first four chapters six years ago. Here's what I have:
$p(\mu,\theta)\propto\left|\frac{\partial \lambda}{\partial \mu}\right|p(\lambda,\theta)=\mu^{-1}.$
So
$\begin{array}{lrl}p\left(N,\theta\right) & = & \int_{0}^... | Homework: Bayesian Data Analysis: Priors on both binomial parameters
I did all of the questions from the first four chapters six years ago. Here's what I have:
$p(\mu,\theta)\propto\left|\frac{\partial \lambda}{\partial \mu}\right|p(\lambda,\theta)=\mu^{-1}.$
So
$\begi |
35,516 | How to statistically compare two algorithms across three datasets in feature selection and classification? | Unless your algorithms have huge differences in performance and you have huge numbers of test cases, you won't be able to detect differences by just looking at the performance.
However, you can make use of apaired design:
run all three algorithms on exactly the same train/test split of a data set, and
do not aggregat... | How to statistically compare two algorithms across three datasets in feature selection and classific | Unless your algorithms have huge differences in performance and you have huge numbers of test cases, you won't be able to detect differences by just looking at the performance.
However, you can make u | How to statistically compare two algorithms across three datasets in feature selection and classification?
Unless your algorithms have huge differences in performance and you have huge numbers of test cases, you won't be able to detect differences by just looking at the performance.
However, you can make use of apaired... | How to statistically compare two algorithms across three datasets in feature selection and classific
Unless your algorithms have huge differences in performance and you have huge numbers of test cases, you won't be able to detect differences by just looking at the performance.
However, you can make u |
35,517 | How to statistically compare two algorithms across three datasets in feature selection and classification? | You are running featuer selection with GA 10 times and every time you get a different output !!
First, If you start by the same seed, you should always get the same selected featuer subset. However, If you are using a random seed, also, most probably, you should get almost the same selected features. One reason for get... | How to statistically compare two algorithms across three datasets in feature selection and classific | You are running featuer selection with GA 10 times and every time you get a different output !!
First, If you start by the same seed, you should always get the same selected featuer subset. However, I | How to statistically compare two algorithms across three datasets in feature selection and classification?
You are running featuer selection with GA 10 times and every time you get a different output !!
First, If you start by the same seed, you should always get the same selected featuer subset. However, If you are usi... | How to statistically compare two algorithms across three datasets in feature selection and classific
You are running featuer selection with GA 10 times and every time you get a different output !!
First, If you start by the same seed, you should always get the same selected featuer subset. However, I |
35,518 | Testing equality of two binomial proportions proportion (one near 100 %) | If you trust wikipedia for rules of thumb for the validity of the normal approximation of the binomial distribution:
One rule is that both $np$ and $n(1−p)$ must be greater than $5$.
However, the specific number varies from source to source, and depends
on how good an approximation one wants; some sources give $1... | Testing equality of two binomial proportions proportion (one near 100 %) | If you trust wikipedia for rules of thumb for the validity of the normal approximation of the binomial distribution:
One rule is that both $np$ and $n(1−p)$ must be greater than $5$.
However, the | Testing equality of two binomial proportions proportion (one near 100 %)
If you trust wikipedia for rules of thumb for the validity of the normal approximation of the binomial distribution:
One rule is that both $np$ and $n(1−p)$ must be greater than $5$.
However, the specific number varies from source to source, a... | Testing equality of two binomial proportions proportion (one near 100 %)
If you trust wikipedia for rules of thumb for the validity of the normal approximation of the binomial distribution:
One rule is that both $np$ and $n(1−p)$ must be greater than $5$.
However, the |
35,519 | Testing equality of two binomial proportions proportion (one near 100 %) | +1 for @Jaime. But as it happens in this case your null hypothesis is that both proportions equal a pooled figure of (87+48)/(88+60) = 0.91. With your sample size this is in the acceptable area for approximations such as this z test or the equivalent chi square test. See that the values in the "expected" (meaning ex... | Testing equality of two binomial proportions proportion (one near 100 %) | +1 for @Jaime. But as it happens in this case your null hypothesis is that both proportions equal a pooled figure of (87+48)/(88+60) = 0.91. With your sample size this is in the acceptable area for | Testing equality of two binomial proportions proportion (one near 100 %)
+1 for @Jaime. But as it happens in this case your null hypothesis is that both proportions equal a pooled figure of (87+48)/(88+60) = 0.91. With your sample size this is in the acceptable area for approximations such as this z test or the equiv... | Testing equality of two binomial proportions proportion (one near 100 %)
+1 for @Jaime. But as it happens in this case your null hypothesis is that both proportions equal a pooled figure of (87+48)/(88+60) = 0.91. With your sample size this is in the acceptable area for |
35,520 | What practical application is there for the Asymptotic Mean Integrated Squared Error in kernel density estimation? | The AMISE allows one to obtain an expression for the optimal bandwidth for the unknown density $f$. Unfortunately, the expression is in terms of derivatives of $f$. However, it is possible to derive a similar expression giving the optimal bandwidth for a kernel estimate of those derivatives. This is expressed in terms ... | What practical application is there for the Asymptotic Mean Integrated Squared Error in kernel densi | The AMISE allows one to obtain an expression for the optimal bandwidth for the unknown density $f$. Unfortunately, the expression is in terms of derivatives of $f$. However, it is possible to derive a | What practical application is there for the Asymptotic Mean Integrated Squared Error in kernel density estimation?
The AMISE allows one to obtain an expression for the optimal bandwidth for the unknown density $f$. Unfortunately, the expression is in terms of derivatives of $f$. However, it is possible to derive a simi... | What practical application is there for the Asymptotic Mean Integrated Squared Error in kernel densi
The AMISE allows one to obtain an expression for the optimal bandwidth for the unknown density $f$. Unfortunately, the expression is in terms of derivatives of $f$. However, it is possible to derive a |
35,521 | Probability of collision (two bivariate normal distributions) | Summary
The problem is not trivial, but obtaining a solution is straightforward. Exact analytical expressions for the distribution of the inter-ship distance can be found (in terms of Bessel functions): it is the square root of a scaled non-central chi-squared variate. Provided the ships are far apart compared to the ... | Probability of collision (two bivariate normal distributions) | Summary
The problem is not trivial, but obtaining a solution is straightforward. Exact analytical expressions for the distribution of the inter-ship distance can be found (in terms of Bessel functions | Probability of collision (two bivariate normal distributions)
Summary
The problem is not trivial, but obtaining a solution is straightforward. Exact analytical expressions for the distribution of the inter-ship distance can be found (in terms of Bessel functions): it is the square root of a scaled non-central chi-squar... | Probability of collision (two bivariate normal distributions)
Summary
The problem is not trivial, but obtaining a solution is straightforward. Exact analytical expressions for the distribution of the inter-ship distance can be found (in terms of Bessel functions |
35,522 | Probability of collision (two bivariate normal distributions) | I'm not sure how much this will help you but I hope it gives some pointers.
Here is a Mathematica function which computes the probability under the distributions for a circle of radius separation/2 for two ships with a normal distribution of position with variance 0.2. A variance of 0.2 is close to the 95% certainly l... | Probability of collision (two bivariate normal distributions) | I'm not sure how much this will help you but I hope it gives some pointers.
Here is a Mathematica function which computes the probability under the distributions for a circle of radius separation/2 f | Probability of collision (two bivariate normal distributions)
I'm not sure how much this will help you but I hope it gives some pointers.
Here is a Mathematica function which computes the probability under the distributions for a circle of radius separation/2 for two ships with a normal distribution of position with v... | Probability of collision (two bivariate normal distributions)
I'm not sure how much this will help you but I hope it gives some pointers.
Here is a Mathematica function which computes the probability under the distributions for a circle of radius separation/2 f |
35,523 | Probability of collision (two bivariate normal distributions) | I've thrown up a simulation with R with increasing dimension in response to Erik's answer. This code also answers the question, by providing a numerical solution (when fixing the dimension to 2) to a special case which can be easily generalized (though it's not very efficient).
Erik proposed to look at the problem as a... | Probability of collision (two bivariate normal distributions) | I've thrown up a simulation with R with increasing dimension in response to Erik's answer. This code also answers the question, by providing a numerical solution (when fixing the dimension to 2) to a | Probability of collision (two bivariate normal distributions)
I've thrown up a simulation with R with increasing dimension in response to Erik's answer. This code also answers the question, by providing a numerical solution (when fixing the dimension to 2) to a special case which can be easily generalized (though it's ... | Probability of collision (two bivariate normal distributions)
I've thrown up a simulation with R with increasing dimension in response to Erik's answer. This code also answers the question, by providing a numerical solution (when fixing the dimension to 2) to a |
35,524 | Why can bigger sample size increase power of a test? | The power of the test depends on the distribution of the test statistic when the null hypothesis is false. If $R_n$ is the rejection region for the test statistic under the null hypothesis and for sample size $n$, the power is $$\beta = \mbox{Prob}(X_n \in R_n | H_A)$$ where $H_A$ is the null hypothesis and $X_n$ is th... | Why can bigger sample size increase power of a test? | The power of the test depends on the distribution of the test statistic when the null hypothesis is false. If $R_n$ is the rejection region for the test statistic under the null hypothesis and for sam | Why can bigger sample size increase power of a test?
The power of the test depends on the distribution of the test statistic when the null hypothesis is false. If $R_n$ is the rejection region for the test statistic under the null hypothesis and for sample size $n$, the power is $$\beta = \mbox{Prob}(X_n \in R_n | H_A)... | Why can bigger sample size increase power of a test?
The power of the test depends on the distribution of the test statistic when the null hypothesis is false. If $R_n$ is the rejection region for the test statistic under the null hypothesis and for sam |
35,525 | Why can bigger sample size increase power of a test? | Here's one intuitive answer: In the real world, you are almost always sampling from a finite population (although it may be very large). If you managed to measure the entire population, power would be infinite (well, 1.0, which is essentially like infinite power - you could detect any difference) - you would know the e... | Why can bigger sample size increase power of a test? | Here's one intuitive answer: In the real world, you are almost always sampling from a finite population (although it may be very large). If you managed to measure the entire population, power would be | Why can bigger sample size increase power of a test?
Here's one intuitive answer: In the real world, you are almost always sampling from a finite population (although it may be very large). If you managed to measure the entire population, power would be infinite (well, 1.0, which is essentially like infinite power - yo... | Why can bigger sample size increase power of a test?
Here's one intuitive answer: In the real world, you are almost always sampling from a finite population (although it may be very large). If you managed to measure the entire population, power would be |
35,526 | Why can bigger sample size increase power of a test? | Thinking a little more about the part of the question:
Does bigger sample size always increase testing power?
If we are only talking about tests generally covered in an introductory statistics course and the conditions for those tests hold (e.g. simple random sample, central limit theorem gives an approximate normal,... | Why can bigger sample size increase power of a test? | Thinking a little more about the part of the question:
Does bigger sample size always increase testing power?
If we are only talking about tests generally covered in an introductory statistics cours | Why can bigger sample size increase power of a test?
Thinking a little more about the part of the question:
Does bigger sample size always increase testing power?
If we are only talking about tests generally covered in an introductory statistics course and the conditions for those tests hold (e.g. simple random sampl... | Why can bigger sample size increase power of a test?
Thinking a little more about the part of the question:
Does bigger sample size always increase testing power?
If we are only talking about tests generally covered in an introductory statistics cours |
35,527 | Why can bigger sample size increase power of a test? | For a more intuitive understanding look at the power.examp function in the TeachingDemos package for R. | Why can bigger sample size increase power of a test? | For a more intuitive understanding look at the power.examp function in the TeachingDemos package for R. | Why can bigger sample size increase power of a test?
For a more intuitive understanding look at the power.examp function in the TeachingDemos package for R. | Why can bigger sample size increase power of a test?
For a more intuitive understanding look at the power.examp function in the TeachingDemos package for R. |
35,528 | Why can bigger sample size increase power of a test? | Imagine a penny that's just slightly imperfect where heads will come up a tiny bit more than tails. If you try to detect that imperfection with just for example 10 flips your chances are low because of sampling error. For instance, you might happen to get a sample where you get more tails than heads. As you increase ... | Why can bigger sample size increase power of a test? | Imagine a penny that's just slightly imperfect where heads will come up a tiny bit more than tails. If you try to detect that imperfection with just for example 10 flips your chances are low because | Why can bigger sample size increase power of a test?
Imagine a penny that's just slightly imperfect where heads will come up a tiny bit more than tails. If you try to detect that imperfection with just for example 10 flips your chances are low because of sampling error. For instance, you might happen to get a sample w... | Why can bigger sample size increase power of a test?
Imagine a penny that's just slightly imperfect where heads will come up a tiny bit more than tails. If you try to detect that imperfection with just for example 10 flips your chances are low because |
35,529 | Meaning of p-values for an interaction between a categorical variable (w/ >2 cats) & continuous variable | The general way to do this is with a full-reduced model test using the anova function. Refit your model without the interaction of interest (the update function can be convenient for this) then run the anova function on the full and reduced models, for a glm fit you probably want to include test="Chisq".
Something lik... | Meaning of p-values for an interaction between a categorical variable (w/ >2 cats) & continuous vari | The general way to do this is with a full-reduced model test using the anova function. Refit your model without the interaction of interest (the update function can be convenient for this) then run t | Meaning of p-values for an interaction between a categorical variable (w/ >2 cats) & continuous variable
The general way to do this is with a full-reduced model test using the anova function. Refit your model without the interaction of interest (the update function can be convenient for this) then run the anova functi... | Meaning of p-values for an interaction between a categorical variable (w/ >2 cats) & continuous vari
The general way to do this is with a full-reduced model test using the anova function. Refit your model without the interaction of interest (the update function can be convenient for this) then run t |
35,530 | Can I perform an exhaustive search with cross-validation for feature selection? | Yes, you are likely to end up with over-fitting in this case, see my answer to this previous question. The important thing to remember is that cross-validation is an estimate of generalisation performance based on a finite sample of data. As it is based on a finite sample of data, the estimator has a non-zero varianc... | Can I perform an exhaustive search with cross-validation for feature selection? | Yes, you are likely to end up with over-fitting in this case, see my answer to this previous question. The important thing to remember is that cross-validation is an estimate of generalisation perfor | Can I perform an exhaustive search with cross-validation for feature selection?
Yes, you are likely to end up with over-fitting in this case, see my answer to this previous question. The important thing to remember is that cross-validation is an estimate of generalisation performance based on a finite sample of data. ... | Can I perform an exhaustive search with cross-validation for feature selection?
Yes, you are likely to end up with over-fitting in this case, see my answer to this previous question. The important thing to remember is that cross-validation is an estimate of generalisation perfor |
35,531 | Can I perform an exhaustive search with cross-validation for feature selection? | I think this is a valid procedure for feature selection which is no more prone to overfitting than other feature selection procedures. The problem with this procedure is that it has large computational complexity and barely can be used for real data sets. | Can I perform an exhaustive search with cross-validation for feature selection? | I think this is a valid procedure for feature selection which is no more prone to overfitting than other feature selection procedures. The problem with this procedure is that it has large computationa | Can I perform an exhaustive search with cross-validation for feature selection?
I think this is a valid procedure for feature selection which is no more prone to overfitting than other feature selection procedures. The problem with this procedure is that it has large computational complexity and barely can be used for ... | Can I perform an exhaustive search with cross-validation for feature selection?
I think this is a valid procedure for feature selection which is no more prone to overfitting than other feature selection procedures. The problem with this procedure is that it has large computationa |
35,532 | Can I perform an exhaustive search with cross-validation for feature selection? | I think if you do feature selection inside each fold of the cross validation you'll be fine. As posters above state you will overfit in any model using the selected features obtained from the procedure outlined above. This is because all data had some influence on the feature selection routine. | Can I perform an exhaustive search with cross-validation for feature selection? | I think if you do feature selection inside each fold of the cross validation you'll be fine. As posters above state you will overfit in any model using the selected features obtained from the procedur | Can I perform an exhaustive search with cross-validation for feature selection?
I think if you do feature selection inside each fold of the cross validation you'll be fine. As posters above state you will overfit in any model using the selected features obtained from the procedure outlined above. This is because all d... | Can I perform an exhaustive search with cross-validation for feature selection?
I think if you do feature selection inside each fold of the cross validation you'll be fine. As posters above state you will overfit in any model using the selected features obtained from the procedur |
35,533 | Contribution of each covariate to a single prediction in a logistic regression model | You can use the predict function in R. Call it with type='terms' and it will give you the contribution of each term in the model (the coefficient times the variable value). This will be on the log-odds scale.
Another option is to use the TkPredict function from the TeachingDemos package. This will show a graph of th... | Contribution of each covariate to a single prediction in a logistic regression model | You can use the predict function in R. Call it with type='terms' and it will give you the contribution of each term in the model (the coefficient times the variable value). This will be on the log-o | Contribution of each covariate to a single prediction in a logistic regression model
You can use the predict function in R. Call it with type='terms' and it will give you the contribution of each term in the model (the coefficient times the variable value). This will be on the log-odds scale.
Another option is to use... | Contribution of each covariate to a single prediction in a logistic regression model
You can use the predict function in R. Call it with type='terms' and it will give you the contribution of each term in the model (the coefficient times the variable value). This will be on the log-o |
35,534 | Construct artificial slightly overlapping data for PCA plot | To simulate a PCA, start with the desired result and work backwards: add some random error in the orthogonal directions and rotate that randomly.
The following example stipulates a two-dimensional result (i.e., two principal components) with two "blobs"; it is readily extended to more blobs. (More dimensions would tak... | Construct artificial slightly overlapping data for PCA plot | To simulate a PCA, start with the desired result and work backwards: add some random error in the orthogonal directions and rotate that randomly.
The following example stipulates a two-dimensional res | Construct artificial slightly overlapping data for PCA plot
To simulate a PCA, start with the desired result and work backwards: add some random error in the orthogonal directions and rotate that randomly.
The following example stipulates a two-dimensional result (i.e., two principal components) with two "blobs"; it is... | Construct artificial slightly overlapping data for PCA plot
To simulate a PCA, start with the desired result and work backwards: add some random error in the orthogonal directions and rotate that randomly.
The following example stipulates a two-dimensional res |
35,535 | How is the inverse gamma distribution related to $n$ and $\sigma$? | I think it is more correct to speak of the posterior distribution of your parameter $\sigma'^{2}$ rather than its posterior estimate. For clarity of notations, I will drop the prime in $\sigma'^{2}$ in what follows.
Suppose that $X$ is distributed as $\mathcal{N}(0, \sigma^2)$, — I drop $\mu$ for now to make a heuristi... | How is the inverse gamma distribution related to $n$ and $\sigma$? | I think it is more correct to speak of the posterior distribution of your parameter $\sigma'^{2}$ rather than its posterior estimate. For clarity of notations, I will drop the prime in $\sigma'^{2}$ i | How is the inverse gamma distribution related to $n$ and $\sigma$?
I think it is more correct to speak of the posterior distribution of your parameter $\sigma'^{2}$ rather than its posterior estimate. For clarity of notations, I will drop the prime in $\sigma'^{2}$ in what follows.
Suppose that $X$ is distributed as $\... | How is the inverse gamma distribution related to $n$ and $\sigma$?
I think it is more correct to speak of the posterior distribution of your parameter $\sigma'^{2}$ rather than its posterior estimate. For clarity of notations, I will drop the prime in $\sigma'^{2}$ i |
35,536 | How is the inverse gamma distribution related to $n$ and $\sigma$? | For question 1, the second equation follows from Bayes' rule as you point out, and I don't see how to avoid that.
For question 2, yes, you can do this. Just use a prior of the same form as your second equation.
For question 3, I would look for something about exponential families. Maybe someone will recommend a good ... | How is the inverse gamma distribution related to $n$ and $\sigma$? | For question 1, the second equation follows from Bayes' rule as you point out, and I don't see how to avoid that.
For question 2, yes, you can do this. Just use a prior of the same form as your secon | How is the inverse gamma distribution related to $n$ and $\sigma$?
For question 1, the second equation follows from Bayes' rule as you point out, and I don't see how to avoid that.
For question 2, yes, you can do this. Just use a prior of the same form as your second equation.
For question 3, I would look for somethin... | How is the inverse gamma distribution related to $n$ and $\sigma$?
For question 1, the second equation follows from Bayes' rule as you point out, and I don't see how to avoid that.
For question 2, yes, you can do this. Just use a prior of the same form as your secon |
35,537 | Does using bootstrapping change how you deal with problems of Type I errors when testing multiple correlations? | I also don't follow your situation 100%, but I suspect it doesn't matter. The problem of multiple comparisons arises simply due to the mathematics of looking at lots of random things. That is, each statistical test can be understood as a Bernoulli trial. If the null hypothesis holds in every case, you have a Binomia... | Does using bootstrapping change how you deal with problems of Type I errors when testing multiple co | I also don't follow your situation 100%, but I suspect it doesn't matter. The problem of multiple comparisons arises simply due to the mathematics of looking at lots of random things. That is, each | Does using bootstrapping change how you deal with problems of Type I errors when testing multiple correlations?
I also don't follow your situation 100%, but I suspect it doesn't matter. The problem of multiple comparisons arises simply due to the mathematics of looking at lots of random things. That is, each statisti... | Does using bootstrapping change how you deal with problems of Type I errors when testing multiple co
I also don't follow your situation 100%, but I suspect it doesn't matter. The problem of multiple comparisons arises simply due to the mathematics of looking at lots of random things. That is, each |
35,538 | Does using bootstrapping change how you deal with problems of Type I errors when testing multiple correlations? | But bootstrapping does offer a simple way to do multiple comparisons (including simultaneous intervals if you don't like testing) in a way that incorporates dependence structures in an asymptotically consistent way. The statement that "bootstrapping does not get you out of this fact" is misleading because it follows a ... | Does using bootstrapping change how you deal with problems of Type I errors when testing multiple co | But bootstrapping does offer a simple way to do multiple comparisons (including simultaneous intervals if you don't like testing) in a way that incorporates dependence structures in an asymptotically | Does using bootstrapping change how you deal with problems of Type I errors when testing multiple correlations?
But bootstrapping does offer a simple way to do multiple comparisons (including simultaneous intervals if you don't like testing) in a way that incorporates dependence structures in an asymptotically consiste... | Does using bootstrapping change how you deal with problems of Type I errors when testing multiple co
But bootstrapping does offer a simple way to do multiple comparisons (including simultaneous intervals if you don't like testing) in a way that incorporates dependence structures in an asymptotically |
35,539 | Time series modeling with high-frequency data | ARIMA and ETS models are designed for relatively short seasonality (e.g., monthly or quarterly) and do not work well for seasonal periods that are much longer. The ets() error should be captured though --- I'll fix it in the next version of the forecast package.
You might try instead a Fourier series model:
library(for... | Time series modeling with high-frequency data | ARIMA and ETS models are designed for relatively short seasonality (e.g., monthly or quarterly) and do not work well for seasonal periods that are much longer. The ets() error should be captured thoug | Time series modeling with high-frequency data
ARIMA and ETS models are designed for relatively short seasonality (e.g., monthly or quarterly) and do not work well for seasonal periods that are much longer. The ets() error should be captured though --- I'll fix it in the next version of the forecast package.
You might t... | Time series modeling with high-frequency data
ARIMA and ETS models are designed for relatively short seasonality (e.g., monthly or quarterly) and do not work well for seasonal periods that are much longer. The ets() error should be captured thoug |
35,540 | Interpreting coefficients for Poisson regression | Not to be critical, but this is kind of a strange example. It's not clear that you're really doing time series analysis, nor what the NASDAQ would have to do with the number of games won by some team. If you're interested in saying something about the number of games a team won, I think it would be best to use binary... | Interpreting coefficients for Poisson regression | Not to be critical, but this is kind of a strange example. It's not clear that you're really doing time series analysis, nor what the NASDAQ would have to do with the number of games won by some team | Interpreting coefficients for Poisson regression
Not to be critical, but this is kind of a strange example. It's not clear that you're really doing time series analysis, nor what the NASDAQ would have to do with the number of games won by some team. If you're interested in saying something about the number of games a... | Interpreting coefficients for Poisson regression
Not to be critical, but this is kind of a strange example. It's not clear that you're really doing time series analysis, nor what the NASDAQ would have to do with the number of games won by some team |
35,541 | Gibbs sampler from conditional distribution | There you go-
Gibbs Sampler:
The burning period is to reach some stationarity in the samples
burning_period=5000
iterations=1000
y=matrix(nrow=(burning_period+iterations),ncol=3)
a=matrix(nrow=iterations,ncol=3)
y[1,1]=0.5 #Initial Sample
y[1,2]=0.6
y[1,3]=0.2
for(i in 2:(burning_period+iterations)){
... | Gibbs sampler from conditional distribution | There you go-
Gibbs Sampler:
The burning period is to reach some stationarity in the samples
burning_period=5000
iterations=1000
y=matrix(nrow=(burning_period+iterations),ncol=3)
a=matrix(nrow=iterati | Gibbs sampler from conditional distribution
There you go-
Gibbs Sampler:
The burning period is to reach some stationarity in the samples
burning_period=5000
iterations=1000
y=matrix(nrow=(burning_period+iterations),ncol=3)
a=matrix(nrow=iterations,ncol=3)
y[1,1]=0.5 #Initial Sample
y[1,2]=0.6
y[1,3]=0.2
f... | Gibbs sampler from conditional distribution
There you go-
Gibbs Sampler:
The burning period is to reach some stationarity in the samples
burning_period=5000
iterations=1000
y=matrix(nrow=(burning_period+iterations),ncol=3)
a=matrix(nrow=iterati |
35,542 | Gibbs sampler from conditional distribution | The full conditional distributions can be found by fixing the values of the two "other" variables, then combining all the terms that you can combine and seeing what you get:
$p(y_1|y_2,y_3) \propto \exp\{-(1+\theta_{12}y_2+\theta_{13}y_3)y_1\}$
which is evidently an exponential distribution with parameter $1+\theta_{1... | Gibbs sampler from conditional distribution | The full conditional distributions can be found by fixing the values of the two "other" variables, then combining all the terms that you can combine and seeing what you get:
$p(y_1|y_2,y_3) \propto \e | Gibbs sampler from conditional distribution
The full conditional distributions can be found by fixing the values of the two "other" variables, then combining all the terms that you can combine and seeing what you get:
$p(y_1|y_2,y_3) \propto \exp\{-(1+\theta_{12}y_2+\theta_{13}y_3)y_1\}$
which is evidently an exponent... | Gibbs sampler from conditional distribution
The full conditional distributions can be found by fixing the values of the two "other" variables, then combining all the terms that you can combine and seeing what you get:
$p(y_1|y_2,y_3) \propto \e |
35,543 | Arithmetic for updating likelihoods using Bayes theorem | I'll start by answering your question about updating events with the "fourth and fifth extensions." As you suspected, the arithmetic is indeed quite simple.
First, recall how Bayes theorem is derived from the definition of conditional probability:
By conditioning on A in the numerator we can get to the more familiar f... | Arithmetic for updating likelihoods using Bayes theorem | I'll start by answering your question about updating events with the "fourth and fifth extensions." As you suspected, the arithmetic is indeed quite simple.
First, recall how Bayes theorem is derived | Arithmetic for updating likelihoods using Bayes theorem
I'll start by answering your question about updating events with the "fourth and fifth extensions." As you suspected, the arithmetic is indeed quite simple.
First, recall how Bayes theorem is derived from the definition of conditional probability:
By conditioning... | Arithmetic for updating likelihoods using Bayes theorem
I'll start by answering your question about updating events with the "fourth and fifth extensions." As you suspected, the arithmetic is indeed quite simple.
First, recall how Bayes theorem is derived |
35,544 | Arithmetic for updating likelihoods using Bayes theorem | There are lots of ways to extend this result. The general form is that
$$P(A|B,C,D...)=\frac{P(A,B,C,D...)}{P(B,C,D,...)}$$
There are many ways to write both numerator and denominator. Your formualae give two examples (assuming $B_2$ and $C$ are the same thing). Of course, for a given problem, you have to formulate the... | Arithmetic for updating likelihoods using Bayes theorem | There are lots of ways to extend this result. The general form is that
$$P(A|B,C,D...)=\frac{P(A,B,C,D...)}{P(B,C,D,...)}$$
There are many ways to write both numerator and denominator. Your formualae | Arithmetic for updating likelihoods using Bayes theorem
There are lots of ways to extend this result. The general form is that
$$P(A|B,C,D...)=\frac{P(A,B,C,D...)}{P(B,C,D,...)}$$
There are many ways to write both numerator and denominator. Your formualae give two examples (assuming $B_2$ and $C$ are the same thing). O... | Arithmetic for updating likelihoods using Bayes theorem
There are lots of ways to extend this result. The general form is that
$$P(A|B,C,D...)=\frac{P(A,B,C,D...)}{P(B,C,D,...)}$$
There are many ways to write both numerator and denominator. Your formualae |
35,545 | Recurrent neural networks in R | There is the RSNNS package that provides access to the "Stuttgart Neural Network Simulator" (SNNS). It contains the classical recurrent network structures of types 'Jordan' and 'Elman'. SNNS is a bit old (before 2000), but may still be worth a try. The R package itself has been updated in September this year. | Recurrent neural networks in R | There is the RSNNS package that provides access to the "Stuttgart Neural Network Simulator" (SNNS). It contains the classical recurrent network structures of types 'Jordan' and 'Elman'. SNNS is a bit | Recurrent neural networks in R
There is the RSNNS package that provides access to the "Stuttgart Neural Network Simulator" (SNNS). It contains the classical recurrent network structures of types 'Jordan' and 'Elman'. SNNS is a bit old (before 2000), but may still be worth a try. The R package itself has been updated in... | Recurrent neural networks in R
There is the RSNNS package that provides access to the "Stuttgart Neural Network Simulator" (SNNS). It contains the classical recurrent network structures of types 'Jordan' and 'Elman'. SNNS is a bit |
35,546 | Recurrent neural networks in R | I am hoping someone with more R knowledge than me will submit an R answer, but I am not aware of anything. Here is one option: Use one of the multiple Python-based implementations (e.g. PyBrain or PyNeurGen) and interface back to R via Rpy or (my prefence) pyRserve. I know this is not ideal, but it could given you an e... | Recurrent neural networks in R | I am hoping someone with more R knowledge than me will submit an R answer, but I am not aware of anything. Here is one option: Use one of the multiple Python-based implementations (e.g. PyBrain or PyN | Recurrent neural networks in R
I am hoping someone with more R knowledge than me will submit an R answer, but I am not aware of anything. Here is one option: Use one of the multiple Python-based implementations (e.g. PyBrain or PyNeurGen) and interface back to R via Rpy or (my prefence) pyRserve. I know this is not ide... | Recurrent neural networks in R
I am hoping someone with more R knowledge than me will submit an R answer, but I am not aware of anything. Here is one option: Use one of the multiple Python-based implementations (e.g. PyBrain or PyN |
35,547 | Recurrent neural networks in R | There is a new package out: rnn (on CRAN, on github), which implements a recurrent neural network in native R code.
A nice example can be found here:
http://firsttimeprogrammer.blogspot.de/2016/08/plain-vanilla-recurrent-neural-networks.html | Recurrent neural networks in R | There is a new package out: rnn (on CRAN, on github), which implements a recurrent neural network in native R code.
A nice example can be found here:
http://firsttimeprogrammer.blogspot.de/2016/08/pl | Recurrent neural networks in R
There is a new package out: rnn (on CRAN, on github), which implements a recurrent neural network in native R code.
A nice example can be found here:
http://firsttimeprogrammer.blogspot.de/2016/08/plain-vanilla-recurrent-neural-networks.html | Recurrent neural networks in R
There is a new package out: rnn (on CRAN, on github), which implements a recurrent neural network in native R code.
A nice example can be found here:
http://firsttimeprogrammer.blogspot.de/2016/08/pl |
35,548 | Finding degree of polynomial in regression analysis | Sorry if this is too elementary, I just wanted to make this answer as self-contained as possible. In fact, you can't do what you're describing: the best polynomial of degree $k+1$ will always fit at least as well as the best polynomial of degree $k$, since the set of $k+1$ degree polynomials includes all $k$ degree pol... | Finding degree of polynomial in regression analysis | Sorry if this is too elementary, I just wanted to make this answer as self-contained as possible. In fact, you can't do what you're describing: the best polynomial of degree $k+1$ will always fit at l | Finding degree of polynomial in regression analysis
Sorry if this is too elementary, I just wanted to make this answer as self-contained as possible. In fact, you can't do what you're describing: the best polynomial of degree $k+1$ will always fit at least as well as the best polynomial of degree $k$, since the set of ... | Finding degree of polynomial in regression analysis
Sorry if this is too elementary, I just wanted to make this answer as self-contained as possible. In fact, you can't do what you're describing: the best polynomial of degree $k+1$ will always fit at l |
35,549 | Finding degree of polynomial in regression analysis | One of the ways to solve this "search" problem is to first start with some meta-heuristic algorithm like Genetic Programming and once the program is able to create a "near" function (of decent fitness), start with traditional machine learning regression algorithms of degree identified by GP. You will still need to perf... | Finding degree of polynomial in regression analysis | One of the ways to solve this "search" problem is to first start with some meta-heuristic algorithm like Genetic Programming and once the program is able to create a "near" function (of decent fitness | Finding degree of polynomial in regression analysis
One of the ways to solve this "search" problem is to first start with some meta-heuristic algorithm like Genetic Programming and once the program is able to create a "near" function (of decent fitness), start with traditional machine learning regression algorithms of ... | Finding degree of polynomial in regression analysis
One of the ways to solve this "search" problem is to first start with some meta-heuristic algorithm like Genetic Programming and once the program is able to create a "near" function (of decent fitness |
35,550 | Fisher's exact test in R | You're doing everything fine. However, I would recommend Barnard's exact test than Fisher exact test. | Fisher's exact test in R | You're doing everything fine. However, I would recommend Barnard's exact test than Fisher exact test. | Fisher's exact test in R
You're doing everything fine. However, I would recommend Barnard's exact test than Fisher exact test. | Fisher's exact test in R
You're doing everything fine. However, I would recommend Barnard's exact test than Fisher exact test. |
35,551 | Looking for mathematical account of ANOVA | Everything you ask for is beautifully accomplished by Jack Kiefer in his classic Introduction to Statistical Inference (Springer-Verlag 1987). ANOVA is introduced as a special case of the General Linear Model (i.e., regression) in chapter 5, then taken up again at the end of chapter 8 as an application of normal-theor... | Looking for mathematical account of ANOVA | Everything you ask for is beautifully accomplished by Jack Kiefer in his classic Introduction to Statistical Inference (Springer-Verlag 1987). ANOVA is introduced as a special case of the General Lin | Looking for mathematical account of ANOVA
Everything you ask for is beautifully accomplished by Jack Kiefer in his classic Introduction to Statistical Inference (Springer-Verlag 1987). ANOVA is introduced as a special case of the General Linear Model (i.e., regression) in chapter 5, then taken up again at the end of c... | Looking for mathematical account of ANOVA
Everything you ask for is beautifully accomplished by Jack Kiefer in his classic Introduction to Statistical Inference (Springer-Verlag 1987). ANOVA is introduced as a special case of the General Lin |
35,552 | Looking for mathematical account of ANOVA | This paper of Terry Speed may interest you.
Special invited paper:
What is an Analysis of Variance?
T. P. Speed
Annals of Statistics Vol 15 No 3 (1987)
Available from project Euclid with commentary from some big names including Tukey (who says he's not equipped to comment adequately on the mathematical niceties and car... | Looking for mathematical account of ANOVA | This paper of Terry Speed may interest you.
Special invited paper:
What is an Analysis of Variance?
T. P. Speed
Annals of Statistics Vol 15 No 3 (1987)
Available from project Euclid with commentary fr | Looking for mathematical account of ANOVA
This paper of Terry Speed may interest you.
Special invited paper:
What is an Analysis of Variance?
T. P. Speed
Annals of Statistics Vol 15 No 3 (1987)
Available from project Euclid with commentary from some big names including Tukey (who says he's not equipped to comment adequ... | Looking for mathematical account of ANOVA
This paper of Terry Speed may interest you.
Special invited paper:
What is an Analysis of Variance?
T. P. Speed
Annals of Statistics Vol 15 No 3 (1987)
Available from project Euclid with commentary fr |
35,553 | Is there a good reason for the name "Missing at Random"? | You gave a perfect explanation, and there isn't a better one (at least I did not find any during my dissertation work and subsequent research on missing data). There is little excuse for poor terminology, and this is one of the most striking examples (along with formative/reflective indicators in psychology, as well as... | Is there a good reason for the name "Missing at Random"? | You gave a perfect explanation, and there isn't a better one (at least I did not find any during my dissertation work and subsequent research on missing data). There is little excuse for poor terminol | Is there a good reason for the name "Missing at Random"?
You gave a perfect explanation, and there isn't a better one (at least I did not find any during my dissertation work and subsequent research on missing data). There is little excuse for poor terminology, and this is one of the most striking examples (along with ... | Is there a good reason for the name "Missing at Random"?
You gave a perfect explanation, and there isn't a better one (at least I did not find any during my dissertation work and subsequent research on missing data). There is little excuse for poor terminol |
35,554 | Is there a good reason for the name "Missing at Random"? | When, given the observed data, the missingness mechanism does not depend on the unobserved data.
Examples of MAR mechanisms
A subject may be removed from a trial if his/her condition is not
controlled sufficiently well (according to pre-defined criteria on
the response).
Two measurements of the same variable are made ... | Is there a good reason for the name "Missing at Random"? | When, given the observed data, the missingness mechanism does not depend on the unobserved data.
Examples of MAR mechanisms
A subject may be removed from a trial if his/her condition is not
controlle | Is there a good reason for the name "Missing at Random"?
When, given the observed data, the missingness mechanism does not depend on the unobserved data.
Examples of MAR mechanisms
A subject may be removed from a trial if his/her condition is not
controlled sufficiently well (according to pre-defined criteria on
the r... | Is there a good reason for the name "Missing at Random"?
When, given the observed data, the missingness mechanism does not depend on the unobserved data.
Examples of MAR mechanisms
A subject may be removed from a trial if his/her condition is not
controlle |
35,555 | Ordered logit in JAGS | By default, JAGS will initialize all elements of alpha0 to the prior mean 0. So the initial value of p is c(0.5, 0, 0, 0.5). Under these prior conditions, it is impossible to have y[i] equal to 2 or 3. But, in your simulated data, y[3] = 3.
The solution is to initialize the elements of alpha0 to distinct values
inits ... | Ordered logit in JAGS | By default, JAGS will initialize all elements of alpha0 to the prior mean 0. So the initial value of p is c(0.5, 0, 0, 0.5). Under these prior conditions, it is impossible to have y[i] equal to 2 or 3 | Ordered logit in JAGS
By default, JAGS will initialize all elements of alpha0 to the prior mean 0. So the initial value of p is c(0.5, 0, 0, 0.5). Under these prior conditions, it is impossible to have y[i] equal to 2 or 3. But, in your simulated data, y[3] = 3.
The solution is to initialize the elements of alpha0 to ... | Ordered logit in JAGS
By default, JAGS will initialize all elements of alpha0 to the prior mean 0. So the initial value of p is c(0.5, 0, 0, 0.5). Under these prior conditions, it is impossible to have y[i] equal to 2 or 3 |
35,556 | Distribution of a ratio of uniforms: What is wrong? | Here is a hint.
Consider carefully the term $\mathbb P( X \leq z Y \mid z Y < 1 )$. In particular, for concreteness, choose $z = 2$, so that we are considering the event $\mathbb P( X \leq 2 Y \mid Y < 1/2 )$.
Now, look at this picture (which is very closely related to the above probability).
Now, does that condition... | Distribution of a ratio of uniforms: What is wrong? | Here is a hint.
Consider carefully the term $\mathbb P( X \leq z Y \mid z Y < 1 )$. In particular, for concreteness, choose $z = 2$, so that we are considering the event $\mathbb P( X \leq 2 Y \mid Y | Distribution of a ratio of uniforms: What is wrong?
Here is a hint.
Consider carefully the term $\mathbb P( X \leq z Y \mid z Y < 1 )$. In particular, for concreteness, choose $z = 2$, so that we are considering the event $\mathbb P( X \leq 2 Y \mid Y < 1/2 )$.
Now, look at this picture (which is very closely related ... | Distribution of a ratio of uniforms: What is wrong?
Here is a hint.
Consider carefully the term $\mathbb P( X \leq z Y \mid z Y < 1 )$. In particular, for concreteness, choose $z = 2$, so that we are considering the event $\mathbb P( X \leq 2 Y \mid Y |
35,557 | How do joint test, r-squared behave when using autocorrelation / heteroskedasticity robust std. errors? | The $R^2$ is the sum of squared residuals divided by the total variation in your outcome; neither of these statistics change when robust/HAC standard errors are applied, so the $R^2$ doesn't change either. Adjusted $R^2$ alters the formula somewhat, but only based upon the number of observations and the number of predi... | How do joint test, r-squared behave when using autocorrelation / heteroskedasticity robust std. erro | The $R^2$ is the sum of squared residuals divided by the total variation in your outcome; neither of these statistics change when robust/HAC standard errors are applied, so the $R^2$ doesn't change ei | How do joint test, r-squared behave when using autocorrelation / heteroskedasticity robust std. errors?
The $R^2$ is the sum of squared residuals divided by the total variation in your outcome; neither of these statistics change when robust/HAC standard errors are applied, so the $R^2$ doesn't change either. Adjusted $... | How do joint test, r-squared behave when using autocorrelation / heteroskedasticity robust std. erro
The $R^2$ is the sum of squared residuals divided by the total variation in your outcome; neither of these statistics change when robust/HAC standard errors are applied, so the $R^2$ doesn't change ei |
35,558 | Explanatory power of a variable | The relaimpo R package does exactly what you want to do, and it also provides bootstrap CIs when assessing relative contribution of individual predictor to the overall $R^2$.
An example of use can be found at the end of this tutorial: Getting Started with a Modern Approach to Regression. | Explanatory power of a variable | The relaimpo R package does exactly what you want to do, and it also provides bootstrap CIs when assessing relative contribution of individual predictor to the overall $R^2$.
An example of use can be | Explanatory power of a variable
The relaimpo R package does exactly what you want to do, and it also provides bootstrap CIs when assessing relative contribution of individual predictor to the overall $R^2$.
An example of use can be found at the end of this tutorial: Getting Started with a Modern Approach to Regression. | Explanatory power of a variable
The relaimpo R package does exactly what you want to do, and it also provides bootstrap CIs when assessing relative contribution of individual predictor to the overall $R^2$.
An example of use can be |
35,559 | Median value on ordinal scales | Definitional issues:
The median is the middle value of the data; it is not by definition the middle value of the scale.
When the sample size is even, then the median is the mean of the values either side of middle most point after rank ordering all values (see wikipedia description).
When to use median on ordinal dat... | Median value on ordinal scales | Definitional issues:
The median is the middle value of the data; it is not by definition the middle value of the scale.
When the sample size is even, then the median is the mean of the values either | Median value on ordinal scales
Definitional issues:
The median is the middle value of the data; it is not by definition the middle value of the scale.
When the sample size is even, then the median is the mean of the values either side of middle most point after rank ordering all values (see wikipedia description).
Wh... | Median value on ordinal scales
Definitional issues:
The median is the middle value of the data; it is not by definition the middle value of the scale.
When the sample size is even, then the median is the mean of the values either |
35,560 | Median value on ordinal scales | No, the median is the value where half the data is less than or equal to that value and half the data is greater than or equal to that value.
So if your ordinal scale had 100 respondents then find the value that has at least 50 less or equal and 50 greater than or equal. It would only be 3 if half the responses were... | Median value on ordinal scales | No, the median is the value where half the data is less than or equal to that value and half the data is greater than or equal to that value.
So if your ordinal scale had 100 respondents then find t | Median value on ordinal scales
No, the median is the value where half the data is less than or equal to that value and half the data is greater than or equal to that value.
So if your ordinal scale had 100 respondents then find the value that has at least 50 less or equal and 50 greater than or equal. It would only ... | Median value on ordinal scales
No, the median is the value where half the data is less than or equal to that value and half the data is greater than or equal to that value.
So if your ordinal scale had 100 respondents then find t |
35,561 | Data preparation for regression | (You may start from the after line section, for a shorter answer) To begin with, you are absolutely right saying that it firstly depends on the purposes of your analysis: forecasting of average price (at macro level) or a particular price (at micro level), causal analysis of consumer preferences (district, size, age, n... | Data preparation for regression | (You may start from the after line section, for a shorter answer) To begin with, you are absolutely right saying that it firstly depends on the purposes of your analysis: forecasting of average price | Data preparation for regression
(You may start from the after line section, for a shorter answer) To begin with, you are absolutely right saying that it firstly depends on the purposes of your analysis: forecasting of average price (at macro level) or a particular price (at micro level), causal analysis of consumer pre... | Data preparation for regression
(You may start from the after line section, for a shorter answer) To begin with, you are absolutely right saying that it firstly depends on the purposes of your analysis: forecasting of average price |
35,562 | Data preparation for regression | The real estate prices that you are tying to predict , are they consecutive/chronological values i.e. time series data or are they prices for different classes e.g. this years prices for different classes for the same time frame. You might want to read something I wrote on these two kinds of problems as it warns that ... | Data preparation for regression | The real estate prices that you are tying to predict , are they consecutive/chronological values i.e. time series data or are they prices for different classes e.g. this years prices for different cl | Data preparation for regression
The real estate prices that you are tying to predict , are they consecutive/chronological values i.e. time series data or are they prices for different classes e.g. this years prices for different classes for the same time frame. You might want to read something I wrote on these two kin... | Data preparation for regression
The real estate prices that you are tying to predict , are they consecutive/chronological values i.e. time series data or are they prices for different classes e.g. this years prices for different cl |
35,563 | Data preparation for regression | Binning your data is usually a bad idea because it will cause you to lose information, which will likely result in loss of power. Also, I would rarely standardise variables before doing regression, although some people may like to.
A really good book to read, if you can get it, is "Regression Modeling Strategies" by Fr... | Data preparation for regression | Binning your data is usually a bad idea because it will cause you to lose information, which will likely result in loss of power. Also, I would rarely standardise variables before doing regression, al | Data preparation for regression
Binning your data is usually a bad idea because it will cause you to lose information, which will likely result in loss of power. Also, I would rarely standardise variables before doing regression, although some people may like to.
A really good book to read, if you can get it, is "Regre... | Data preparation for regression
Binning your data is usually a bad idea because it will cause you to lose information, which will likely result in loss of power. Also, I would rarely standardise variables before doing regression, al |
35,564 | Data preparation for regression | For preprocessing I always like to include outlier detection, and removing bad data. If your data is of different scales, normalizing the data is a good idea (standardization). As far as technique goes, it always pays to graph and plot all of your variables with each other, as well as with the predicted variable. Th... | Data preparation for regression | For preprocessing I always like to include outlier detection, and removing bad data. If your data is of different scales, normalizing the data is a good idea (standardization). As far as technique g | Data preparation for regression
For preprocessing I always like to include outlier detection, and removing bad data. If your data is of different scales, normalizing the data is a good idea (standardization). As far as technique goes, it always pays to graph and plot all of your variables with each other, as well as ... | Data preparation for regression
For preprocessing I always like to include outlier detection, and removing bad data. If your data is of different scales, normalizing the data is a good idea (standardization). As far as technique g |
35,565 | How to visualize the true dimensionality of the data? | A standard approach would be to do PCA and then show a scree plot, which you ought to be able to get that out of any software you might choose. A little tinkering and you could make it more interpretable for your particular audience if necessary. Sometimes they can be convincing, but often they're ambiguous and there'a... | How to visualize the true dimensionality of the data? | A standard approach would be to do PCA and then show a scree plot, which you ought to be able to get that out of any software you might choose. A little tinkering and you could make it more interpreta | How to visualize the true dimensionality of the data?
A standard approach would be to do PCA and then show a scree plot, which you ought to be able to get that out of any software you might choose. A little tinkering and you could make it more interpretable for your particular audience if necessary. Sometimes they can ... | How to visualize the true dimensionality of the data?
A standard approach would be to do PCA and then show a scree plot, which you ought to be able to get that out of any software you might choose. A little tinkering and you could make it more interpreta |
35,566 | How to visualize the true dimensionality of the data? | One way to visualize this would be as follows:
Perform a PCA on the data.
Let $V$ be the vector space spanned by the first two principal component vectors, and let $V^\top$ be the complement.
Decompose each vector $x_i$ in your data set as the sum of an element in $V$ plus a remainder term (which is in $V^\top$). Wri... | How to visualize the true dimensionality of the data? | One way to visualize this would be as follows:
Perform a PCA on the data.
Let $V$ be the vector space spanned by the first two principal component vectors, and let $V^\top$ be the complement.
Decomp | How to visualize the true dimensionality of the data?
One way to visualize this would be as follows:
Perform a PCA on the data.
Let $V$ be the vector space spanned by the first two principal component vectors, and let $V^\top$ be the complement.
Decompose each vector $x_i$ in your data set as the sum of an element in... | How to visualize the true dimensionality of the data?
One way to visualize this would be as follows:
Perform a PCA on the data.
Let $V$ be the vector space spanned by the first two principal component vectors, and let $V^\top$ be the complement.
Decomp |
35,567 | How to visualize the true dimensionality of the data? | I've done similar using PROC Varclus in SAS. The basic idea is to generate a 4 cluster solution, pick the highest correlated variable with each cluster, and then to demonstrate that this 4 cluster solution explains more of the variation than the two cluster solution. For the 2 cluster solution you could use either Va... | How to visualize the true dimensionality of the data? | I've done similar using PROC Varclus in SAS. The basic idea is to generate a 4 cluster solution, pick the highest correlated variable with each cluster, and then to demonstrate that this 4 cluster so | How to visualize the true dimensionality of the data?
I've done similar using PROC Varclus in SAS. The basic idea is to generate a 4 cluster solution, pick the highest correlated variable with each cluster, and then to demonstrate that this 4 cluster solution explains more of the variation than the two cluster solutio... | How to visualize the true dimensionality of the data?
I've done similar using PROC Varclus in SAS. The basic idea is to generate a 4 cluster solution, pick the highest correlated variable with each cluster, and then to demonstrate that this 4 cluster so |
35,568 | Which one should be applied first: data sampling or dimensionality reduction? | Generally, you want your training and validation data sets be separate as much as possible. Ideally, the validation set data would have been obtained only after the model has been trained. If you perform dimensionality reduction before splitting your data to separate sets, you break this isolation between the training ... | Which one should be applied first: data sampling or dimensionality reduction? | Generally, you want your training and validation data sets be separate as much as possible. Ideally, the validation set data would have been obtained only after the model has been trained. If you perf | Which one should be applied first: data sampling or dimensionality reduction?
Generally, you want your training and validation data sets be separate as much as possible. Ideally, the validation set data would have been obtained only after the model has been trained. If you perform dimensionality reduction before splitt... | Which one should be applied first: data sampling or dimensionality reduction?
Generally, you want your training and validation data sets be separate as much as possible. Ideally, the validation set data would have been obtained only after the model has been trained. If you perf |
35,569 | Which one should be applied first: data sampling or dimensionality reduction? | Do the dimensionality reduction first: Your error in estimating the principal components will be smaller due to the larger sample (your Corr/Cov-matrix used in PCA has to be estimated!).
The other way around only makes sense for computational reasons. | Which one should be applied first: data sampling or dimensionality reduction? | Do the dimensionality reduction first: Your error in estimating the principal components will be smaller due to the larger sample (your Corr/Cov-matrix used in PCA has to be estimated!).
The other way | Which one should be applied first: data sampling or dimensionality reduction?
Do the dimensionality reduction first: Your error in estimating the principal components will be smaller due to the larger sample (your Corr/Cov-matrix used in PCA has to be estimated!).
The other way around only makes sense for computational... | Which one should be applied first: data sampling or dimensionality reduction?
Do the dimensionality reduction first: Your error in estimating the principal components will be smaller due to the larger sample (your Corr/Cov-matrix used in PCA has to be estimated!).
The other way |
35,570 | Which one should be applied first: data sampling or dimensionality reduction? | Devil's advocate: I could imagine the principal components differing depending on who's sampled. I'd think this validity issue would take precedence over the precision issue Richard points out. | Which one should be applied first: data sampling or dimensionality reduction? | Devil's advocate: I could imagine the principal components differing depending on who's sampled. I'd think this validity issue would take precedence over the precision issue Richard points out. | Which one should be applied first: data sampling or dimensionality reduction?
Devil's advocate: I could imagine the principal components differing depending on who's sampled. I'd think this validity issue would take precedence over the precision issue Richard points out. | Which one should be applied first: data sampling or dimensionality reduction?
Devil's advocate: I could imagine the principal components differing depending on who's sampled. I'd think this validity issue would take precedence over the precision issue Richard points out. |
35,571 | Which one should be applied first: data sampling or dimensionality reduction? | You should perform sampling and dimensionality reduction in combination.
The best way to do this is undersample the majority class, and run a decision tree. It is the best variable selector you can imagine.
Perform this a number of times (each time another sample). The result will be a number of list of candidate pre... | Which one should be applied first: data sampling or dimensionality reduction? | You should perform sampling and dimensionality reduction in combination.
The best way to do this is undersample the majority class, and run a decision tree. It is the best variable selector you can i | Which one should be applied first: data sampling or dimensionality reduction?
You should perform sampling and dimensionality reduction in combination.
The best way to do this is undersample the majority class, and run a decision tree. It is the best variable selector you can imagine.
Perform this a number of times (ea... | Which one should be applied first: data sampling or dimensionality reduction?
You should perform sampling and dimensionality reduction in combination.
The best way to do this is undersample the majority class, and run a decision tree. It is the best variable selector you can i |
35,572 | Proving that the squares of normal rv's is Chi-square distributed | We have $X_1\sim N(\mu_1,\sigma^2)$ and $X_2\sim N(\mu_2,\sigma^2)$, hence
$$EY_1=E(-X_1/\sqrt{2}+X_2/\sqrt{2})=-1/\sqrt{2}EX_1+1/\sqrt{2}EX_2=0$$
\begin{align*}
EY_1^2&=E(-X_1/\sqrt{2}+X_2/\sqrt{2})^2\\\\
&=E(X_1/\sqrt{2})^2-2E(X_1X_2/2)+E(X_2/\sqrt{2})^2\\\\
&=1/2\sigma^2+1/2\sigma^2=\sigma^2
\end{align*}
Hence $Y_1... | Proving that the squares of normal rv's is Chi-square distributed | We have $X_1\sim N(\mu_1,\sigma^2)$ and $X_2\sim N(\mu_2,\sigma^2)$, hence
$$EY_1=E(-X_1/\sqrt{2}+X_2/\sqrt{2})=-1/\sqrt{2}EX_1+1/\sqrt{2}EX_2=0$$
\begin{align*}
EY_1^2&=E(-X_1/\sqrt{2}+X_2/\sqrt{2}) | Proving that the squares of normal rv's is Chi-square distributed
We have $X_1\sim N(\mu_1,\sigma^2)$ and $X_2\sim N(\mu_2,\sigma^2)$, hence
$$EY_1=E(-X_1/\sqrt{2}+X_2/\sqrt{2})=-1/\sqrt{2}EX_1+1/\sqrt{2}EX_2=0$$
\begin{align*}
EY_1^2&=E(-X_1/\sqrt{2}+X_2/\sqrt{2})^2\\\\
&=E(X_1/\sqrt{2})^2-2E(X_1X_2/2)+E(X_2/\sqrt{2}... | Proving that the squares of normal rv's is Chi-square distributed
We have $X_1\sim N(\mu_1,\sigma^2)$ and $X_2\sim N(\mu_2,\sigma^2)$, hence
$$EY_1=E(-X_1/\sqrt{2}+X_2/\sqrt{2})=-1/\sqrt{2}EX_1+1/\sqrt{2}EX_2=0$$
\begin{align*}
EY_1^2&=E(-X_1/\sqrt{2}+X_2/\sqrt{2}) |
35,573 | Proving that the squares of normal rv's is Chi-square distributed | I want to offer a solution in the view of matrix algebra.
Let
$$ U' = \left[\begin{matrix}
-1/\sqrt{2} && 1/\sqrt{2} && 0 \\
-1/\sqrt{3} && -1/\sqrt{3} && 1/\sqrt{3} \\
1/\sqrt{6} && 1/\sqrt{6} && 2/\sqrt{6}
\end{matrix}\right]$$
As $Y = U'X$,
$$E(Y) = E(U'X) = U' \cdot 0 = 0$$
$$Var(Y) = U' Var(X) U = \sigma^2 U' U =... | Proving that the squares of normal rv's is Chi-square distributed | I want to offer a solution in the view of matrix algebra.
Let
$$ U' = \left[\begin{matrix}
-1/\sqrt{2} && 1/\sqrt{2} && 0 \\
-1/\sqrt{3} && -1/\sqrt{3} && 1/\sqrt{3} \\
1/\sqrt{6} && 1/\sqrt{6} && 2/\ | Proving that the squares of normal rv's is Chi-square distributed
I want to offer a solution in the view of matrix algebra.
Let
$$ U' = \left[\begin{matrix}
-1/\sqrt{2} && 1/\sqrt{2} && 0 \\
-1/\sqrt{3} && -1/\sqrt{3} && 1/\sqrt{3} \\
1/\sqrt{6} && 1/\sqrt{6} && 2/\sqrt{6}
\end{matrix}\right]$$
As $Y = U'X$,
$$E(Y) = ... | Proving that the squares of normal rv's is Chi-square distributed
I want to offer a solution in the view of matrix algebra.
Let
$$ U' = \left[\begin{matrix}
-1/\sqrt{2} && 1/\sqrt{2} && 0 \\
-1/\sqrt{3} && -1/\sqrt{3} && 1/\sqrt{3} \\
1/\sqrt{6} && 1/\sqrt{6} && 2/\ |
35,574 | Proving that the squares of normal rv's is Chi-square distributed | Have you tried simply multiplying out the squared Y^2's in terms of the X[1:3] terms. I suspect that when you are all done that you will see that you simply have: (1/2 +1/3 +1/6)* X1^2 + (1/2 +1/3 +1/6)*X2^2 + (1/2 +1/3 +1/6)*X3^2 . This, of course, assumes that X1X3=X3X1, i.e. that your random variable algebra is comm... | Proving that the squares of normal rv's is Chi-square distributed | Have you tried simply multiplying out the squared Y^2's in terms of the X[1:3] terms. I suspect that when you are all done that you will see that you simply have: (1/2 +1/3 +1/6)* X1^2 + (1/2 +1/3 +1/ | Proving that the squares of normal rv's is Chi-square distributed
Have you tried simply multiplying out the squared Y^2's in terms of the X[1:3] terms. I suspect that when you are all done that you will see that you simply have: (1/2 +1/3 +1/6)* X1^2 + (1/2 +1/3 +1/6)*X2^2 + (1/2 +1/3 +1/6)*X3^2 . This, of course, assu... | Proving that the squares of normal rv's is Chi-square distributed
Have you tried simply multiplying out the squared Y^2's in terms of the X[1:3] terms. I suspect that when you are all done that you will see that you simply have: (1/2 +1/3 +1/6)* X1^2 + (1/2 +1/3 +1/ |
35,575 | Problems with libRblas.so on ubuntu with rpy2 [closed] | It looks like you tried to do things locally but didn't quite get there. I happen to maintain the Debian packages of R (which get rebuilt for Ubuntu and are accessible at CRAN. These builds use external BLAS. rpy2 then builds just fine as well.
I would recommend that you read the README, try to install r-base-core and... | Problems with libRblas.so on ubuntu with rpy2 [closed] | It looks like you tried to do things locally but didn't quite get there. I happen to maintain the Debian packages of R (which get rebuilt for Ubuntu and are accessible at CRAN. These builds use extern | Problems with libRblas.so on ubuntu with rpy2 [closed]
It looks like you tried to do things locally but didn't quite get there. I happen to maintain the Debian packages of R (which get rebuilt for Ubuntu and are accessible at CRAN. These builds use external BLAS. rpy2 then builds just fine as well.
I would recommend t... | Problems with libRblas.so on ubuntu with rpy2 [closed]
It looks like you tried to do things locally but didn't quite get there. I happen to maintain the Debian packages of R (which get rebuilt for Ubuntu and are accessible at CRAN. These builds use extern |
35,576 | Problems with libRblas.so on ubuntu with rpy2 [closed] | For others running into this issue, I was able to solve it by making sure to add the R libraries to my library path in bashrc:
export LD_LIBRARY_PATH="R-install-location/lib65/R/lib:$LD_LIBRARY_PATH" | Problems with libRblas.so on ubuntu with rpy2 [closed] | For others running into this issue, I was able to solve it by making sure to add the R libraries to my library path in bashrc:
export LD_LIBRARY_PATH="R-install-location/lib65/R/lib:$LD_LIBRARY_PATH" | Problems with libRblas.so on ubuntu with rpy2 [closed]
For others running into this issue, I was able to solve it by making sure to add the R libraries to my library path in bashrc:
export LD_LIBRARY_PATH="R-install-location/lib65/R/lib:$LD_LIBRARY_PATH" | Problems with libRblas.so on ubuntu with rpy2 [closed]
For others running into this issue, I was able to solve it by making sure to add the R libraries to my library path in bashrc:
export LD_LIBRARY_PATH="R-install-location/lib65/R/lib:$LD_LIBRARY_PATH" |
35,577 | Why "supremum", not "maximum" in Kolmogorov-Smirnov test? | Suppose a difference is an increasing continuous function on open interval and zero everywhere else. Then the maximum will not exist, but supremum will. | Why "supremum", not "maximum" in Kolmogorov-Smirnov test? | Suppose a difference is an increasing continuous function on open interval and zero everywhere else. Then the maximum will not exist, but supremum will. | Why "supremum", not "maximum" in Kolmogorov-Smirnov test?
Suppose a difference is an increasing continuous function on open interval and zero everywhere else. Then the maximum will not exist, but supremum will. | Why "supremum", not "maximum" in Kolmogorov-Smirnov test?
Suppose a difference is an increasing continuous function on open interval and zero everywhere else. Then the maximum will not exist, but supremum will. |
35,578 | Yates' continuity correction in confidence interval returned by prop.test | The help page indicates that "Continuity correction is used only if it does not exceed the difference between sample and null proportions in absolute value." This is what line 5 is checking: x/n is the empirical proportion, p is the null proportion. (Actually, I find the "if" slightly misleading since it's more of a "i... | Yates' continuity correction in confidence interval returned by prop.test | The help page indicates that "Continuity correction is used only if it does not exceed the difference between sample and null proportions in absolute value." This is what line 5 is checking: x/n is th | Yates' continuity correction in confidence interval returned by prop.test
The help page indicates that "Continuity correction is used only if it does not exceed the difference between sample and null proportions in absolute value." This is what line 5 is checking: x/n is the empirical proportion, p is the null proporti... | Yates' continuity correction in confidence interval returned by prop.test
The help page indicates that "Continuity correction is used only if it does not exceed the difference between sample and null proportions in absolute value." This is what line 5 is checking: x/n is th |
35,579 | Yates' continuity correction in confidence interval returned by prop.test | On the second question of where you can find more info on this continuity correction (attributed to Yates in the help for prop.test but not in the refs below, I think as Yates orginally proposed a continuity correction only to the chi-squared test for contingency tables):
Newcombe RG. Two-sided confidence intervals fo... | Yates' continuity correction in confidence interval returned by prop.test | On the second question of where you can find more info on this continuity correction (attributed to Yates in the help for prop.test but not in the refs below, I think as Yates orginally proposed a con | Yates' continuity correction in confidence interval returned by prop.test
On the second question of where you can find more info on this continuity correction (attributed to Yates in the help for prop.test but not in the refs below, I think as Yates orginally proposed a continuity correction only to the chi-squared tes... | Yates' continuity correction in confidence interval returned by prop.test
On the second question of where you can find more info on this continuity correction (attributed to Yates in the help for prop.test but not in the refs below, I think as Yates orginally proposed a con |
35,580 | Seeking a distribution, perhaps uncommon, consistent with two data points and expert constraints? | If, given an answer to my comment above, you wish to bound the range of the distribution, why not simply fit a Beta distribution where you rescale to the unit interval? In other words, if you know that the parameter of interest should fall between $[2 , 8]$, then why not define $Y = \frac{X - 5}{6} + \frac{1}{2} = \fr... | Seeking a distribution, perhaps uncommon, consistent with two data points and expert constraints? | If, given an answer to my comment above, you wish to bound the range of the distribution, why not simply fit a Beta distribution where you rescale to the unit interval? In other words, if you know th | Seeking a distribution, perhaps uncommon, consistent with two data points and expert constraints?
If, given an answer to my comment above, you wish to bound the range of the distribution, why not simply fit a Beta distribution where you rescale to the unit interval? In other words, if you know that the parameter of in... | Seeking a distribution, perhaps uncommon, consistent with two data points and expert constraints?
If, given an answer to my comment above, you wish to bound the range of the distribution, why not simply fit a Beta distribution where you rescale to the unit interval? In other words, if you know th |
35,581 | Seeking a distribution, perhaps uncommon, consistent with two data points and expert constraints? | What about the Kumaraswamy distribution, which has the following pdf:
$$
f(x; a,b) = a b x^{a-1}{ (1-x^a)}^{b-1}
$$
for $a>0$, $b>0$, $0 < x < 1$. This distribution can be rescaled to have the required support. | Seeking a distribution, perhaps uncommon, consistent with two data points and expert constraints? | What about the Kumaraswamy distribution, which has the following pdf:
$$
f(x; a,b) = a b x^{a-1}{ (1-x^a)}^{b-1}
$$
for $a>0$, $b>0$, $0 < x < 1$. This distribution can be rescaled to have the req | Seeking a distribution, perhaps uncommon, consistent with two data points and expert constraints?
What about the Kumaraswamy distribution, which has the following pdf:
$$
f(x; a,b) = a b x^{a-1}{ (1-x^a)}^{b-1}
$$
for $a>0$, $b>0$, $0 < x < 1$. This distribution can be rescaled to have the required support. | Seeking a distribution, perhaps uncommon, consistent with two data points and expert constraints?
What about the Kumaraswamy distribution, which has the following pdf:
$$
f(x; a,b) = a b x^{a-1}{ (1-x^a)}^{b-1}
$$
for $a>0$, $b>0$, $0 < x < 1$. This distribution can be rescaled to have the req |
35,582 | Seeking a distribution, perhaps uncommon, consistent with two data points and expert constraints? | Since the log-normal distribution has two parameters, you can't satisfactorily fit it to three constraints that don't naturally fit it. With extreme quantiles of 2.5 and 7.5, the mode is ~4, and there is not much you can do about it. Since the scale of the errors for a and b is much smaller than for c, one of them will... | Seeking a distribution, perhaps uncommon, consistent with two data points and expert constraints? | Since the log-normal distribution has two parameters, you can't satisfactorily fit it to three constraints that don't naturally fit it. With extreme quantiles of 2.5 and 7.5, the mode is ~4, and there | Seeking a distribution, perhaps uncommon, consistent with two data points and expert constraints?
Since the log-normal distribution has two parameters, you can't satisfactorily fit it to three constraints that don't naturally fit it. With extreme quantiles of 2.5 and 7.5, the mode is ~4, and there is not much you can d... | Seeking a distribution, perhaps uncommon, consistent with two data points and expert constraints?
Since the log-normal distribution has two parameters, you can't satisfactorily fit it to three constraints that don't naturally fit it. With extreme quantiles of 2.5 and 7.5, the mode is ~4, and there |
35,583 | Seeking a distribution, perhaps uncommon, consistent with two data points and expert constraints? | You could also try the triangular distribution. To fit this, you basically specify a lower bound (this would be X=2), an upper bound (this would be X=8), and a "most likely" value. The wikepedia page http://en.wikipedia.org/wiki/Triangular_distribution has more info on this distribution. If there is not much faith i... | Seeking a distribution, perhaps uncommon, consistent with two data points and expert constraints? | You could also try the triangular distribution. To fit this, you basically specify a lower bound (this would be X=2), an upper bound (this would be X=8), and a "most likely" value. The wikepedia pag | Seeking a distribution, perhaps uncommon, consistent with two data points and expert constraints?
You could also try the triangular distribution. To fit this, you basically specify a lower bound (this would be X=2), an upper bound (this would be X=8), and a "most likely" value. The wikepedia page http://en.wikipedia.... | Seeking a distribution, perhaps uncommon, consistent with two data points and expert constraints?
You could also try the triangular distribution. To fit this, you basically specify a lower bound (this would be X=2), an upper bound (this would be X=8), and a "most likely" value. The wikepedia pag |
35,584 | How to compute the steady state gain from the transfer function of a discrete time system? | The "mechanical" result of just plugging in $z = 1$ into the transfer response is essentially a product of two facts. The steady-state gain is (usually, I believe) defined as the (magnitude of the) limiting response as $t \to \infty$ of the system to a unit-step input.
The so-called final-value theorem states that, if ... | How to compute the steady state gain from the transfer function of a discrete time system? | The "mechanical" result of just plugging in $z = 1$ into the transfer response is essentially a product of two facts. The steady-state gain is (usually, I believe) defined as the (magnitude of the) li | How to compute the steady state gain from the transfer function of a discrete time system?
The "mechanical" result of just plugging in $z = 1$ into the transfer response is essentially a product of two facts. The steady-state gain is (usually, I believe) defined as the (magnitude of the) limiting response as $t \to \in... | How to compute the steady state gain from the transfer function of a discrete time system?
The "mechanical" result of just plugging in $z = 1$ into the transfer response is essentially a product of two facts. The steady-state gain is (usually, I believe) defined as the (magnitude of the) li |
35,585 | How to compute the steady state gain from the transfer function of a discrete time system? | I asked this question at another stack exchange site. It's fairly simple:
Steady state gain is the gain the systems has when DC is applied to it, which has a frequency of f=0 or omega = 0
The variable z in the z-transform is defined as z = r * exp(j*omega). Set omega to 0 and you have z = r
r = 1 because to get the f... | How to compute the steady state gain from the transfer function of a discrete time system? | I asked this question at another stack exchange site. It's fairly simple:
Steady state gain is the gain the systems has when DC is applied to it, which has a frequency of f=0 or omega = 0
The variab | How to compute the steady state gain from the transfer function of a discrete time system?
I asked this question at another stack exchange site. It's fairly simple:
Steady state gain is the gain the systems has when DC is applied to it, which has a frequency of f=0 or omega = 0
The variable z in the z-transform is de... | How to compute the steady state gain from the transfer function of a discrete time system?
I asked this question at another stack exchange site. It's fairly simple:
Steady state gain is the gain the systems has when DC is applied to it, which has a frequency of f=0 or omega = 0
The variab |
35,586 | How to compute the steady state gain from the transfer function of a discrete time system? | The term Steady state gain comes up when your input function is the unit step function $u(t)=1$. If your input is the unit step function, then the gain is the system's value at steady state, $t= \infty$. The steady state value is also called the final value.
The Final Value Theorem lets you calculate this steady state ... | How to compute the steady state gain from the transfer function of a discrete time system? | The term Steady state gain comes up when your input function is the unit step function $u(t)=1$. If your input is the unit step function, then the gain is the system's value at steady state, $t= \inft | How to compute the steady state gain from the transfer function of a discrete time system?
The term Steady state gain comes up when your input function is the unit step function $u(t)=1$. If your input is the unit step function, then the gain is the system's value at steady state, $t= \infty$. The steady state value is... | How to compute the steady state gain from the transfer function of a discrete time system?
The term Steady state gain comes up when your input function is the unit step function $u(t)=1$. If your input is the unit step function, then the gain is the system's value at steady state, $t= \inft |
35,587 | How to compute the steady state gain from the transfer function of a discrete time system? | find steady state gain of transfer function H(s), we let s=0.
since z=exp(sT), to find steady state gain of H(z), let z=exp(0)=1. | How to compute the steady state gain from the transfer function of a discrete time system? | find steady state gain of transfer function H(s), we let s=0.
since z=exp(sT), to find steady state gain of H(z), let z=exp(0)=1. | How to compute the steady state gain from the transfer function of a discrete time system?
find steady state gain of transfer function H(s), we let s=0.
since z=exp(sT), to find steady state gain of H(z), let z=exp(0)=1. | How to compute the steady state gain from the transfer function of a discrete time system?
find steady state gain of transfer function H(s), we let s=0.
since z=exp(sT), to find steady state gain of H(z), let z=exp(0)=1. |
35,588 | Subsetting a data-frame in R based on dates [closed] | ok timeseries seem to have done the trick:
aets <- as.xts(read.zoo("n8_energy_actual2009_2010.csv", header=TRUE, sep=",", FUN=as.POSIXct))
eats.2010 <- aets["2010-01::2010-10"] | Subsetting a data-frame in R based on dates [closed] | ok timeseries seem to have done the trick:
aets <- as.xts(read.zoo("n8_energy_actual2009_2010.csv", header=TRUE, sep=",", FUN=as.POSIXct))
eats.2010 <- aets["2010-01::2010-10"] | Subsetting a data-frame in R based on dates [closed]
ok timeseries seem to have done the trick:
aets <- as.xts(read.zoo("n8_energy_actual2009_2010.csv", header=TRUE, sep=",", FUN=as.POSIXct))
eats.2010 <- aets["2010-01::2010-10"] | Subsetting a data-frame in R based on dates [closed]
ok timeseries seem to have done the trick:
aets <- as.xts(read.zoo("n8_energy_actual2009_2010.csv", header=TRUE, sep=",", FUN=as.POSIXct))
eats.2010 <- aets["2010-01::2010-10"] |
35,589 | Subsetting a data-frame in R based on dates [closed] | A few points:
I'm not sure why that's happening. Clearly the POSIXlt slots are wrong. I typically use POSIXct unless I absolutely need to adjust the slots.
One option is to use the dates directly rather than messing with the slots, and say <= and >= to subset. Something like ae[ae$date >= as.POSIXlt("2009-10-01") &... | Subsetting a data-frame in R based on dates [closed] | A few points:
I'm not sure why that's happening. Clearly the POSIXlt slots are wrong. I typically use POSIXct unless I absolutely need to adjust the slots.
One option is to use the dates directly r | Subsetting a data-frame in R based on dates [closed]
A few points:
I'm not sure why that's happening. Clearly the POSIXlt slots are wrong. I typically use POSIXct unless I absolutely need to adjust the slots.
One option is to use the dates directly rather than messing with the slots, and say <= and >= to subset. So... | Subsetting a data-frame in R based on dates [closed]
A few points:
I'm not sure why that's happening. Clearly the POSIXlt slots are wrong. I typically use POSIXct unless I absolutely need to adjust the slots.
One option is to use the dates directly r |
35,590 | Statistical test for difference between two odds ratios? | Assuming the odds ratios are independent, you can proceed as you would in general with any estimate, only you have to look at the log odds.
Take the difference of the log odds, $\delta$. The standard error of $\delta$ is $\sqrt{SE_{1}^2 + SE_{2}^2}$. Then you can obtain a p-value for the ratio $z = \delta/SE(\delta)$... | Statistical test for difference between two odds ratios? | Assuming the odds ratios are independent, you can proceed as you would in general with any estimate, only you have to look at the log odds.
Take the difference of the log odds, $\delta$. The standard | Statistical test for difference between two odds ratios?
Assuming the odds ratios are independent, you can proceed as you would in general with any estimate, only you have to look at the log odds.
Take the difference of the log odds, $\delta$. The standard error of $\delta$ is $\sqrt{SE_{1}^2 + SE_{2}^2}$. Then you c... | Statistical test for difference between two odds ratios?
Assuming the odds ratios are independent, you can proceed as you would in general with any estimate, only you have to look at the log odds.
Take the difference of the log odds, $\delta$. The standard |
35,591 | Statistical test for difference between two odds ratios? | If you have the 95% CIs for all of your odds ratios, you can do a quick check for statistical difference by looking for overlap in the odds ratios. If 95% CI's for two OR overlap, they aren't significantly different. | Statistical test for difference between two odds ratios? | If you have the 95% CIs for all of your odds ratios, you can do a quick check for statistical difference by looking for overlap in the odds ratios. If 95% CI's for two OR overlap, they aren't signific | Statistical test for difference between two odds ratios?
If you have the 95% CIs for all of your odds ratios, you can do a quick check for statistical difference by looking for overlap in the odds ratios. If 95% CI's for two OR overlap, they aren't significantly different. | Statistical test for difference between two odds ratios?
If you have the 95% CIs for all of your odds ratios, you can do a quick check for statistical difference by looking for overlap in the odds ratios. If 95% CI's for two OR overlap, they aren't signific |
35,592 | Difference between Spline and Piecewise Regression | Here are some of the differences
Piecewise regression yields continuous functions which are not, generally, differentiable and hence not smooth.
Regression with splines yields smooth continuous functions. The degree of smoothness will depend on what kind of spline you use, but cubic splines are differentiable at leas... | Difference between Spline and Piecewise Regression | Here are some of the differences
Piecewise regression yields continuous functions which are not, generally, differentiable and hence not smooth.
Regression with splines yields smooth continuous funct | Difference between Spline and Piecewise Regression
Here are some of the differences
Piecewise regression yields continuous functions which are not, generally, differentiable and hence not smooth.
Regression with splines yields smooth continuous functions. The degree of smoothness will depend on what kind of spline yo... | Difference between Spline and Piecewise Regression
Here are some of the differences
Piecewise regression yields continuous functions which are not, generally, differentiable and hence not smooth.
Regression with splines yields smooth continuous funct |
35,593 | Non negative least square on some coefficient | Your approach with the extra parameters will be problematic as multiple values for the coefficients will provide a same solution (the solution won't be unique).
Non-negative least squares regression is often solved by an active set method that updates in steps the active constraints (see for instance How do Lawson and ... | Non negative least square on some coefficient | Your approach with the extra parameters will be problematic as multiple values for the coefficients will provide a same solution (the solution won't be unique).
Non-negative least squares regression i | Non negative least square on some coefficient
Your approach with the extra parameters will be problematic as multiple values for the coefficients will provide a same solution (the solution won't be unique).
Non-negative least squares regression is often solved by an active set method that updates in steps the active co... | Non negative least square on some coefficient
Your approach with the extra parameters will be problematic as multiple values for the coefficients will provide a same solution (the solution won't be unique).
Non-negative least squares regression i |
35,594 | Non negative least square on some coefficient | Here is an example of multiple linear regression in which some of the variables are unbounded while others are bounded. I'm going to have ten unbounded parameters and ten non-negative parameters in this example. The quick gist is to use scipy.optimize.Bounds in an optimizer that supports this argument such as 'trust-co... | Non negative least square on some coefficient | Here is an example of multiple linear regression in which some of the variables are unbounded while others are bounded. I'm going to have ten unbounded parameters and ten non-negative parameters in th | Non negative least square on some coefficient
Here is an example of multiple linear regression in which some of the variables are unbounded while others are bounded. I'm going to have ten unbounded parameters and ten non-negative parameters in this example. The quick gist is to use scipy.optimize.Bounds in an optimizer... | Non negative least square on some coefficient
Here is an example of multiple linear regression in which some of the variables are unbounded while others are bounded. I'm going to have ten unbounded parameters and ten non-negative parameters in th |
35,595 | Non negative least square on some coefficient | The brute force approach would be using constrained minimization, applying the non-negativity constraints only to certain variables - along the lines of the python implementation provided in an answer to How to include constraint to Scipy NNLS function solution so that it sums to 1.
Another trick is variable transforma... | Non negative least square on some coefficient | The brute force approach would be using constrained minimization, applying the non-negativity constraints only to certain variables - along the lines of the python implementation provided in an answer | Non negative least square on some coefficient
The brute force approach would be using constrained minimization, applying the non-negativity constraints only to certain variables - along the lines of the python implementation provided in an answer to How to include constraint to Scipy NNLS function solution so that it s... | Non negative least square on some coefficient
The brute force approach would be using constrained minimization, applying the non-negativity constraints only to certain variables - along the lines of the python implementation provided in an answer |
35,596 | Lasso regression Mathematical intuition | You have three different questions. Let's tackle them in a somewhat different order. I'll refer to ISLR 2nd edition.
First off, here are the two different formulations of the lasso:
$$ \text{minimize } ||\mathbf{y}-\mathbf{X}\mathbf{\beta}||_2+\lambda||\mathbf{\beta}||_1\text{ with respect to }\mathbf{\beta}\text{ for ... | Lasso regression Mathematical intuition | You have three different questions. Let's tackle them in a somewhat different order. I'll refer to ISLR 2nd edition.
First off, here are the two different formulations of the lasso:
$$ \text{minimize | Lasso regression Mathematical intuition
You have three different questions. Let's tackle them in a somewhat different order. I'll refer to ISLR 2nd edition.
First off, here are the two different formulations of the lasso:
$$ \text{minimize } ||\mathbf{y}-\mathbf{X}\mathbf{\beta}||_2+\lambda||\mathbf{\beta}||_1\text{ wi... | Lasso regression Mathematical intuition
You have three different questions. Let's tackle them in a somewhat different order. I'll refer to ISLR 2nd edition.
First off, here are the two different formulations of the lasso:
$$ \text{minimize |
35,597 | Lasso regression Mathematical intuition | The other answer here covers the specific transformation issues you have asked about, so I'll focus solely on the intuition of the LASSO regression. One useful way to look at LASSO regression is that it is equivalent to Bayesian maximum-posterior (MAP) estimation when you use an IID Laplace prior for the coefficient v... | Lasso regression Mathematical intuition | The other answer here covers the specific transformation issues you have asked about, so I'll focus solely on the intuition of the LASSO regression. One useful way to look at LASSO regression is that | Lasso regression Mathematical intuition
The other answer here covers the specific transformation issues you have asked about, so I'll focus solely on the intuition of the LASSO regression. One useful way to look at LASSO regression is that it is equivalent to Bayesian maximum-posterior (MAP) estimation when you use an... | Lasso regression Mathematical intuition
The other answer here covers the specific transformation issues you have asked about, so I'll focus solely on the intuition of the LASSO regression. One useful way to look at LASSO regression is that |
35,598 | Regression model for integer response | As an alternative we would try using a Skellam distribution as our response distribution. (i.e. our outcome variable is the difference between two Poisson-distributed random variables). It is sometimes used to predict football/rugby goal difference. Do note though that maybe more straightforward to just have to Poisson... | Regression model for integer response | As an alternative we would try using a Skellam distribution as our response distribution. (i.e. our outcome variable is the difference between two Poisson-distributed random variables). It is sometime | Regression model for integer response
As an alternative we would try using a Skellam distribution as our response distribution. (i.e. our outcome variable is the difference between two Poisson-distributed random variables). It is sometimes used to predict football/rugby goal difference. Do note though that maybe more s... | Regression model for integer response
As an alternative we would try using a Skellam distribution as our response distribution. (i.e. our outcome variable is the difference between two Poisson-distributed random variables). It is sometime |
35,599 | Regression model for integer response | Ideally, you would use a regression model with a discrete distribution with support over the integers for your response variable. This could be approximated by a continuous distribution, so long as the standard error in the model (i.e., the standard deviation of the error term) is not too small compared to the unit in... | Regression model for integer response | Ideally, you would use a regression model with a discrete distribution with support over the integers for your response variable. This could be approximated by a continuous distribution, so long as t | Regression model for integer response
Ideally, you would use a regression model with a discrete distribution with support over the integers for your response variable. This could be approximated by a continuous distribution, so long as the standard error in the model (i.e., the standard deviation of the error term) is... | Regression model for integer response
Ideally, you would use a regression model with a discrete distribution with support over the integers for your response variable. This could be approximated by a continuous distribution, so long as t |
35,600 | Null hypothesis stated as "there is an effect" | You are, perhaps, thinking about a 'negativist' null hypothesis of the general form $\text{H}_{0}^{-}\text{: }|\theta|\ge \Delta$, with $\text{H}_{\text{A}}^{-}\text{: }|\theta|< \Delta$, as used in tests for equivalence, and where $\Delta$ is the smallest effect size that you care about a priori to the test. (As expre... | Null hypothesis stated as "there is an effect" | You are, perhaps, thinking about a 'negativist' null hypothesis of the general form $\text{H}_{0}^{-}\text{: }|\theta|\ge \Delta$, with $\text{H}_{\text{A}}^{-}\text{: }|\theta|< \Delta$, as used in t | Null hypothesis stated as "there is an effect"
You are, perhaps, thinking about a 'negativist' null hypothesis of the general form $\text{H}_{0}^{-}\text{: }|\theta|\ge \Delta$, with $\text{H}_{\text{A}}^{-}\text{: }|\theta|< \Delta$, as used in tests for equivalence, and where $\Delta$ is the smallest effect size that... | Null hypothesis stated as "there is an effect"
You are, perhaps, thinking about a 'negativist' null hypothesis of the general form $\text{H}_{0}^{-}\text{: }|\theta|\ge \Delta$, with $\text{H}_{\text{A}}^{-}\text{: }|\theta|< \Delta$, as used in t |
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