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 |
|---|---|---|---|---|---|---|
40,301 | What is the probability mass function of the scaled Poisson distribution? | To avoid confusion, use subscripts to denote the corresponding random variable.
Let $y\in\{0,c,2c,\ldots\}$ and observe that when $c\ne 0$,
$$p_Y(y) = p_X\left(\{x\mid cx=y\}\right) = p_X\left(\{y/c\}\right) = e^{-\lambda}\frac{\lambda^{y/c}}{(y/c)!}.$$
When $c=0$ the only possible value of $y$ is $0$ and
$$p_Y(0) = ... | What is the probability mass function of the scaled Poisson distribution? | To avoid confusion, use subscripts to denote the corresponding random variable.
Let $y\in\{0,c,2c,\ldots\}$ and observe that when $c\ne 0$,
$$p_Y(y) = p_X\left(\{x\mid cx=y\}\right) = p_X\left(\{y/c\ | What is the probability mass function of the scaled Poisson distribution?
To avoid confusion, use subscripts to denote the corresponding random variable.
Let $y\in\{0,c,2c,\ldots\}$ and observe that when $c\ne 0$,
$$p_Y(y) = p_X\left(\{x\mid cx=y\}\right) = p_X\left(\{y/c\}\right) = e^{-\lambda}\frac{\lambda^{y/c}}{(y... | What is the probability mass function of the scaled Poisson distribution?
To avoid confusion, use subscripts to denote the corresponding random variable.
Let $y\in\{0,c,2c,\ldots\}$ and observe that when $c\ne 0$,
$$p_Y(y) = p_X\left(\{x\mid cx=y\}\right) = p_X\left(\{y/c\ |
40,302 | Non-Parametric altervative to one sample t-test | The 4 doesn't pose any problem. Just subtract 4 from every observation and you can test $\mu=0$ on the shifted data.
There are two common nonparametric tests of location which might be relevant to you -- the Wilcoxon signed rank test and the sign test.
The signed rank test is a test for the pseudo-median. When accompan... | Non-Parametric altervative to one sample t-test | The 4 doesn't pose any problem. Just subtract 4 from every observation and you can test $\mu=0$ on the shifted data.
There are two common nonparametric tests of location which might be relevant to you | Non-Parametric altervative to one sample t-test
The 4 doesn't pose any problem. Just subtract 4 from every observation and you can test $\mu=0$ on the shifted data.
There are two common nonparametric tests of location which might be relevant to you -- the Wilcoxon signed rank test and the sign test.
The signed rank tes... | Non-Parametric altervative to one sample t-test
The 4 doesn't pose any problem. Just subtract 4 from every observation and you can test $\mu=0$ on the shifted data.
There are two common nonparametric tests of location which might be relevant to you |
40,303 | Non-Parametric altervative to one sample t-test | How large is your sample? Normality of the data is not required for testing the sample mean if the sample size is large enough. A common cutoff given to students is $n=30$.
Alternatively, you could use the Wilcoxon Signed-Rank test, but for one sample that's actually testing the median.
Finally, the bootstrap might wor... | Non-Parametric altervative to one sample t-test | How large is your sample? Normality of the data is not required for testing the sample mean if the sample size is large enough. A common cutoff given to students is $n=30$.
Alternatively, you could us | Non-Parametric altervative to one sample t-test
How large is your sample? Normality of the data is not required for testing the sample mean if the sample size is large enough. A common cutoff given to students is $n=30$.
Alternatively, you could use the Wilcoxon Signed-Rank test, but for one sample that's actually test... | Non-Parametric altervative to one sample t-test
How large is your sample? Normality of the data is not required for testing the sample mean if the sample size is large enough. A common cutoff given to students is $n=30$.
Alternatively, you could us |
40,304 | Maximum of a probability vector distributed as a Dirichlet variate | I am not sure there is a closed-form solution for the distribution of
$p_{(k)}$ when
$(p_1,\ldots,p_k)\sim\text{Dir}(\alpha_1,\ldots,\alpha_k)$ and the
$\alpha_i$'s are different. At least, it seems to be the case when following the natural derivation of the density of $p_{(k)}$.
Indeed, if we start with the Ga... | Maximum of a probability vector distributed as a Dirichlet variate | I am not sure there is a closed-form solution for the distribution of
$p_{(k)}$ when
$(p_1,\ldots,p_k)\sim\text{Dir}(\alpha_1,\ldots,\alpha_k)$ and the
$\alpha_i$'s are different. At least, it | Maximum of a probability vector distributed as a Dirichlet variate
I am not sure there is a closed-form solution for the distribution of
$p_{(k)}$ when
$(p_1,\ldots,p_k)\sim\text{Dir}(\alpha_1,\ldots,\alpha_k)$ and the
$\alpha_i$'s are different. At least, it seems to be the case when following the natural deriv... | Maximum of a probability vector distributed as a Dirichlet variate
I am not sure there is a closed-form solution for the distribution of
$p_{(k)}$ when
$(p_1,\ldots,p_k)\sim\text{Dir}(\alpha_1,\ldots,\alpha_k)$ and the
$\alpha_i$'s are different. At least, it |
40,305 | Intuition behind regression sum of squares | Just a bit of a misunderstanding with the definitions, I believe:
\begin{align}
\text{SST}_{\text{otal}} &= \color{red}{\text{SSE}_{\text{xplained}}}+\color{blue}{\text{SSR}_{\text{esidual}}}\\
\end{align}
or, equivalently,
\begin{align}
\sum(y_i-\bar y)^2 &=\color{red}{\sum(\hat y_i-\bar y)^2}+\color{blue}{\sum(y_i-\h... | Intuition behind regression sum of squares | Just a bit of a misunderstanding with the definitions, I believe:
\begin{align}
\text{SST}_{\text{otal}} &= \color{red}{\text{SSE}_{\text{xplained}}}+\color{blue}{\text{SSR}_{\text{esidual}}}\\
\end{a | Intuition behind regression sum of squares
Just a bit of a misunderstanding with the definitions, I believe:
\begin{align}
\text{SST}_{\text{otal}} &= \color{red}{\text{SSE}_{\text{xplained}}}+\color{blue}{\text{SSR}_{\text{esidual}}}\\
\end{align}
or, equivalently,
\begin{align}
\sum(y_i-\bar y)^2 &=\color{red}{\sum(\... | Intuition behind regression sum of squares
Just a bit of a misunderstanding with the definitions, I believe:
\begin{align}
\text{SST}_{\text{otal}} &= \color{red}{\text{SSE}_{\text{xplained}}}+\color{blue}{\text{SSR}_{\text{esidual}}}\\
\end{a |
40,306 | Intuition behind regression sum of squares | why do we want a big difference between ŷ and ȳ?
maybe the graphs A, B, C, and D can be intuitively useful by visualizing the differences or distances between the
1. systolic blood pressure of each person from the mean systolic blood pressure(y-ȳ),
2. between the systolic blood pressure of each person from the regres... | Intuition behind regression sum of squares | why do we want a big difference between ŷ and ȳ?
maybe the graphs A, B, C, and D can be intuitively useful by visualizing the differences or distances between the
1. systolic blood pressure of each p | Intuition behind regression sum of squares
why do we want a big difference between ŷ and ȳ?
maybe the graphs A, B, C, and D can be intuitively useful by visualizing the differences or distances between the
1. systolic blood pressure of each person from the mean systolic blood pressure(y-ȳ),
2. between the systolic bl... | Intuition behind regression sum of squares
why do we want a big difference between ŷ and ȳ?
maybe the graphs A, B, C, and D can be intuitively useful by visualizing the differences or distances between the
1. systolic blood pressure of each p |
40,307 | Intuition behind regression sum of squares | This is the note I wrote for self studying purpose. I don't have much time to improve this due to lack of my English ability. But I guess this would be helpful. So I just paste this here. I will add some details later.
linear models
We can come up with several linear models with error $\vec \epsilon$
$\vec y=\vec \e... | Intuition behind regression sum of squares | This is the note I wrote for self studying purpose. I don't have much time to improve this due to lack of my English ability. But I guess this would be helpful. So I just paste this here. I will add s | Intuition behind regression sum of squares
This is the note I wrote for self studying purpose. I don't have much time to improve this due to lack of my English ability. But I guess this would be helpful. So I just paste this here. I will add some details later.
linear models
We can come up with several linear models w... | Intuition behind regression sum of squares
This is the note I wrote for self studying purpose. I don't have much time to improve this due to lack of my English ability. But I guess this would be helpful. So I just paste this here. I will add s |
40,308 | How, in practice, are spatial covariances determined? | To expand on my comment, commonly "spatial covariance" is associated with Gaussian Processes, which are typically assumed to be stationary. Furthermore, in practice the spatial covariance function (kernel) is assumed to be non-negative and decay with distance. The standard setup is then to assume that your spatial (sam... | How, in practice, are spatial covariances determined? | To expand on my comment, commonly "spatial covariance" is associated with Gaussian Processes, which are typically assumed to be stationary. Furthermore, in practice the spatial covariance function (ke | How, in practice, are spatial covariances determined?
To expand on my comment, commonly "spatial covariance" is associated with Gaussian Processes, which are typically assumed to be stationary. Furthermore, in practice the spatial covariance function (kernel) is assumed to be non-negative and decay with distance. The s... | How, in practice, are spatial covariances determined?
To expand on my comment, commonly "spatial covariance" is associated with Gaussian Processes, which are typically assumed to be stationary. Furthermore, in practice the spatial covariance function (ke |
40,309 | How caret calculates R Squared | The code is here:
> R2
function(pred, obs, formula = "corr", na.rm = FALSE) {
n <- sum(complete.cases(pred))
switch(formula,
corr = cor(obs, pred, use = ifelse(na.rm, "complete.obs", "everything"))^2,
traditional = 1 - (sum((obs-pred)^2, na.rm = na.rm)/((n-1)*var(obs, na.rm = na.rm))))
... | How caret calculates R Squared | The code is here:
> R2
function(pred, obs, formula = "corr", na.rm = FALSE) {
n <- sum(complete.cases(pred))
switch(formula,
corr = cor(obs, pred, use = ifelse(na.rm, "complete.obs | How caret calculates R Squared
The code is here:
> R2
function(pred, obs, formula = "corr", na.rm = FALSE) {
n <- sum(complete.cases(pred))
switch(formula,
corr = cor(obs, pred, use = ifelse(na.rm, "complete.obs", "everything"))^2,
traditional = 1 - (sum((obs-pred)^2, na.rm = na.rm)/((n-1... | How caret calculates R Squared
The code is here:
> R2
function(pred, obs, formula = "corr", na.rm = FALSE) {
n <- sum(complete.cases(pred))
switch(formula,
corr = cor(obs, pred, use = ifelse(na.rm, "complete.obs |
40,310 | How caret calculates R Squared | Update: The R2 function is deprecated.
You can get R2 by the postResample function now.
The code is here and shows in line 136 and 142 the formula:
resamplCor <- try(cor(pred, obs, use = "pairwise.complete.obs"), silent = TRUE
...
out <- c(sqrt(mse), resamplCor^2, mae)
So postResample uses the squared correlation to ... | How caret calculates R Squared | Update: The R2 function is deprecated.
You can get R2 by the postResample function now.
The code is here and shows in line 136 and 142 the formula:
resamplCor <- try(cor(pred, obs, use = "pairwise.co | How caret calculates R Squared
Update: The R2 function is deprecated.
You can get R2 by the postResample function now.
The code is here and shows in line 136 and 142 the formula:
resamplCor <- try(cor(pred, obs, use = "pairwise.complete.obs"), silent = TRUE
...
out <- c(sqrt(mse), resamplCor^2, mae)
So postResample u... | How caret calculates R Squared
Update: The R2 function is deprecated.
You can get R2 by the postResample function now.
The code is here and shows in line 136 and 142 the formula:
resamplCor <- try(cor(pred, obs, use = "pairwise.co |
40,311 | Where does the number 12 come from and why is it the same 12 in Wilcoxon and Kruskal Wallis? | In both cases 12 appears when approximating the distribution of the test statistic with a normal and chi-square respectively because the statistic must first be written in a standardized form (if you were performing a permutation test these constants would be unnecessary). With continuous data, the ranks from $1$ to $n... | Where does the number 12 come from and why is it the same 12 in Wilcoxon and Kruskal Wallis? | In both cases 12 appears when approximating the distribution of the test statistic with a normal and chi-square respectively because the statistic must first be written in a standardized form (if you | Where does the number 12 come from and why is it the same 12 in Wilcoxon and Kruskal Wallis?
In both cases 12 appears when approximating the distribution of the test statistic with a normal and chi-square respectively because the statistic must first be written in a standardized form (if you were performing a permutati... | Where does the number 12 come from and why is it the same 12 in Wilcoxon and Kruskal Wallis?
In both cases 12 appears when approximating the distribution of the test statistic with a normal and chi-square respectively because the statistic must first be written in a standardized form (if you |
40,312 | multiple imputation and propensity scores | My understanding is that you should generate individual propensity score models for each data set, then match, then estimate outcomes, then combine the estimates into one.
1) Match() in Matching accepts a user's own propensity score (include it as the X parameter in the call to Match(). matchit() in MatchIt does the sa... | multiple imputation and propensity scores | My understanding is that you should generate individual propensity score models for each data set, then match, then estimate outcomes, then combine the estimates into one.
1) Match() in Matching accep | multiple imputation and propensity scores
My understanding is that you should generate individual propensity score models for each data set, then match, then estimate outcomes, then combine the estimates into one.
1) Match() in Matching accepts a user's own propensity score (include it as the X parameter in the call to... | multiple imputation and propensity scores
My understanding is that you should generate individual propensity score models for each data set, then match, then estimate outcomes, then combine the estimates into one.
1) Match() in Matching accep |
40,313 | multiple imputation and propensity scores | As I previously stated, instead of doing propensity matching it can be reasonable to use inverse probability of treatment weighting after missing data imputation.
Suitable Stata examples follow:
clear all
webuse mheart5
*dataset
replace smokes = . in 20/70
*creates missing values for smokes variable in observations 2... | multiple imputation and propensity scores | As I previously stated, instead of doing propensity matching it can be reasonable to use inverse probability of treatment weighting after missing data imputation.
Suitable Stata examples follow:
clear | multiple imputation and propensity scores
As I previously stated, instead of doing propensity matching it can be reasonable to use inverse probability of treatment weighting after missing data imputation.
Suitable Stata examples follow:
clear all
webuse mheart5
*dataset
replace smokes = . in 20/70
*creates missing va... | multiple imputation and propensity scores
As I previously stated, instead of doing propensity matching it can be reasonable to use inverse probability of treatment weighting after missing data imputation.
Suitable Stata examples follow:
clear |
40,314 | Fourier terms to model seasonality in ARIMA models | It appears to me that this approach is sufficiently intuitive that many people must have looked at it, but I can't locate a useful reference in my bib file, either. Searching for "Fourier ARIMA" or similar at the International Journal of Forecasting (IJF) does not yield anything very useful. Ludlow & Enders (2000, IJF)... | Fourier terms to model seasonality in ARIMA models | It appears to me that this approach is sufficiently intuitive that many people must have looked at it, but I can't locate a useful reference in my bib file, either. Searching for "Fourier ARIMA" or si | Fourier terms to model seasonality in ARIMA models
It appears to me that this approach is sufficiently intuitive that many people must have looked at it, but I can't locate a useful reference in my bib file, either. Searching for "Fourier ARIMA" or similar at the International Journal of Forecasting (IJF) does not yiel... | Fourier terms to model seasonality in ARIMA models
It appears to me that this approach is sufficiently intuitive that many people must have looked at it, but I can't locate a useful reference in my bib file, either. Searching for "Fourier ARIMA" or si |
40,315 | Fourier terms to model seasonality in ARIMA models | Maybe you can look this https://medium.com/intive-developers/forecasting-time-series-with-multiple-seasonalities-using-tbats-in-python-398a00ac0e8a
This article compared tbats and SARIMAX with Fourier Terms .
The answer to your question :
SARIMAX with Fourier Terms One can apply a trick [4] to utilize
exogenous var... | Fourier terms to model seasonality in ARIMA models | Maybe you can look this https://medium.com/intive-developers/forecasting-time-series-with-multiple-seasonalities-using-tbats-in-python-398a00ac0e8a
This article compared tbats and SARIMAX with Fourier | Fourier terms to model seasonality in ARIMA models
Maybe you can look this https://medium.com/intive-developers/forecasting-time-series-with-multiple-seasonalities-using-tbats-in-python-398a00ac0e8a
This article compared tbats and SARIMAX with Fourier Terms .
The answer to your question :
SARIMAX with Fourier Terms O... | Fourier terms to model seasonality in ARIMA models
Maybe you can look this https://medium.com/intive-developers/forecasting-time-series-with-multiple-seasonalities-using-tbats-in-python-398a00ac0e8a
This article compared tbats and SARIMAX with Fourier |
40,316 | Probabilistic classification and loss functions | The "probability loss" function has sometimes been called the "linear score" in the literature. Although it looks appealing, this loss function is improper, which means that it does not set the incentive to forecast the true probability that $y_i = 1$. For details, see p. 366 of Gneiting and Raftery ("Strictly Proper S... | Probabilistic classification and loss functions | The "probability loss" function has sometimes been called the "linear score" in the literature. Although it looks appealing, this loss function is improper, which means that it does not set the incent | Probabilistic classification and loss functions
The "probability loss" function has sometimes been called the "linear score" in the literature. Although it looks appealing, this loss function is improper, which means that it does not set the incentive to forecast the true probability that $y_i = 1$. For details, see p.... | Probabilistic classification and loss functions
The "probability loss" function has sometimes been called the "linear score" in the literature. Although it looks appealing, this loss function is improper, which means that it does not set the incent |
40,317 | Is AUC via CV a good procedure for selecting optimal model? | The concordance probability ($c$-index; ROC area) is not sensitive enough to be used to compare two models let alone a whole series of models. It rewards extreme predictions that are right too little because it uses only the ranks of the predictions, not their absolute values. Classification accuracy is even worse, b... | Is AUC via CV a good procedure for selecting optimal model? | The concordance probability ($c$-index; ROC area) is not sensitive enough to be used to compare two models let alone a whole series of models. It rewards extreme predictions that are right too little | Is AUC via CV a good procedure for selecting optimal model?
The concordance probability ($c$-index; ROC area) is not sensitive enough to be used to compare two models let alone a whole series of models. It rewards extreme predictions that are right too little because it uses only the ranks of the predictions, not thei... | Is AUC via CV a good procedure for selecting optimal model?
The concordance probability ($c$-index; ROC area) is not sensitive enough to be used to compare two models let alone a whole series of models. It rewards extreme predictions that are right too little |
40,318 | Is there a method to plot the output of a random forest in R? | There are many packages that implement randomForest. Party is one of them that supports plotting
First build a forest:
library("party")
cf <- cforest(Species~., data=iris)
Then extract a tree and build a binary tree that can be plotted:
pt <- prettytree(cf@ensemble[[1]], names(cf@data@get("input")))
nt <- new("Binary... | Is there a method to plot the output of a random forest in R? | There are many packages that implement randomForest. Party is one of them that supports plotting
First build a forest:
library("party")
cf <- cforest(Species~., data=iris)
Then extract a tree and bui | Is there a method to plot the output of a random forest in R?
There are many packages that implement randomForest. Party is one of them that supports plotting
First build a forest:
library("party")
cf <- cforest(Species~., data=iris)
Then extract a tree and build a binary tree that can be plotted:
pt <- prettytree(cf@... | Is there a method to plot the output of a random forest in R?
There are many packages that implement randomForest. Party is one of them that supports plotting
First build a forest:
library("party")
cf <- cforest(Species~., data=iris)
Then extract a tree and bui |
40,319 | Combining multiple variables into one "score" | Taking your example literally, I'd say the approach is problematic from the outset.
If the problem is assessing the total burden, then absolute numbers of deaths and people living with AIDS are key variables, but any PCA is likely to be dominated by a small number of countries with large populations. Even if you use ... | Combining multiple variables into one "score" | Taking your example literally, I'd say the approach is problematic from the outset.
If the problem is assessing the total burden, then absolute numbers of deaths and people living with AIDS are key | Combining multiple variables into one "score"
Taking your example literally, I'd say the approach is problematic from the outset.
If the problem is assessing the total burden, then absolute numbers of deaths and people living with AIDS are key variables, but any PCA is likely to be dominated by a small number of coun... | Combining multiple variables into one "score"
Taking your example literally, I'd say the approach is problematic from the outset.
If the problem is assessing the total burden, then absolute numbers of deaths and people living with AIDS are key |
40,320 | Combining multiple variables into one "score" | Suggest an exploratory factor analysis. Rather than assume the dimensionality behind your HIV measures, take one half of the sample randomly, extract 4 factors, by almost any method, and plot the eigenvalues. Use the scree test or just use the "eigenvalues greater than one thumb rule": Rotate to simple structure via ... | Combining multiple variables into one "score" | Suggest an exploratory factor analysis. Rather than assume the dimensionality behind your HIV measures, take one half of the sample randomly, extract 4 factors, by almost any method, and plot the eig | Combining multiple variables into one "score"
Suggest an exploratory factor analysis. Rather than assume the dimensionality behind your HIV measures, take one half of the sample randomly, extract 4 factors, by almost any method, and plot the eigenvalues. Use the scree test or just use the "eigenvalues greater than one... | Combining multiple variables into one "score"
Suggest an exploratory factor analysis. Rather than assume the dimensionality behind your HIV measures, take one half of the sample randomly, extract 4 factors, by almost any method, and plot the eig |
40,321 | Markov chain,transition matrix and jordan form | The result is easy to prove by induction once it has been shown to you, so let's focus on how to find these powers on your own. The point of the Jordan Normal Form of a square matrix is clearly revealed by its geometrical interpretation. Each of its blocks, of dimensions $k\times k$, corresponds to a subspace on whic... | Markov chain,transition matrix and jordan form | The result is easy to prove by induction once it has been shown to you, so let's focus on how to find these powers on your own. The point of the Jordan Normal Form of a square matrix is clearly revea | Markov chain,transition matrix and jordan form
The result is easy to prove by induction once it has been shown to you, so let's focus on how to find these powers on your own. The point of the Jordan Normal Form of a square matrix is clearly revealed by its geometrical interpretation. Each of its blocks, of dimensions... | Markov chain,transition matrix and jordan form
The result is easy to prove by induction once it has been shown to you, so let's focus on how to find these powers on your own. The point of the Jordan Normal Form of a square matrix is clearly revea |
40,322 | Feature selection using RFE in SVM kernel (other than linear eg rbf, poly etc) | To use RFE, it is a must to have a supervised learning estimator which attribute coef_ is available, this is the case of the linear kernel. The error you are getting is because coef_ is not for SVM using kernels different from Linear. It is in RFE documentation
A walk-around solution is presented in Feature selection f... | Feature selection using RFE in SVM kernel (other than linear eg rbf, poly etc) | To use RFE, it is a must to have a supervised learning estimator which attribute coef_ is available, this is the case of the linear kernel. The error you are getting is because coef_ is not for SVM us | Feature selection using RFE in SVM kernel (other than linear eg rbf, poly etc)
To use RFE, it is a must to have a supervised learning estimator which attribute coef_ is available, this is the case of the linear kernel. The error you are getting is because coef_ is not for SVM using kernels different from Linear. It is ... | Feature selection using RFE in SVM kernel (other than linear eg rbf, poly etc)
To use RFE, it is a must to have a supervised learning estimator which attribute coef_ is available, this is the case of the linear kernel. The error you are getting is because coef_ is not for SVM us |
40,323 | Is this Simpson's Paradox on the Titanic data set? | Although Simpson's paradox (or Simpson's reversal) is more often referred in 3-way contingency tables than in correlation between continuous variables, it's the same phenomenon.
Here, the explanation in simple words seems clear: Although inside each class there is a slight tendency of decreasing fares with age, people ... | Is this Simpson's Paradox on the Titanic data set? | Although Simpson's paradox (or Simpson's reversal) is more often referred in 3-way contingency tables than in correlation between continuous variables, it's the same phenomenon.
Here, the explanation | Is this Simpson's Paradox on the Titanic data set?
Although Simpson's paradox (or Simpson's reversal) is more often referred in 3-way contingency tables than in correlation between continuous variables, it's the same phenomenon.
Here, the explanation in simple words seems clear: Although inside each class there is a sl... | Is this Simpson's Paradox on the Titanic data set?
Although Simpson's paradox (or Simpson's reversal) is more often referred in 3-way contingency tables than in correlation between continuous variables, it's the same phenomenon.
Here, the explanation |
40,324 | Weak first stage in 2SLS | To test for weak instruments you would test the joint significance of your instruments' coefficients via an F-test. The typical rule of thumb is that an F-statistic of more than 10 is fine (see Stock and Yogo, 2002), however, this is not a theorem and people may still give you a hard time if your test statistic is clos... | Weak first stage in 2SLS | To test for weak instruments you would test the joint significance of your instruments' coefficients via an F-test. The typical rule of thumb is that an F-statistic of more than 10 is fine (see Stock | Weak first stage in 2SLS
To test for weak instruments you would test the joint significance of your instruments' coefficients via an F-test. The typical rule of thumb is that an F-statistic of more than 10 is fine (see Stock and Yogo, 2002), however, this is not a theorem and people may still give you a hard time if yo... | Weak first stage in 2SLS
To test for weak instruments you would test the joint significance of your instruments' coefficients via an F-test. The typical rule of thumb is that an F-statistic of more than 10 is fine (see Stock |
40,325 | Weak first stage in 2SLS | Since you have only one instrument and one treatment, you can use the Anderson-Rubin (AR) confidence interval by inverting the AR test.
The AR test is uniformly most powerful unbiased in this setting, and it has correct coverage rates regardless of the strength of the instrument. This review might be useful.
This and ... | Weak first stage in 2SLS | Since you have only one instrument and one treatment, you can use the Anderson-Rubin (AR) confidence interval by inverting the AR test.
The AR test is uniformly most powerful unbiased in this setting | Weak first stage in 2SLS
Since you have only one instrument and one treatment, you can use the Anderson-Rubin (AR) confidence interval by inverting the AR test.
The AR test is uniformly most powerful unbiased in this setting, and it has correct coverage rates regardless of the strength of the instrument. This review m... | Weak first stage in 2SLS
Since you have only one instrument and one treatment, you can use the Anderson-Rubin (AR) confidence interval by inverting the AR test.
The AR test is uniformly most powerful unbiased in this setting |
40,326 | Interpretation of correlogram | On the y axis is the autocorrelation. The x axis tells you the lag. So, if x=1 we are looking at the correlation of December with November, November with October, etc. If x=2, we have a lag of 2 and we are looking at the correlation of December with October, November with September, etc.
In the first graph, there are... | Interpretation of correlogram | On the y axis is the autocorrelation. The x axis tells you the lag. So, if x=1 we are looking at the correlation of December with November, November with October, etc. If x=2, we have a lag of 2 and | Interpretation of correlogram
On the y axis is the autocorrelation. The x axis tells you the lag. So, if x=1 we are looking at the correlation of December with November, November with October, etc. If x=2, we have a lag of 2 and we are looking at the correlation of December with October, November with September, etc.... | Interpretation of correlogram
On the y axis is the autocorrelation. The x axis tells you the lag. So, if x=1 we are looking at the correlation of December with November, November with October, etc. If x=2, we have a lag of 2 and |
40,327 | Bernstein's inequality for heavy-tailed random variables | Yes, see Theorem 6.21 of [LT13], Michel Ledoux and Michel Talagrand. Probability in Banach Spaces: isoperimetry and processes, volume 23. Springer Science & Business Media, 2013.
For simplicity you may also look at section 8 of my paper.
http://arxiv.org/pdf/1507.06370v2.pdf
(I just summarized those theorems -- the pu... | Bernstein's inequality for heavy-tailed random variables | Yes, see Theorem 6.21 of [LT13], Michel Ledoux and Michel Talagrand. Probability in Banach Spaces: isoperimetry and processes, volume 23. Springer Science & Business Media, 2013.
For simplicity you ma | Bernstein's inequality for heavy-tailed random variables
Yes, see Theorem 6.21 of [LT13], Michel Ledoux and Michel Talagrand. Probability in Banach Spaces: isoperimetry and processes, volume 23. Springer Science & Business Media, 2013.
For simplicity you may also look at section 8 of my paper.
http://arxiv.org/pdf/150... | Bernstein's inequality for heavy-tailed random variables
Yes, see Theorem 6.21 of [LT13], Michel Ledoux and Michel Talagrand. Probability in Banach Spaces: isoperimetry and processes, volume 23. Springer Science & Business Media, 2013.
For simplicity you ma |
40,328 | What happens if I use Z-test instead of T test? | There is little to add to @Glen_b expert and eloquent discussion; rather, there is only room for making concepts less precise with the excuse or intention of appealing to intuition. That being said, here're a couple of plots that helped me come to terms with these concepts:
1. t-Student Distributions have "fatter" tail... | What happens if I use Z-test instead of T test? | There is little to add to @Glen_b expert and eloquent discussion; rather, there is only room for making concepts less precise with the excuse or intention of appealing to intuition. That being said, h | What happens if I use Z-test instead of T test?
There is little to add to @Glen_b expert and eloquent discussion; rather, there is only room for making concepts less precise with the excuse or intention of appealing to intuition. That being said, here're a couple of plots that helped me come to terms with these concept... | What happens if I use Z-test instead of T test?
There is little to add to @Glen_b expert and eloquent discussion; rather, there is only room for making concepts less precise with the excuse or intention of appealing to intuition. That being said, h |
40,329 | What happens if I use Z-test instead of T test? | Because the critical values are smaller with the Z, the rejection region is larger.
So yes, significance level goes up, and consequently the rest of the power curve comes with it, as it does whenever you move the significance level. | What happens if I use Z-test instead of T test? | Because the critical values are smaller with the Z, the rejection region is larger.
So yes, significance level goes up, and consequently the rest of the power curve comes with it, as it does whenever | What happens if I use Z-test instead of T test?
Because the critical values are smaller with the Z, the rejection region is larger.
So yes, significance level goes up, and consequently the rest of the power curve comes with it, as it does whenever you move the significance level. | What happens if I use Z-test instead of T test?
Because the critical values are smaller with the Z, the rejection region is larger.
So yes, significance level goes up, and consequently the rest of the power curve comes with it, as it does whenever |
40,330 | Plotting the results of GLM in R | "I was told the R value was too low compared to the significance of the p value" -- sounds like nonsense to me.
On the other hand, some form of glm may be a good idea (but it looks to me like the spread may be increasing more than you might expect with a quasipoisson).
Note that nothing about the glm changes the sprea... | Plotting the results of GLM in R | "I was told the R value was too low compared to the significance of the p value" -- sounds like nonsense to me.
On the other hand, some form of glm may be a good idea (but it looks to me like the spr | Plotting the results of GLM in R
"I was told the R value was too low compared to the significance of the p value" -- sounds like nonsense to me.
On the other hand, some form of glm may be a good idea (but it looks to me like the spread may be increasing more than you might expect with a quasipoisson).
Note that nothin... | Plotting the results of GLM in R
"I was told the R value was too low compared to the significance of the p value" -- sounds like nonsense to me.
On the other hand, some form of glm may be a good idea (but it looks to me like the spr |
40,331 | Understanding Bagged Logistic Regression (and a Python Implementation) | Bagging is an ensemble method where you train model on independent samples of the training data and combine (average, vote, ...) their predictions. This generally produces more accurate predictions than the individual models. Technically bagging means that the samples are drawn with replacement and of the same size as ... | Understanding Bagged Logistic Regression (and a Python Implementation) | Bagging is an ensemble method where you train model on independent samples of the training data and combine (average, vote, ...) their predictions. This generally produces more accurate predictions th | Understanding Bagged Logistic Regression (and a Python Implementation)
Bagging is an ensemble method where you train model on independent samples of the training data and combine (average, vote, ...) their predictions. This generally produces more accurate predictions than the individual models. Technically bagging mea... | Understanding Bagged Logistic Regression (and a Python Implementation)
Bagging is an ensemble method where you train model on independent samples of the training data and combine (average, vote, ...) their predictions. This generally produces more accurate predictions th |
40,332 | Implement Fisher Scoring for linear regression | I have fixed the code according to the suggestions by @Randel. Now it works, except $\sigma^2$ takes a very long time to converge.
Here is the code:
fisher.scoring <- function(y, x, start = runif(ncol(x)+1)){
n <- nrow(x)
p <- ncol(x)
theta <- start
score <- rep(0, p+1)
for (i in 1:1000){
# betas
scor... | Implement Fisher Scoring for linear regression | I have fixed the code according to the suggestions by @Randel. Now it works, except $\sigma^2$ takes a very long time to converge.
Here is the code:
fisher.scoring <- function(y, x, start = runif(ncol | Implement Fisher Scoring for linear regression
I have fixed the code according to the suggestions by @Randel. Now it works, except $\sigma^2$ takes a very long time to converge.
Here is the code:
fisher.scoring <- function(y, x, start = runif(ncol(x)+1)){
n <- nrow(x)
p <- ncol(x)
theta <- start
score <- rep(0,... | Implement Fisher Scoring for linear regression
I have fixed the code according to the suggestions by @Randel. Now it works, except $\sigma^2$ takes a very long time to converge.
Here is the code:
fisher.scoring <- function(y, x, start = runif(ncol |
40,333 | Implement Fisher Scoring for linear regression | The short answer is that there is a bug in @guðmundur-einarsson's code.
For each observation, the score function for $\sigma^2$ is $$\frac{\partial L_i}{\partial \sigma^2} = -\frac{1}{2\sigma^{2}}+\frac{1}{2\sigma^{4}}(y_i-X_i\beta)^{'}(y_i-X_i\beta),$$ not $\frac{\partial L_i}{\partial \sigma^2} = -\frac{{\color{red}... | Implement Fisher Scoring for linear regression | The short answer is that there is a bug in @guðmundur-einarsson's code.
For each observation, the score function for $\sigma^2$ is $$\frac{\partial L_i}{\partial \sigma^2} = -\frac{1}{2\sigma^{2}}+\f | Implement Fisher Scoring for linear regression
The short answer is that there is a bug in @guðmundur-einarsson's code.
For each observation, the score function for $\sigma^2$ is $$\frac{\partial L_i}{\partial \sigma^2} = -\frac{1}{2\sigma^{2}}+\frac{1}{2\sigma^{4}}(y_i-X_i\beta)^{'}(y_i-X_i\beta),$$ not $\frac{\partia... | Implement Fisher Scoring for linear regression
The short answer is that there is a bug in @guðmundur-einarsson's code.
For each observation, the score function for $\sigma^2$ is $$\frac{\partial L_i}{\partial \sigma^2} = -\frac{1}{2\sigma^{2}}+\f |
40,334 | SVM why do we maximize 2/||w|| | I assume that you understand that the margin is given by the equation $\langle w,x\rangle+b=\pm k$ where the width of the margin is equal to $2k$ and one has to maximise the width $k$.
Notice that the equation represents a hyperplane with normal vector $w$. Furthermore, if $w$ is a normal vector, then $\lambda w$ ... | SVM why do we maximize 2/||w|| | I assume that you understand that the margin is given by the equation $\langle w,x\rangle+b=\pm k$ where the width of the margin is equal to $2k$ and one has to maximise the width $k$.
Notice that | SVM why do we maximize 2/||w||
I assume that you understand that the margin is given by the equation $\langle w,x\rangle+b=\pm k$ where the width of the margin is equal to $2k$ and one has to maximise the width $k$.
Notice that the equation represents a hyperplane with normal vector $w$. Furthermore, if $w$ is a n... | SVM why do we maximize 2/||w||
I assume that you understand that the margin is given by the equation $\langle w,x\rangle+b=\pm k$ where the width of the margin is equal to $2k$ and one has to maximise the width $k$.
Notice that |
40,335 | Combining Linear Regression and Time Series | Previously I was thinking I would figure out what lags/ARIMA model I should be using (it’s looking like a (2,0,0)) and then apply the AR2 to the residuals (or even the whole of the dependent variable) to produce a new independent variable that I then use in the linear regression. But this doesn’t seem mathematically so... | Combining Linear Regression and Time Series | Previously I was thinking I would figure out what lags/ARIMA model I should be using (it’s looking like a (2,0,0)) and then apply the AR2 to the residuals (or even the whole of the dependent variable) | Combining Linear Regression and Time Series
Previously I was thinking I would figure out what lags/ARIMA model I should be using (it’s looking like a (2,0,0)) and then apply the AR2 to the residuals (or even the whole of the dependent variable) to produce a new independent variable that I then use in the linear regress... | Combining Linear Regression and Time Series
Previously I was thinking I would figure out what lags/ARIMA model I should be using (it’s looking like a (2,0,0)) and then apply the AR2 to the residuals (or even the whole of the dependent variable) |
40,336 | Combining Linear Regression and Time Series | The combination is called Transfer Function modelling . See Cross correlation influenced by self auto correlation for my answer and a very good tutorial from Penn State on model identifviaction. Also look at http://www.autobox.com/cms/index.php/afs-university/intro-to-forecasting/doc_download/24-regression-vs-box-jenki... | Combining Linear Regression and Time Series | The combination is called Transfer Function modelling . See Cross correlation influenced by self auto correlation for my answer and a very good tutorial from Penn State on model identifviaction. Also | Combining Linear Regression and Time Series
The combination is called Transfer Function modelling . See Cross correlation influenced by self auto correlation for my answer and a very good tutorial from Penn State on model identifviaction. Also look at http://www.autobox.com/cms/index.php/afs-university/intro-to-forecas... | Combining Linear Regression and Time Series
The combination is called Transfer Function modelling . See Cross correlation influenced by self auto correlation for my answer and a very good tutorial from Penn State on model identifviaction. Also |
40,337 | How to calculate decision boundary from support vectors? | A binary SVM tries to separate subjects belonging to one of two classes based on some features, the class will be denoted as $y_i \in \{-1,+1\}$ and the features as $x_i$, note the $y_i$ is a single number while $x_i$ is a vector. The index $i$ identifies the subject.
The SVM solves a quadratic programming problem an... | How to calculate decision boundary from support vectors? | A binary SVM tries to separate subjects belonging to one of two classes based on some features, the class will be denoted as $y_i \in \{-1,+1\}$ and the features as $x_i$, note the $y_i$ is a single n | How to calculate decision boundary from support vectors?
A binary SVM tries to separate subjects belonging to one of two classes based on some features, the class will be denoted as $y_i \in \{-1,+1\}$ and the features as $x_i$, note the $y_i$ is a single number while $x_i$ is a vector. The index $i$ identifies the su... | How to calculate decision boundary from support vectors?
A binary SVM tries to separate subjects belonging to one of two classes based on some features, the class will be denoted as $y_i \in \{-1,+1\}$ and the features as $x_i$, note the $y_i$ is a single n |
40,338 | How does linear SVMs function in multi dimensional feature space? | Linear SVM always works in the exact same way, even if you can't mentally wrap your head around the geometrics. Humans are generally bad at reasoning in more than three dimensions, so don't let that worry you.
Imagine linear SVM in one dimension. This would look something like this:
+ + + + + | - - - -
where | is your ... | How does linear SVMs function in multi dimensional feature space? | Linear SVM always works in the exact same way, even if you can't mentally wrap your head around the geometrics. Humans are generally bad at reasoning in more than three dimensions, so don't let that w | How does linear SVMs function in multi dimensional feature space?
Linear SVM always works in the exact same way, even if you can't mentally wrap your head around the geometrics. Humans are generally bad at reasoning in more than three dimensions, so don't let that worry you.
Imagine linear SVM in one dimension. This wo... | How does linear SVMs function in multi dimensional feature space?
Linear SVM always works in the exact same way, even if you can't mentally wrap your head around the geometrics. Humans are generally bad at reasoning in more than three dimensions, so don't let that w |
40,339 | How does linear SVMs function in multi dimensional feature space? | I was even stuck at same question for sometime, then I reffered some of the websites through which I was able yo get the intution.
If you are not able to visualise in mind consider this..
For 1 dimensional dataset a point will be suitable to discriminate between different classes.
Increase a dimension up for a 2 dime... | How does linear SVMs function in multi dimensional feature space? | I was even stuck at same question for sometime, then I reffered some of the websites through which I was able yo get the intution.
If you are not able to visualise in mind consider this..
For 1 dimen | How does linear SVMs function in multi dimensional feature space?
I was even stuck at same question for sometime, then I reffered some of the websites through which I was able yo get the intution.
If you are not able to visualise in mind consider this..
For 1 dimensional dataset a point will be suitable to discriminat... | How does linear SVMs function in multi dimensional feature space?
I was even stuck at same question for sometime, then I reffered some of the websites through which I was able yo get the intution.
If you are not able to visualise in mind consider this..
For 1 dimen |
40,340 | Linear regression: Intercept isn't significant | It is not necessarily a problem that an intercept is not significant(ly different from zero) and indeed that may be scientifically or practically what you expect. But much more can be said.
The estimate of the intercept for any linear regression that includes one will be determined by all the data, especially includin... | Linear regression: Intercept isn't significant | It is not necessarily a problem that an intercept is not significant(ly different from zero) and indeed that may be scientifically or practically what you expect. But much more can be said.
The estim | Linear regression: Intercept isn't significant
It is not necessarily a problem that an intercept is not significant(ly different from zero) and indeed that may be scientifically or practically what you expect. But much more can be said.
The estimate of the intercept for any linear regression that includes one will be ... | Linear regression: Intercept isn't significant
It is not necessarily a problem that an intercept is not significant(ly different from zero) and indeed that may be scientifically or practically what you expect. But much more can be said.
The estim |
40,341 | Linear regression: Intercept isn't significant | I think you understand correctly :)
The intercept isn't significant because there isn't sufficient statistical evidence that it's different from zero. And as you say, it seems reasonable that a Movie not mentioned by anyone would make no money. | Linear regression: Intercept isn't significant | I think you understand correctly :)
The intercept isn't significant because there isn't sufficient statistical evidence that it's different from zero. And as you say, it seems reasonable that a Movie | Linear regression: Intercept isn't significant
I think you understand correctly :)
The intercept isn't significant because there isn't sufficient statistical evidence that it's different from zero. And as you say, it seems reasonable that a Movie not mentioned by anyone would make no money. | Linear regression: Intercept isn't significant
I think you understand correctly :)
The intercept isn't significant because there isn't sufficient statistical evidence that it's different from zero. And as you say, it seems reasonable that a Movie |
40,342 | $\chi^2$ tabulated value | The following say the same thing:
For a given "area to the right of the critical value," called $\alpha$ (Greek "alpha"), the critical value increases with the degrees of freedom, called $\nu$ (Greek "nu").
For a given critical value $c$, $\alpha$ increases with $\nu$.
For any given number $c$, the chance that a $\chi... | $\chi^2$ tabulated value | The following say the same thing:
For a given "area to the right of the critical value," called $\alpha$ (Greek "alpha"), the critical value increases with the degrees of freedom, called $\nu$ (Greek | $\chi^2$ tabulated value
The following say the same thing:
For a given "area to the right of the critical value," called $\alpha$ (Greek "alpha"), the critical value increases with the degrees of freedom, called $\nu$ (Greek "nu").
For a given critical value $c$, $\alpha$ increases with $\nu$.
For any given number $c$... | $\chi^2$ tabulated value
The following say the same thing:
For a given "area to the right of the critical value," called $\alpha$ (Greek "alpha"), the critical value increases with the degrees of freedom, called $\nu$ (Greek |
40,343 | $\chi^2$ tabulated value | Let's recall what a $p$-value is. It is the probability of getting a value as far or further away from a reference / null value as your observed value, if the null hypothesis is true. In your case, you are working with $\chi^2$, so it is the probability of getting an observed $\chi^2$ test statistic as far or further... | $\chi^2$ tabulated value | Let's recall what a $p$-value is. It is the probability of getting a value as far or further away from a reference / null value as your observed value, if the null hypothesis is true. In your case, | $\chi^2$ tabulated value
Let's recall what a $p$-value is. It is the probability of getting a value as far or further away from a reference / null value as your observed value, if the null hypothesis is true. In your case, you are working with $\chi^2$, so it is the probability of getting an observed $\chi^2$ test st... | $\chi^2$ tabulated value
Let's recall what a $p$-value is. It is the probability of getting a value as far or further away from a reference / null value as your observed value, if the null hypothesis is true. In your case, |
40,344 | $\chi^2$ tabulated value | The chi-squared distribution with $n$ degrees of freedom is the sum of the squares of $n$ independent (0,1)-normal distributions. Each summand has positive expected value, so the chi-squared distribution will have larger and larger mean as $n$ increases. In addition, the standard deviation also increases, and the criti... | $\chi^2$ tabulated value | The chi-squared distribution with $n$ degrees of freedom is the sum of the squares of $n$ independent (0,1)-normal distributions. Each summand has positive expected value, so the chi-squared distribut | $\chi^2$ tabulated value
The chi-squared distribution with $n$ degrees of freedom is the sum of the squares of $n$ independent (0,1)-normal distributions. Each summand has positive expected value, so the chi-squared distribution will have larger and larger mean as $n$ increases. In addition, the standard deviation also... | $\chi^2$ tabulated value
The chi-squared distribution with $n$ degrees of freedom is the sum of the squares of $n$ independent (0,1)-normal distributions. Each summand has positive expected value, so the chi-squared distribut |
40,345 | $\chi^2$ tabulated value | I guess the best way of understanding is looking at density plot for different degrees of freedom.
If you run the R code below,
x = seq(0, 25, length.out=100)
plot(x, dchisq(x=x, df=2), type='l', col=2, ylab='density')
for(i in 3:9){
y = dchisq(x=x, df=i)
lines(x, y, col=i)
}
legend('topright', legend=paste('df ... | $\chi^2$ tabulated value | I guess the best way of understanding is looking at density plot for different degrees of freedom.
If you run the R code below,
x = seq(0, 25, length.out=100)
plot(x, dchisq(x=x, df=2), type='l', col | $\chi^2$ tabulated value
I guess the best way of understanding is looking at density plot for different degrees of freedom.
If you run the R code below,
x = seq(0, 25, length.out=100)
plot(x, dchisq(x=x, df=2), type='l', col=2, ylab='density')
for(i in 3:9){
y = dchisq(x=x, df=i)
lines(x, y, col=i)
}
legend('top... | $\chi^2$ tabulated value
I guess the best way of understanding is looking at density plot for different degrees of freedom.
If you run the R code below,
x = seq(0, 25, length.out=100)
plot(x, dchisq(x=x, df=2), type='l', col |
40,346 | How to interpret a two-dimensional contingency table? | In general, there isn't much to a 2-way contingency table, but you are trying to unpack this at such a level of detail that some confusions are arising. Typically, with a simple contingency table like this, people just want to know if the variables (sex and citizen) are independent. To assess that, you can run a chi-... | How to interpret a two-dimensional contingency table? | In general, there isn't much to a 2-way contingency table, but you are trying to unpack this at such a level of detail that some confusions are arising. Typically, with a simple contingency table lik | How to interpret a two-dimensional contingency table?
In general, there isn't much to a 2-way contingency table, but you are trying to unpack this at such a level of detail that some confusions are arising. Typically, with a simple contingency table like this, people just want to know if the variables (sex and citizen... | How to interpret a two-dimensional contingency table?
In general, there isn't much to a 2-way contingency table, but you are trying to unpack this at such a level of detail that some confusions are arising. Typically, with a simple contingency table lik |
40,347 | How to interpret a two-dimensional contingency table? | In addition to @gung's answer, I discovered that mosaic plots are very useful in assessing the relative relationships with categorical data. Once we establish (actually, we assume here) departure from independence, one can use package vcd to graphically display such contingency tables.
A mosaic plot:
mosaic(tab.sex.c... | How to interpret a two-dimensional contingency table? | In addition to @gung's answer, I discovered that mosaic plots are very useful in assessing the relative relationships with categorical data. Once we establish (actually, we assume here) departure from | How to interpret a two-dimensional contingency table?
In addition to @gung's answer, I discovered that mosaic plots are very useful in assessing the relative relationships with categorical data. Once we establish (actually, we assume here) departure from independence, one can use package vcd to graphically display such... | How to interpret a two-dimensional contingency table?
In addition to @gung's answer, I discovered that mosaic plots are very useful in assessing the relative relationships with categorical data. Once we establish (actually, we assume here) departure from |
40,348 | Looking for a distribution where: Mean=0, variance is variable, Skew=0 and kurtosis is variable | There are many possibilities. One possibility is to take a pair of families to cover positive and negative excess kurtosis, and when matching the first four moments the obvious candidates are Pearson-family distributions.
The family of scaled t-distributions have parameters ($\sigma$ and $\nu$) that affect the variance... | Looking for a distribution where: Mean=0, variance is variable, Skew=0 and kurtosis is variable | There are many possibilities. One possibility is to take a pair of families to cover positive and negative excess kurtosis, and when matching the first four moments the obvious candidates are Pearson- | Looking for a distribution where: Mean=0, variance is variable, Skew=0 and kurtosis is variable
There are many possibilities. One possibility is to take a pair of families to cover positive and negative excess kurtosis, and when matching the first four moments the obvious candidates are Pearson-family distributions.
Th... | Looking for a distribution where: Mean=0, variance is variable, Skew=0 and kurtosis is variable
There are many possibilities. One possibility is to take a pair of families to cover positive and negative excess kurtosis, and when matching the first four moments the obvious candidates are Pearson- |
40,349 | Looking for a distribution where: Mean=0, variance is variable, Skew=0 and kurtosis is variable | Have a look at heavy tail Lambert W x F distributions (disclaimer: I am the author).
The random variable $Y \sim Lambert W \times F$ is a heavy-tail version of $X\sim F$, where you control the tails with tail parameter $\delta \geq 0$: for $\delta = 0$, $X = Y$ and thus Lambert W x F is the same as F; and for $\delta \... | Looking for a distribution where: Mean=0, variance is variable, Skew=0 and kurtosis is variable | Have a look at heavy tail Lambert W x F distributions (disclaimer: I am the author).
The random variable $Y \sim Lambert W \times F$ is a heavy-tail version of $X\sim F$, where you control the tails w | Looking for a distribution where: Mean=0, variance is variable, Skew=0 and kurtosis is variable
Have a look at heavy tail Lambert W x F distributions (disclaimer: I am the author).
The random variable $Y \sim Lambert W \times F$ is a heavy-tail version of $X\sim F$, where you control the tails with tail parameter $\del... | Looking for a distribution where: Mean=0, variance is variable, Skew=0 and kurtosis is variable
Have a look at heavy tail Lambert W x F distributions (disclaimer: I am the author).
The random variable $Y \sim Lambert W \times F$ is a heavy-tail version of $X\sim F$, where you control the tails w |
40,350 | What is the intuition behind the sparsity parameter in sparse autoencoders? | An autoencoder attempts to reconstruct the input. During the process it could learn the identity function if the size of the hidden layers is greater than the number of inputs. However that is not desirable.
During learning, the autoencoder discovers the most common features in the input. For example if the input is a ... | What is the intuition behind the sparsity parameter in sparse autoencoders? | An autoencoder attempts to reconstruct the input. During the process it could learn the identity function if the size of the hidden layers is greater than the number of inputs. However that is not des | What is the intuition behind the sparsity parameter in sparse autoencoders?
An autoencoder attempts to reconstruct the input. During the process it could learn the identity function if the size of the hidden layers is greater than the number of inputs. However that is not desirable.
During learning, the autoencoder dis... | What is the intuition behind the sparsity parameter in sparse autoencoders?
An autoencoder attempts to reconstruct the input. During the process it could learn the identity function if the size of the hidden layers is greater than the number of inputs. However that is not des |
40,351 | What is the intuition behind the sparsity parameter in sparse autoencoders? | Autoencoder is a NN-versioned POD
Sparsity results from the assumption "the law behind complexity is simple". And your job is to try to find the most simple one by changing your weights. | What is the intuition behind the sparsity parameter in sparse autoencoders? | Autoencoder is a NN-versioned POD
Sparsity results from the assumption "the law behind complexity is simple". And your job is to try to find the most simple one by changing your weights. | What is the intuition behind the sparsity parameter in sparse autoencoders?
Autoencoder is a NN-versioned POD
Sparsity results from the assumption "the law behind complexity is simple". And your job is to try to find the most simple one by changing your weights. | What is the intuition behind the sparsity parameter in sparse autoencoders?
Autoencoder is a NN-versioned POD
Sparsity results from the assumption "the law behind complexity is simple". And your job is to try to find the most simple one by changing your weights. |
40,352 | cv.glmnet - choose lambda to include specific number of variables | I don't think that your colleague had anything fancy in mind -- fit a glmnet model with cross-validation as you ordinarily would and then examine how many nonzero features you have at each value of $\lambda$. When you have 5 (or however many) nonzero features, that's the value of $\lambda$ to choose.
glmnet even keeps ... | cv.glmnet - choose lambda to include specific number of variables | I don't think that your colleague had anything fancy in mind -- fit a glmnet model with cross-validation as you ordinarily would and then examine how many nonzero features you have at each value of $\ | cv.glmnet - choose lambda to include specific number of variables
I don't think that your colleague had anything fancy in mind -- fit a glmnet model with cross-validation as you ordinarily would and then examine how many nonzero features you have at each value of $\lambda$. When you have 5 (or however many) nonzero fea... | cv.glmnet - choose lambda to include specific number of variables
I don't think that your colleague had anything fancy in mind -- fit a glmnet model with cross-validation as you ordinarily would and then examine how many nonzero features you have at each value of $\ |
40,353 | Word2Vec : Interpretation of Subtraction or addition of vectors | Yes, that's my understanding of their interpretation; that's the reasoning behind why you'd expect (as observed) that [man] - [woman] + [king] ≈ [queen], or [Paris] - [France] + [China] ≈ [Beijing].
The idea is perhaps that vectors are approximately sums of their semantic components, so that [king] includes a "male" co... | Word2Vec : Interpretation of Subtraction or addition of vectors | Yes, that's my understanding of their interpretation; that's the reasoning behind why you'd expect (as observed) that [man] - [woman] + [king] ≈ [queen], or [Paris] - [France] + [China] ≈ [Beijing].
T | Word2Vec : Interpretation of Subtraction or addition of vectors
Yes, that's my understanding of their interpretation; that's the reasoning behind why you'd expect (as observed) that [man] - [woman] + [king] ≈ [queen], or [Paris] - [France] + [China] ≈ [Beijing].
The idea is perhaps that vectors are approximately sums o... | Word2Vec : Interpretation of Subtraction or addition of vectors
Yes, that's my understanding of their interpretation; that's the reasoning behind why you'd expect (as observed) that [man] - [woman] + [king] ≈ [queen], or [Paris] - [France] + [China] ≈ [Beijing].
T |
40,354 | Word2Vec : Interpretation of Subtraction or addition of vectors | Actually there has been some recent theoretical advances in understanding how the addition/subtraction of vectors works. See here:
http://andyljones.tumblr.com/post/111299309808/why-word2vec-works
http://arxiv.org/abs/1502.03520
I would give a summary here - but I don't think I could do any better than Andy in his blo... | Word2Vec : Interpretation of Subtraction or addition of vectors | Actually there has been some recent theoretical advances in understanding how the addition/subtraction of vectors works. See here:
http://andyljones.tumblr.com/post/111299309808/why-word2vec-works
ht | Word2Vec : Interpretation of Subtraction or addition of vectors
Actually there has been some recent theoretical advances in understanding how the addition/subtraction of vectors works. See here:
http://andyljones.tumblr.com/post/111299309808/why-word2vec-works
http://arxiv.org/abs/1502.03520
I would give a summary her... | Word2Vec : Interpretation of Subtraction or addition of vectors
Actually there has been some recent theoretical advances in understanding how the addition/subtraction of vectors works. See here:
http://andyljones.tumblr.com/post/111299309808/why-word2vec-works
ht |
40,355 | If $\operatorname{Var}\left(\epsilon_i\right) = h\left(X\right) \neq \sigma^2$, what can we know about $\operatorname{Var}\left(\hat{\beta}\right)$? | It's an easy derivation to show that the least squares estimator:
$$
\hat{\beta} = \left( \mathbf{X}^T\mathbf{X} \right)^{-1} \mathbf{X}^T Y
$$
has variance:
$$
\mbox{var} \left(\hat{\beta} \right)= \left( \mathbf{X}^T\mathbf{X} \right)^{-1} \mathbf{X}^T \mbox{var} \left(Y\right)\mathbf{X} \left( \mathbf{X}^T\mathbf{... | If $\operatorname{Var}\left(\epsilon_i\right) = h\left(X\right) \neq \sigma^2$, what can we know abo | It's an easy derivation to show that the least squares estimator:
$$
\hat{\beta} = \left( \mathbf{X}^T\mathbf{X} \right)^{-1} \mathbf{X}^T Y
$$
has variance:
$$
\mbox{var} \left(\hat{\beta} \right)= | If $\operatorname{Var}\left(\epsilon_i\right) = h\left(X\right) \neq \sigma^2$, what can we know about $\operatorname{Var}\left(\hat{\beta}\right)$?
It's an easy derivation to show that the least squares estimator:
$$
\hat{\beta} = \left( \mathbf{X}^T\mathbf{X} \right)^{-1} \mathbf{X}^T Y
$$
has variance:
$$
\mbox{var... | If $\operatorname{Var}\left(\epsilon_i\right) = h\left(X\right) \neq \sigma^2$, what can we know abo
It's an easy derivation to show that the least squares estimator:
$$
\hat{\beta} = \left( \mathbf{X}^T\mathbf{X} \right)^{-1} \mathbf{X}^T Y
$$
has variance:
$$
\mbox{var} \left(\hat{\beta} \right)= |
40,356 | Encompassing Tests to compare models in R | If you have two competing linear models with different regressors, say:
m1 <- lm(y ~ x1 + x2, data = ...)
m2 <- lm(y ~ z1 + z2, data = ...)
then the encompassing model is
m12 <- lm(y ~ x1 + x2 + z1 + z2, data = ...)
and the encompassing test compares
anova(m1, m12)
anova(m2, m12)
The "hope" would be that one of the ... | Encompassing Tests to compare models in R | If you have two competing linear models with different regressors, say:
m1 <- lm(y ~ x1 + x2, data = ...)
m2 <- lm(y ~ z1 + z2, data = ...)
then the encompassing model is
m12 <- lm(y ~ x1 + x2 + z1 + | Encompassing Tests to compare models in R
If you have two competing linear models with different regressors, say:
m1 <- lm(y ~ x1 + x2, data = ...)
m2 <- lm(y ~ z1 + z2, data = ...)
then the encompassing model is
m12 <- lm(y ~ x1 + x2 + z1 + z2, data = ...)
and the encompassing test compares
anova(m1, m12)
anova(m2, ... | Encompassing Tests to compare models in R
If you have two competing linear models with different regressors, say:
m1 <- lm(y ~ x1 + x2, data = ...)
m2 <- lm(y ~ z1 + z2, data = ...)
then the encompassing model is
m12 <- lm(y ~ x1 + x2 + z1 + |
40,357 | Encompassing Tests to compare models in R | There are different encompassing tests. I'll give you an example of forecast encompassing test from "A Companion to Economic Forecasting" edited by Michael P. Clements, David F. Hendry, see Eq (14.2) on p.302.
Let's say you have competing forecast $\hat y_{1,t+1}$ and $\hat y_{2,t+1}$, and the actual observations $y_{... | Encompassing Tests to compare models in R | There are different encompassing tests. I'll give you an example of forecast encompassing test from "A Companion to Economic Forecasting" edited by Michael P. Clements, David F. Hendry, see Eq (14.2) | Encompassing Tests to compare models in R
There are different encompassing tests. I'll give you an example of forecast encompassing test from "A Companion to Economic Forecasting" edited by Michael P. Clements, David F. Hendry, see Eq (14.2) on p.302.
Let's say you have competing forecast $\hat y_{1,t+1}$ and $\hat y_... | Encompassing Tests to compare models in R
There are different encompassing tests. I'll give you an example of forecast encompassing test from "A Companion to Economic Forecasting" edited by Michael P. Clements, David F. Hendry, see Eq (14.2) |
40,358 | Speeding up hat matrices like $X(X'X)^{-1}X'$ (projection matrices) and other aspects of custom-built estimator when software runs out of memory | Using QR decomposition (which ought to be available if you already have calculated the regression):
Let $X$ have $n$ rows and $p$ columns and be of full column rank.
$H=X(X'X)^{-1}X'$
$=QR(R'Q'QR)^{-1}R'Q'$
$=QR(R'R)^{-1}R'Q'$
But if $R_1$ is the first $p$ rows of $R$ then $R'R=R_1'R_1$
$=QR(R_1'R_1)^{-1}R'Q'$
Now let ... | Speeding up hat matrices like $X(X'X)^{-1}X'$ (projection matrices) and other aspects of custom-buil | Using QR decomposition (which ought to be available if you already have calculated the regression):
Let $X$ have $n$ rows and $p$ columns and be of full column rank.
$H=X(X'X)^{-1}X'$
$=QR(R'Q'QR)^{-1 | Speeding up hat matrices like $X(X'X)^{-1}X'$ (projection matrices) and other aspects of custom-built estimator when software runs out of memory
Using QR decomposition (which ought to be available if you already have calculated the regression):
Let $X$ have $n$ rows and $p$ columns and be of full column rank.
$H=X(X'X)... | Speeding up hat matrices like $X(X'X)^{-1}X'$ (projection matrices) and other aspects of custom-buil
Using QR decomposition (which ought to be available if you already have calculated the regression):
Let $X$ have $n$ rows and $p$ columns and be of full column rank.
$H=X(X'X)^{-1}X'$
$=QR(R'Q'QR)^{-1 |
40,359 | Speeding up hat matrices like $X(X'X)^{-1}X'$ (projection matrices) and other aspects of custom-built estimator when software runs out of memory | Try using the SVD. E.g., since
$$
X = U\Sigma V^T,
$$
then
$$
(X^T X)^{-1} = (V\Sigma^2 V^T)^{-1} = V\Sigma^{-2} V^T,
$$
and thus
$$
X(X^T X)^{-1}X^T = U I_r U^T = U_r U_r^T,
$$
where $I_r$ is an $n\times n$ identity matrix with $r\leq n$ ones on the diagonal (upper part), and $n-r$ zeros on the lower diago... | Speeding up hat matrices like $X(X'X)^{-1}X'$ (projection matrices) and other aspects of custom-buil | Try using the SVD. E.g., since
$$
X = U\Sigma V^T,
$$
then
$$
(X^T X)^{-1} = (V\Sigma^2 V^T)^{-1} = V\Sigma^{-2} V^T,
$$
and thus
$$
X(X^T X)^{-1}X^T = U I_r U^T = U_r U_r^T,
$$
where $I_r | Speeding up hat matrices like $X(X'X)^{-1}X'$ (projection matrices) and other aspects of custom-built estimator when software runs out of memory
Try using the SVD. E.g., since
$$
X = U\Sigma V^T,
$$
then
$$
(X^T X)^{-1} = (V\Sigma^2 V^T)^{-1} = V\Sigma^{-2} V^T,
$$
and thus
$$
X(X^T X)^{-1}X^T = U I_r U^T =... | Speeding up hat matrices like $X(X'X)^{-1}X'$ (projection matrices) and other aspects of custom-buil
Try using the SVD. E.g., since
$$
X = U\Sigma V^T,
$$
then
$$
(X^T X)^{-1} = (V\Sigma^2 V^T)^{-1} = V\Sigma^{-2} V^T,
$$
and thus
$$
X(X^T X)^{-1}X^T = U I_r U^T = U_r U_r^T,
$$
where $I_r |
40,360 | Regression trees to model rates | One way would be to adopt a formal model-based tree. The glmtree() function in the partykit package implements the general MOB algorithm for model-based recursive partitioning (Zeileis et al. 2008, Journal of Computational and Graphical Statistics, 17(2), 492-514). This supports Poisson responses and also allows for th... | Regression trees to model rates | One way would be to adopt a formal model-based tree. The glmtree() function in the partykit package implements the general MOB algorithm for model-based recursive partitioning (Zeileis et al. 2008, Jo | Regression trees to model rates
One way would be to adopt a formal model-based tree. The glmtree() function in the partykit package implements the general MOB algorithm for model-based recursive partitioning (Zeileis et al. 2008, Journal of Computational and Graphical Statistics, 17(2), 492-514). This supports Poisson ... | Regression trees to model rates
One way would be to adopt a formal model-based tree. The glmtree() function in the partykit package implements the general MOB algorithm for model-based recursive partitioning (Zeileis et al. 2008, Jo |
40,361 | can someone fix this cognitive dissonance I have about marginals? | This is one of the first results I give in my Bayesian Analysis class. You are confused by notations: using the same symbol $p$ all over is a reason for this confusion and hence let me introduce $\pi(\cdot)$ for the prior, $p_1(x_1|\theta)$ for the density of $X_1$, $p_{2|1}(x_2|\theta,x_1)$ for the conditional density... | can someone fix this cognitive dissonance I have about marginals? | This is one of the first results I give in my Bayesian Analysis class. You are confused by notations: using the same symbol $p$ all over is a reason for this confusion and hence let me introduce $\pi( | can someone fix this cognitive dissonance I have about marginals?
This is one of the first results I give in my Bayesian Analysis class. You are confused by notations: using the same symbol $p$ all over is a reason for this confusion and hence let me introduce $\pi(\cdot)$ for the prior, $p_1(x_1|\theta)$ for the densi... | can someone fix this cognitive dissonance I have about marginals?
This is one of the first results I give in my Bayesian Analysis class. You are confused by notations: using the same symbol $p$ all over is a reason for this confusion and hence let me introduce $\pi( |
40,362 | Why is this random variable both continuous and discrete? | It's wrong because - as the answer explained - there are discrete atoms at 0 and 2.
By that cdf, you can wait exactly 0 time with positive probability (similarly with 2). Because of that, the waiting time is mixed, not continuous.
Presumably you've been given definitions of all three. How are continuous r.v.s defined?
... | Why is this random variable both continuous and discrete? | It's wrong because - as the answer explained - there are discrete atoms at 0 and 2.
By that cdf, you can wait exactly 0 time with positive probability (similarly with 2). Because of that, the waiting | Why is this random variable both continuous and discrete?
It's wrong because - as the answer explained - there are discrete atoms at 0 and 2.
By that cdf, you can wait exactly 0 time with positive probability (similarly with 2). Because of that, the waiting time is mixed, not continuous.
Presumably you've been given de... | Why is this random variable both continuous and discrete?
It's wrong because - as the answer explained - there are discrete atoms at 0 and 2.
By that cdf, you can wait exactly 0 time with positive probability (similarly with 2). Because of that, the waiting |
40,363 | SARIMA model equation | Excerpt from a comment clarifying the actual confusion:
I always found it a odd way to define the model. Consider the SARIMA(1,0,0)(1,0,0)24... isn't this the same as the much simpler rendering $y_t=\beta_0+\beta_1 y_{t-1}+\beta_2 y_{t-24}+\beta_3 y_{t-25}$? Why define it in that weird way?
Now
$$ y_t = \beta_0 + \... | SARIMA model equation | Excerpt from a comment clarifying the actual confusion:
I always found it a odd way to define the model. Consider the SARIMA(1,0,0)(1,0,0)24... isn't this the same as the much simpler rendering $y_t | SARIMA model equation
Excerpt from a comment clarifying the actual confusion:
I always found it a odd way to define the model. Consider the SARIMA(1,0,0)(1,0,0)24... isn't this the same as the much simpler rendering $y_t=\beta_0+\beta_1 y_{t-1}+\beta_2 y_{t-24}+\beta_3 y_{t-25}$? Why define it in that weird way?
Now... | SARIMA model equation
Excerpt from a comment clarifying the actual confusion:
I always found it a odd way to define the model. Consider the SARIMA(1,0,0)(1,0,0)24... isn't this the same as the much simpler rendering $y_t |
40,364 | SARIMA model equation | ARIMA model uses the historical information within the own variable to predict the future values and this model have two parts. On the one hand we have the AR structure and on the other hand we have the MA structure. The AR structure is very intuitive because we are multiplying one past variable's value by one estimate... | SARIMA model equation | ARIMA model uses the historical information within the own variable to predict the future values and this model have two parts. On the one hand we have the AR structure and on the other hand we have t | SARIMA model equation
ARIMA model uses the historical information within the own variable to predict the future values and this model have two parts. On the one hand we have the AR structure and on the other hand we have the MA structure. The AR structure is very intuitive because we are multiplying one past variable's... | SARIMA model equation
ARIMA model uses the historical information within the own variable to predict the future values and this model have two parts. On the one hand we have the AR structure and on the other hand we have t |
40,365 | SARIMA model equation | $Y(t)=α1*Y(t−1)+e(t)$
Since $Y(t-1)=B*Y(t)$ we get
$Y(t)=α1*B*Y(t)+e(t)$
Collecting like terms
$Y(t)-α1*B*Y(t)=e(t)$
or
$Y(t)[1-α1*B]=e(t)$
the forecast equation is $YPRED(t)=α1*Y(t−1)$ since the expected value of $e(t)=0.0$ | SARIMA model equation | $Y(t)=α1*Y(t−1)+e(t)$
Since $Y(t-1)=B*Y(t)$ we get
$Y(t)=α1*B*Y(t)+e(t)$
Collecting like terms
$Y(t)-α1*B*Y(t)=e(t)$
or
$Y(t)[1-α1*B]=e(t)$
the forecast equation is $YPRED(t)=α1*Y(t−1)$ since the expe | SARIMA model equation
$Y(t)=α1*Y(t−1)+e(t)$
Since $Y(t-1)=B*Y(t)$ we get
$Y(t)=α1*B*Y(t)+e(t)$
Collecting like terms
$Y(t)-α1*B*Y(t)=e(t)$
or
$Y(t)[1-α1*B]=e(t)$
the forecast equation is $YPRED(t)=α1*Y(t−1)$ since the expected value of $e(t)=0.0$ | SARIMA model equation
$Y(t)=α1*Y(t−1)+e(t)$
Since $Y(t-1)=B*Y(t)$ we get
$Y(t)=α1*B*Y(t)+e(t)$
Collecting like terms
$Y(t)-α1*B*Y(t)=e(t)$
or
$Y(t)[1-α1*B]=e(t)$
the forecast equation is $YPRED(t)=α1*Y(t−1)$ since the expe |
40,366 | Is 'indirect effect' the same as 'mediation'? | No, "mediation" and "indirect effect" are not synonymous. For example, when analyzing complex causal systems in which any variable in the system at time $t$ contributes causally to every variable in the system at times $>t$, the term "mediator" is largely meaningless, whereas indirect effects may or may not exist due b... | Is 'indirect effect' the same as 'mediation'? | No, "mediation" and "indirect effect" are not synonymous. For example, when analyzing complex causal systems in which any variable in the system at time $t$ contributes causally to every variable in t | Is 'indirect effect' the same as 'mediation'?
No, "mediation" and "indirect effect" are not synonymous. For example, when analyzing complex causal systems in which any variable in the system at time $t$ contributes causally to every variable in the system at times $>t$, the term "mediator" is largely meaningless, where... | Is 'indirect effect' the same as 'mediation'?
No, "mediation" and "indirect effect" are not synonymous. For example, when analyzing complex causal systems in which any variable in the system at time $t$ contributes causally to every variable in t |
40,367 | Is 'indirect effect' the same as 'mediation'? | There seem to be two distinct aspects to this question:
Are the terms 'indirect effect' and 'mediation' synonymous?
I would say largely yes (edit: assuming--cf. @Alexis' answer--that you are referring to a terminal causal model). Bear in mind that you can have full or partial mediation. That is, the effect of A on C... | Is 'indirect effect' the same as 'mediation'? | There seem to be two distinct aspects to this question:
Are the terms 'indirect effect' and 'mediation' synonymous?
I would say largely yes (edit: assuming--cf. @Alexis' answer--that you are referrin | Is 'indirect effect' the same as 'mediation'?
There seem to be two distinct aspects to this question:
Are the terms 'indirect effect' and 'mediation' synonymous?
I would say largely yes (edit: assuming--cf. @Alexis' answer--that you are referring to a terminal causal model). Bear in mind that you can have full or par... | Is 'indirect effect' the same as 'mediation'?
There seem to be two distinct aspects to this question:
Are the terms 'indirect effect' and 'mediation' synonymous?
I would say largely yes (edit: assuming--cf. @Alexis' answer--that you are referrin |
40,368 | Is 'indirect effect' the same as 'mediation'? | The word mediation is inappropriate when the influence from A to C is not significant. However, you can say that A influences C indirectly through B, i.e. indirect effect. | Is 'indirect effect' the same as 'mediation'? | The word mediation is inappropriate when the influence from A to C is not significant. However, you can say that A influences C indirectly through B, i.e. indirect effect. | Is 'indirect effect' the same as 'mediation'?
The word mediation is inappropriate when the influence from A to C is not significant. However, you can say that A influences C indirectly through B, i.e. indirect effect. | Is 'indirect effect' the same as 'mediation'?
The word mediation is inappropriate when the influence from A to C is not significant. However, you can say that A influences C indirectly through B, i.e. indirect effect. |
40,369 | Define the joint pmf of a particle moving randomly on a grid | I'm going to focus attention on some specifics of your example, but the arguments carry over to larger examples.
As you saw, there are 25 cells inside a 3-step radius of the origin:
.
. . .
. . . . .
. . . o . . .
. . . . .
. . .
... | Define the joint pmf of a particle moving randomly on a grid | I'm going to focus attention on some specifics of your example, but the arguments carry over to larger examples.
As you saw, there are 25 cells inside a 3-step radius of the origin:
. | Define the joint pmf of a particle moving randomly on a grid
I'm going to focus attention on some specifics of your example, but the arguments carry over to larger examples.
As you saw, there are 25 cells inside a 3-step radius of the origin:
.
. . .
. . . . .
. . ... | Define the joint pmf of a particle moving randomly on a grid
I'm going to focus attention on some specifics of your example, but the arguments carry over to larger examples.
As you saw, there are 25 cells inside a 3-step radius of the origin:
. |
40,370 | Define the joint pmf of a particle moving randomly on a grid | Are you allowing the particle to move backwards?
Either way, I would model it in terms of a matrix $A$ giving the transition probabilities between each pairs of cells. You can then find the probabilities of all paths from i to j after k steps by calculating $A^K$. This representation may lead you to a set of equation... | Define the joint pmf of a particle moving randomly on a grid | Are you allowing the particle to move backwards?
Either way, I would model it in terms of a matrix $A$ giving the transition probabilities between each pairs of cells. You can then find the probabili | Define the joint pmf of a particle moving randomly on a grid
Are you allowing the particle to move backwards?
Either way, I would model it in terms of a matrix $A$ giving the transition probabilities between each pairs of cells. You can then find the probabilities of all paths from i to j after k steps by calculating ... | Define the joint pmf of a particle moving randomly on a grid
Are you allowing the particle to move backwards?
Either way, I would model it in terms of a matrix $A$ giving the transition probabilities between each pairs of cells. You can then find the probabili |
40,371 | Define the joint pmf of a particle moving randomly on a grid | Your approach would lead to the correct answer, but you have missed some ways to get into the squares marked with $4$ and $2$. For example, 'right-up-right', 'right-right-up' and 'up-right-right' are 3 ways to end up at the same square, which you have marked with $2$. | Define the joint pmf of a particle moving randomly on a grid | Your approach would lead to the correct answer, but you have missed some ways to get into the squares marked with $4$ and $2$. For example, 'right-up-right', 'right-right-up' and 'up-right-right' are | Define the joint pmf of a particle moving randomly on a grid
Your approach would lead to the correct answer, but you have missed some ways to get into the squares marked with $4$ and $2$. For example, 'right-up-right', 'right-right-up' and 'up-right-right' are 3 ways to end up at the same square, which you have marked ... | Define the joint pmf of a particle moving randomly on a grid
Your approach would lead to the correct answer, but you have missed some ways to get into the squares marked with $4$ and $2$. For example, 'right-up-right', 'right-right-up' and 'up-right-right' are |
40,372 | Outer crossvalidation cycle in caret package (R)? | Inner and outer CV are used to perform classifier selection not to get a better prediction on the estimate. To get a better estimate, do a repeated cv. So to perform a 10-repeates 5-fold CV use
trainControl(method = "repeatedcv",number = 5,
## repeated ten times
repeats = 10)
But if what you ... | Outer crossvalidation cycle in caret package (R)? | Inner and outer CV are used to perform classifier selection not to get a better prediction on the estimate. To get a better estimate, do a repeated cv. So to perform a 10-repeates 5-fold CV use
trainC | Outer crossvalidation cycle in caret package (R)?
Inner and outer CV are used to perform classifier selection not to get a better prediction on the estimate. To get a better estimate, do a repeated cv. So to perform a 10-repeates 5-fold CV use
trainControl(method = "repeatedcv",number = 5,
## repeated ten ... | Outer crossvalidation cycle in caret package (R)?
Inner and outer CV are used to perform classifier selection not to get a better prediction on the estimate. To get a better estimate, do a repeated cv. So to perform a 10-repeates 5-fold CV use
trainC |
40,373 | Mixed effects model for power function data | (Disclaimer: answering my own question after fiddling around - I'm really not an expert on this so please read critically)
Step 1: create a power function, including the intercept, using the deriv function which adds the necessary properties to the object. You have to be somewhat verbose, specifying which parameters to... | Mixed effects model for power function data | (Disclaimer: answering my own question after fiddling around - I'm really not an expert on this so please read critically)
Step 1: create a power function, including the intercept, using the deriv fun | Mixed effects model for power function data
(Disclaimer: answering my own question after fiddling around - I'm really not an expert on this so please read critically)
Step 1: create a power function, including the intercept, using the deriv function which adds the necessary properties to the object. You have to be some... | Mixed effects model for power function data
(Disclaimer: answering my own question after fiddling around - I'm really not an expert on this so please read critically)
Step 1: create a power function, including the intercept, using the deriv fun |
40,374 | What is the variance of a Polya Gamma distribution? | In equation (6), the paper obtains the Laplace transform of these distributions as
$$\phi(t) = \prod_{k=1}^\infty \left(1 + \frac{t}{d_k}
\right)^{-b};\ d_k = 2\left(k-\frac{1}{2}\right)^2 \pi^2 + c^2/2$$
where $b\gt 0$ and $c\in \mathbb R$ are the parameters. Taking logarithms yields
$$\psi(t) = \frac{d}{dt}\phi(t) ... | What is the variance of a Polya Gamma distribution? | In equation (6), the paper obtains the Laplace transform of these distributions as
$$\phi(t) = \prod_{k=1}^\infty \left(1 + \frac{t}{d_k}
\right)^{-b};\ d_k = 2\left(k-\frac{1}{2}\right)^2 \pi^2 + c^2 | What is the variance of a Polya Gamma distribution?
In equation (6), the paper obtains the Laplace transform of these distributions as
$$\phi(t) = \prod_{k=1}^\infty \left(1 + \frac{t}{d_k}
\right)^{-b};\ d_k = 2\left(k-\frac{1}{2}\right)^2 \pi^2 + c^2/2$$
where $b\gt 0$ and $c\in \mathbb R$ are the parameters. Taking... | What is the variance of a Polya Gamma distribution?
In equation (6), the paper obtains the Laplace transform of these distributions as
$$\phi(t) = \prod_{k=1}^\infty \left(1 + \frac{t}{d_k}
\right)^{-b};\ d_k = 2\left(k-\frac{1}{2}\right)^2 \pi^2 + c^2 |
40,375 | Can we average over a Cauchy random variable? | I don't know of any results from integration theory that would give full description of such functions, but I can give a few observations that might be helpful.
0) If the function $g$ is always positive or always negative, then the integral exists, although it might by infinite.
1) The set of $g$ for which the integral... | Can we average over a Cauchy random variable? | I don't know of any results from integration theory that would give full description of such functions, but I can give a few observations that might be helpful.
0) If the function $g$ is always positi | Can we average over a Cauchy random variable?
I don't know of any results from integration theory that would give full description of such functions, but I can give a few observations that might be helpful.
0) If the function $g$ is always positive or always negative, then the integral exists, although it might by infi... | Can we average over a Cauchy random variable?
I don't know of any results from integration theory that would give full description of such functions, but I can give a few observations that might be helpful.
0) If the function $g$ is always positi |
40,376 | Can we average over a Cauchy random variable? | This started out as a comment (just thinking out loud here), but I got further along than I thought. I haven't read any other answers yet so there's probably some overlap.
[This is clearly not anything like a definitive answer, since it doesn't characterize when such integrals converge in general. What it does after so... | Can we average over a Cauchy random variable? | This started out as a comment (just thinking out loud here), but I got further along than I thought. I haven't read any other answers yet so there's probably some overlap.
[This is clearly not anythin | Can we average over a Cauchy random variable?
This started out as a comment (just thinking out loud here), but I got further along than I thought. I haven't read any other answers yet so there's probably some overlap.
[This is clearly not anything like a definitive answer, since it doesn't characterize when such integr... | Can we average over a Cauchy random variable?
This started out as a comment (just thinking out loud here), but I got further along than I thought. I haven't read any other answers yet so there's probably some overlap.
[This is clearly not anythin |
40,377 | Can anyone provide a peer reviewed reference for the calculation of least squares means as implemented in the R package lsmeans? | The history of the least squares mean, its appearance in SAS, and its interpretation is discussed in Searle, Milliken, and Speed (1979).
Some discussion of the concepts around least squares means (population marginal means) is found in Searle, Speed, and Milliken (1980). Earliest mention of the concept that they note ... | Can anyone provide a peer reviewed reference for the calculation of least squares means as implement | The history of the least squares mean, its appearance in SAS, and its interpretation is discussed in Searle, Milliken, and Speed (1979).
Some discussion of the concepts around least squares means (pop | Can anyone provide a peer reviewed reference for the calculation of least squares means as implemented in the R package lsmeans?
The history of the least squares mean, its appearance in SAS, and its interpretation is discussed in Searle, Milliken, and Speed (1979).
Some discussion of the concepts around least squares m... | Can anyone provide a peer reviewed reference for the calculation of least squares means as implement
The history of the least squares mean, its appearance in SAS, and its interpretation is discussed in Searle, Milliken, and Speed (1979).
Some discussion of the concepts around least squares means (pop |
40,378 | Sum of truncated normal with two normal distributions | I think this is a very nice problem. If I may change notation slightly ...
The Problem
Let $\quad W \sim N(\mu_0, \sigma_0^2), \quad X_1 \sim N(\mu_1, \sigma_1^2), \quad X_2 \sim N(\mu_2, \sigma_2^2)$
denote independent random variables, and let $c$ denote a constant.
Find the pdf of $Z$, where:
$$ Z = \begin{cases}W... | Sum of truncated normal with two normal distributions | I think this is a very nice problem. If I may change notation slightly ...
The Problem
Let $\quad W \sim N(\mu_0, \sigma_0^2), \quad X_1 \sim N(\mu_1, \sigma_1^2), \quad X_2 \sim N(\mu_2, \sigma_2^2) | Sum of truncated normal with two normal distributions
I think this is a very nice problem. If I may change notation slightly ...
The Problem
Let $\quad W \sim N(\mu_0, \sigma_0^2), \quad X_1 \sim N(\mu_1, \sigma_1^2), \quad X_2 \sim N(\mu_2, \sigma_2^2)$
denote independent random variables, and let $c$ denote a consta... | Sum of truncated normal with two normal distributions
I think this is a very nice problem. If I may change notation slightly ...
The Problem
Let $\quad W \sim N(\mu_0, \sigma_0^2), \quad X_1 \sim N(\mu_1, \sigma_1^2), \quad X_2 \sim N(\mu_2, \sigma_2^2) |
40,379 | Conditional Expectation Constant | Regarding the second part, the answer is yes
$$
E(Z)=E(E(Z|X))=E(k)=k
$$ | Conditional Expectation Constant | Regarding the second part, the answer is yes
$$
E(Z)=E(E(Z|X))=E(k)=k
$$ | Conditional Expectation Constant
Regarding the second part, the answer is yes
$$
E(Z)=E(E(Z|X))=E(k)=k
$$ | Conditional Expectation Constant
Regarding the second part, the answer is yes
$$
E(Z)=E(E(Z|X))=E(k)=k
$$ |
40,380 | If I divide my data by its mean, does it still have a unit? | Since the series and the mean are measured in the same units, the ratio is unit-free.
Adding or subtracting two things in the same units leaves you with the sum or difference in the same units again. But ratios are in the ratio of the units.
If the numerator is in dollars and the denominator is in weeks, you have the ... | If I divide my data by its mean, does it still have a unit? | Since the series and the mean are measured in the same units, the ratio is unit-free.
Adding or subtracting two things in the same units leaves you with the sum or difference in the same units again. | If I divide my data by its mean, does it still have a unit?
Since the series and the mean are measured in the same units, the ratio is unit-free.
Adding or subtracting two things in the same units leaves you with the sum or difference in the same units again. But ratios are in the ratio of the units.
If the numerator ... | If I divide my data by its mean, does it still have a unit?
Since the series and the mean are measured in the same units, the ratio is unit-free.
Adding or subtracting two things in the same units leaves you with the sum or difference in the same units again. |
40,381 | How to derive the gradient formula for the Maximum Likelihood in RBM? | Although coldmoon's answer is perfectly valid, I would like to propose a slightly different approach:
General gradient expression
First, let's simply restrict our model to be of the form $P_{model}(X) = \frac{f(x; \Theta)}{Z(\Theta)}$ with $f$ a positive parametric function and $Z$ a partition function (=normalizing co... | How to derive the gradient formula for the Maximum Likelihood in RBM? | Although coldmoon's answer is perfectly valid, I would like to propose a slightly different approach:
General gradient expression
First, let's simply restrict our model to be of the form $P_{model}(X) | How to derive the gradient formula for the Maximum Likelihood in RBM?
Although coldmoon's answer is perfectly valid, I would like to propose a slightly different approach:
General gradient expression
First, let's simply restrict our model to be of the form $P_{model}(X) = \frac{f(x; \Theta)}{Z(\Theta)}$ with $f$ a posi... | How to derive the gradient formula for the Maximum Likelihood in RBM?
Although coldmoon's answer is perfectly valid, I would like to propose a slightly different approach:
General gradient expression
First, let's simply restrict our model to be of the form $P_{model}(X) |
40,382 | How to derive the gradient formula for the Maximum Likelihood in RBM? | S represents all of samples you collect. Suppose that we consider only one sample and the red "v" represents the sample: | How to derive the gradient formula for the Maximum Likelihood in RBM? | S represents all of samples you collect. Suppose that we consider only one sample and the red "v" represents the sample: | How to derive the gradient formula for the Maximum Likelihood in RBM?
S represents all of samples you collect. Suppose that we consider only one sample and the red "v" represents the sample: | How to derive the gradient formula for the Maximum Likelihood in RBM?
S represents all of samples you collect. Suppose that we consider only one sample and the red "v" represents the sample: |
40,383 | How to derive the gradient formula for the Maximum Likelihood in RBM? | Want to improve this post? Provide detailed answers to this question, including citations and an explanation of why your answer is correct. Answers without enough detail may be edited or deleted.
I have the same problem. Refer to this book page 567 a... | How to derive the gradient formula for the Maximum Likelihood in RBM? | Want to improve this post? Provide detailed answers to this question, including citations and an explanation of why your answer is correct. Answers without enough detail may be edited or deleted.
| How to derive the gradient formula for the Maximum Likelihood in RBM?
Want to improve this post? Provide detailed answers to this question, including citations and an explanation of why your answer is correct. Answers without enough detail may be edited or deleted.
... | How to derive the gradient formula for the Maximum Likelihood in RBM?
Want to improve this post? Provide detailed answers to this question, including citations and an explanation of why your answer is correct. Answers without enough detail may be edited or deleted.
|
40,384 | Can neural net extrapolate output value | More generally an output neuron of a feed-forward neural net is defined as $f(\sum \Theta_i a_i)$, where $f$ is the link function of the output neuron (which was the identity function in your question) and the other notations are as in your question. The activation values of the neurons of the previous layer $a_i$ depe... | Can neural net extrapolate output value | More generally an output neuron of a feed-forward neural net is defined as $f(\sum \Theta_i a_i)$, where $f$ is the link function of the output neuron (which was the identity function in your question | Can neural net extrapolate output value
More generally an output neuron of a feed-forward neural net is defined as $f(\sum \Theta_i a_i)$, where $f$ is the link function of the output neuron (which was the identity function in your question) and the other notations are as in your question. The activation values of the ... | Can neural net extrapolate output value
More generally an output neuron of a feed-forward neural net is defined as $f(\sum \Theta_i a_i)$, where $f$ is the link function of the output neuron (which was the identity function in your question |
40,385 | Logistic regression and error terms | There are many kinds of residuals. This is true of linear regression (e.g., raw, studentized, standardized, etc.), but is even more true of logistic regression. R has options available for retrieving 5 different types of residuals from a logistic regression fit (see ?residuals.glm: type = c("deviance", "pearson", "wo... | Logistic regression and error terms | There are many kinds of residuals. This is true of linear regression (e.g., raw, studentized, standardized, etc.), but is even more true of logistic regression. R has options available for retrievin | Logistic regression and error terms
There are many kinds of residuals. This is true of linear regression (e.g., raw, studentized, standardized, etc.), but is even more true of logistic regression. R has options available for retrieving 5 different types of residuals from a logistic regression fit (see ?residuals.glm:... | Logistic regression and error terms
There are many kinds of residuals. This is true of linear regression (e.g., raw, studentized, standardized, etc.), but is even more true of logistic regression. R has options available for retrievin |
40,386 | Logistic regression and error terms | There are no error terms in logistic regression. And in my opinion the only residuals that are useful are partial residuals useful for checking departures from the assumed shape of regression effects. But even that can be dealt with more directly using regression splines in the first place. There are no intrinsic re... | Logistic regression and error terms | There are no error terms in logistic regression. And in my opinion the only residuals that are useful are partial residuals useful for checking departures from the assumed shape of regression effects | Logistic regression and error terms
There are no error terms in logistic regression. And in my opinion the only residuals that are useful are partial residuals useful for checking departures from the assumed shape of regression effects. But even that can be dealt with more directly using regression splines in the fir... | Logistic regression and error terms
There are no error terms in logistic regression. And in my opinion the only residuals that are useful are partial residuals useful for checking departures from the assumed shape of regression effects |
40,387 | Faith in an extrapolated result | Answering your edited question.
Take the simplest regression possible:
$\text{Netflow} \sim\alpha + \epsilon$
Intercept only. The $\alpha$ will be your average daily netflow.
Now, let's say that you want to know when will the data storage fill up? Simulate. Data storage will follow this formula:
$Y_{t+1} \sim Y_t + \al... | Faith in an extrapolated result | Answering your edited question.
Take the simplest regression possible:
$\text{Netflow} \sim\alpha + \epsilon$
Intercept only. The $\alpha$ will be your average daily netflow.
Now, let's say that you w | Faith in an extrapolated result
Answering your edited question.
Take the simplest regression possible:
$\text{Netflow} \sim\alpha + \epsilon$
Intercept only. The $\alpha$ will be your average daily netflow.
Now, let's say that you want to know when will the data storage fill up? Simulate. Data storage will follow this ... | Faith in an extrapolated result
Answering your edited question.
Take the simplest regression possible:
$\text{Netflow} \sim\alpha + \epsilon$
Intercept only. The $\alpha$ will be your average daily netflow.
Now, let's say that you w |
40,388 | Faith in an extrapolated result | To expand on my comments, a typical simple "level of dam" or "level of tank" type model might produce results that look vaguely something like this, say:
It's not really appropriate to fit a linear regression to this kind of process, for a variety of reasons (not least, dependence and barrier effects). You need a mode... | Faith in an extrapolated result | To expand on my comments, a typical simple "level of dam" or "level of tank" type model might produce results that look vaguely something like this, say:
It's not really appropriate to fit a linear r | Faith in an extrapolated result
To expand on my comments, a typical simple "level of dam" or "level of tank" type model might produce results that look vaguely something like this, say:
It's not really appropriate to fit a linear regression to this kind of process, for a variety of reasons (not least, dependence and b... | Faith in an extrapolated result
To expand on my comments, a typical simple "level of dam" or "level of tank" type model might produce results that look vaguely something like this, say:
It's not really appropriate to fit a linear r |
40,389 | Residual plot for nonlinear regression | Are the residuals from a nonlinear regression model supposed to be randomly distributed too (as in linear regression)?
Yes. The error term is the same and the residuals represent estimated errors. The fitting of the model will induce some structure among the residuals, and that won't be identical in form for a nonli... | Residual plot for nonlinear regression | Are the residuals from a nonlinear regression model supposed to be randomly distributed too (as in linear regression)?
Yes. The error term is the same and the residuals represent estimated errors. | Residual plot for nonlinear regression
Are the residuals from a nonlinear regression model supposed to be randomly distributed too (as in linear regression)?
Yes. The error term is the same and the residuals represent estimated errors. The fitting of the model will induce some structure among the residuals, and that... | Residual plot for nonlinear regression
Are the residuals from a nonlinear regression model supposed to be randomly distributed too (as in linear regression)?
Yes. The error term is the same and the residuals represent estimated errors. |
40,390 | Bayesian alternative or complement to the Student t-test | Two come to mind.
Morey and Rouder present "Bayesian t tests for accepting and rejecting the null hypothesis". The reference paper is here, there is a handy web interface, and an R package. There are also equivalent programs for ANOVA and correlation.
John Kruschke claims that "Bayesian estimation supersedes the t test... | Bayesian alternative or complement to the Student t-test | Two come to mind.
Morey and Rouder present "Bayesian t tests for accepting and rejecting the null hypothesis". The reference paper is here, there is a handy web interface, and an R package. There are | Bayesian alternative or complement to the Student t-test
Two come to mind.
Morey and Rouder present "Bayesian t tests for accepting and rejecting the null hypothesis". The reference paper is here, there is a handy web interface, and an R package. There are also equivalent programs for ANOVA and correlation.
John Krusch... | Bayesian alternative or complement to the Student t-test
Two come to mind.
Morey and Rouder present "Bayesian t tests for accepting and rejecting the null hypothesis". The reference paper is here, there is a handy web interface, and an R package. There are |
40,391 | Entropy and information content | Based on your phrasing, it seems you are equating thermodynamic entropy with information entropy. The concepts are related, but you have to be careful because they are used differently in the two fields.
Shannon entropy measures unpredictability. You are correct that entropy is maximum when the outcome is the most unce... | Entropy and information content | Based on your phrasing, it seems you are equating thermodynamic entropy with information entropy. The concepts are related, but you have to be careful because they are used differently in the two fiel | Entropy and information content
Based on your phrasing, it seems you are equating thermodynamic entropy with information entropy. The concepts are related, but you have to be careful because they are used differently in the two fields.
Shannon entropy measures unpredictability. You are correct that entropy is maximum w... | Entropy and information content
Based on your phrasing, it seems you are equating thermodynamic entropy with information entropy. The concepts are related, but you have to be careful because they are used differently in the two fiel |
40,392 | Entropy and information content | So, would this imply that Max Entropy = minimum information?
No, max entropy means the event you have observed conveys the max information. If an event happens with equal probability of each possibility you have no any idear what to expect, then the outcome of an event tells you the most information. But when you are ... | Entropy and information content | So, would this imply that Max Entropy = minimum information?
No, max entropy means the event you have observed conveys the max information. If an event happens with equal probability of each possibil | Entropy and information content
So, would this imply that Max Entropy = minimum information?
No, max entropy means the event you have observed conveys the max information. If an event happens with equal probability of each possibility you have no any idear what to expect, then the outcome of an event tells you the mos... | Entropy and information content
So, would this imply that Max Entropy = minimum information?
No, max entropy means the event you have observed conveys the max information. If an event happens with equal probability of each possibil |
40,393 | Conjugate mixture of beta distributions - weights | Assuming you meant a binomial likelihood,
$$
\begin{eqnarray*}
\text{Posterior}(\theta) & \propto & \text{Likelihood}(\theta) \times \text{Prior}(\theta) \\ \\
& = & \text{Binomial}(20 \mid 30, \theta) \times \bigg[ \lambda \times \text{Beta}(\theta \mid 20,10) + (1-\lambda) \times \text{Beta}(\theta \mid 20, 20) \big... | Conjugate mixture of beta distributions - weights | Assuming you meant a binomial likelihood,
$$
\begin{eqnarray*}
\text{Posterior}(\theta) & \propto & \text{Likelihood}(\theta) \times \text{Prior}(\theta) \\ \\
& = & \text{Binomial}(20 \mid 30, \thet | Conjugate mixture of beta distributions - weights
Assuming you meant a binomial likelihood,
$$
\begin{eqnarray*}
\text{Posterior}(\theta) & \propto & \text{Likelihood}(\theta) \times \text{Prior}(\theta) \\ \\
& = & \text{Binomial}(20 \mid 30, \theta) \times \bigg[ \lambda \times \text{Beta}(\theta \mid 20,10) + (1-\l... | Conjugate mixture of beta distributions - weights
Assuming you meant a binomial likelihood,
$$
\begin{eqnarray*}
\text{Posterior}(\theta) & \propto & \text{Likelihood}(\theta) \times \text{Prior}(\theta) \\ \\
& = & \text{Binomial}(20 \mid 30, \thet |
40,394 | Confused about sensitivity, specificity and area under ROC curve (AUC) | An alternative interpretation of AUC is that it gives the probability that a randomly selected positive is ranked above a randomly selected negative (see, e.g., Wikipedia). Thus, AUC is 1 if and only if all positives are ranked above all negatives. However, it is still possible to obtain sensitivity or specificity unde... | Confused about sensitivity, specificity and area under ROC curve (AUC) | An alternative interpretation of AUC is that it gives the probability that a randomly selected positive is ranked above a randomly selected negative (see, e.g., Wikipedia). Thus, AUC is 1 if and only | Confused about sensitivity, specificity and area under ROC curve (AUC)
An alternative interpretation of AUC is that it gives the probability that a randomly selected positive is ranked above a randomly selected negative (see, e.g., Wikipedia). Thus, AUC is 1 if and only if all positives are ranked above all negatives. ... | Confused about sensitivity, specificity and area under ROC curve (AUC)
An alternative interpretation of AUC is that it gives the probability that a randomly selected positive is ranked above a randomly selected negative (see, e.g., Wikipedia). Thus, AUC is 1 if and only |
40,395 | Confused about sensitivity, specificity and area under ROC curve (AUC) | AUC=1 means for all specificities in [0,1] the sensitivity is 1. It is IMPOSSIBLE to get a sensitivity of 95%. So that paper is reporting a fundamental error. Hope this helps. | Confused about sensitivity, specificity and area under ROC curve (AUC) | AUC=1 means for all specificities in [0,1] the sensitivity is 1. It is IMPOSSIBLE to get a sensitivity of 95%. So that paper is reporting a fundamental error. Hope this helps. | Confused about sensitivity, specificity and area under ROC curve (AUC)
AUC=1 means for all specificities in [0,1] the sensitivity is 1. It is IMPOSSIBLE to get a sensitivity of 95%. So that paper is reporting a fundamental error. Hope this helps. | Confused about sensitivity, specificity and area under ROC curve (AUC)
AUC=1 means for all specificities in [0,1] the sensitivity is 1. It is IMPOSSIBLE to get a sensitivity of 95%. So that paper is reporting a fundamental error. Hope this helps. |
40,396 | Probability Interval for Gamma Distribution | Your algebra sounds like it's all fine.
You don't give enough information to guess how you decided "according to $\text{R}$, $P(W<c_1)=1$, instead of the desired $0.025$".
This is a common issue with the gamma distribution - there are two different common parameterizations, both reasonably widespread, and if we're not... | Probability Interval for Gamma Distribution | Your algebra sounds like it's all fine.
You don't give enough information to guess how you decided "according to $\text{R}$, $P(W<c_1)=1$, instead of the desired $0.025$".
This is a common issue with | Probability Interval for Gamma Distribution
Your algebra sounds like it's all fine.
You don't give enough information to guess how you decided "according to $\text{R}$, $P(W<c_1)=1$, instead of the desired $0.025$".
This is a common issue with the gamma distribution - there are two different common parameterizations, ... | Probability Interval for Gamma Distribution
Your algebra sounds like it's all fine.
You don't give enough information to guess how you decided "according to $\text{R}$, $P(W<c_1)=1$, instead of the desired $0.025$".
This is a common issue with |
40,397 | Hamiltonian Monte Carlo: why is reparameterizing needed? | Hamiltonian Monte Carlo is often quoted as being rotation invariant, but what does that actually mean?
In theory Hamiltonian Monte Carlo (HMC) is independent of the coordinates chosen to represent your distribution, which actually means it is both rotation and scale invariant. The problem is that, in practice, we can'... | Hamiltonian Monte Carlo: why is reparameterizing needed? | Hamiltonian Monte Carlo is often quoted as being rotation invariant, but what does that actually mean?
In theory Hamiltonian Monte Carlo (HMC) is independent of the coordinates chosen to represent you | Hamiltonian Monte Carlo: why is reparameterizing needed?
Hamiltonian Monte Carlo is often quoted as being rotation invariant, but what does that actually mean?
In theory Hamiltonian Monte Carlo (HMC) is independent of the coordinates chosen to represent your distribution, which actually means it is both rotation and sc... | Hamiltonian Monte Carlo: why is reparameterizing needed?
Hamiltonian Monte Carlo is often quoted as being rotation invariant, but what does that actually mean?
In theory Hamiltonian Monte Carlo (HMC) is independent of the coordinates chosen to represent you |
40,398 | How to identify the distribution of data? | Although your question is very general, the rule is that there isn't a standard way of fitting a distribution to a vector of observations and several methods exist for it. You can start by creating a histogram of your data. In this way, you can immediately see if the shape of the histogram resembles any of the widely k... | How to identify the distribution of data? | Although your question is very general, the rule is that there isn't a standard way of fitting a distribution to a vector of observations and several methods exist for it. You can start by creating a | How to identify the distribution of data?
Although your question is very general, the rule is that there isn't a standard way of fitting a distribution to a vector of observations and several methods exist for it. You can start by creating a histogram of your data. In this way, you can immediately see if the shape of t... | How to identify the distribution of data?
Although your question is very general, the rule is that there isn't a standard way of fitting a distribution to a vector of observations and several methods exist for it. You can start by creating a |
40,399 | How are partial regression slopes calculated in multiple regression? | if I wanted to plot Y against X1 so that I could visualise how strongly the two were related while also controlling for any confounding with X2, would I plot [Y]~[residuals of X1~X2], or [residuals of Y~X2] ~ [residuals of X1~X2]?
The second one. You want to plot $ e(Y|X_2) \sim e(X_1|X_2)$ to obtain the added variab... | How are partial regression slopes calculated in multiple regression? | if I wanted to plot Y against X1 so that I could visualise how strongly the two were related while also controlling for any confounding with X2, would I plot [Y]~[residuals of X1~X2], or [residuals of | How are partial regression slopes calculated in multiple regression?
if I wanted to plot Y against X1 so that I could visualise how strongly the two were related while also controlling for any confounding with X2, would I plot [Y]~[residuals of X1~X2], or [residuals of Y~X2] ~ [residuals of X1~X2]?
The second one. Yo... | How are partial regression slopes calculated in multiple regression?
if I wanted to plot Y against X1 so that I could visualise how strongly the two were related while also controlling for any confounding with X2, would I plot [Y]~[residuals of X1~X2], or [residuals of |
40,400 | How are partial regression slopes calculated in multiple regression? | To avoid blackening the place, I will not use bold symbols -but the answer will be carried out in matrix form. Vectors are column vectors, a prime will denote the transpose.
Let a linear regression model
$$y = X_1b_1 + X_2b_2 + u_A \qquad [A]$$
The normal equations for the OLS estimator are
$$\begin{align}
\left(X_1'X_... | How are partial regression slopes calculated in multiple regression? | To avoid blackening the place, I will not use bold symbols -but the answer will be carried out in matrix form. Vectors are column vectors, a prime will denote the transpose.
Let a linear regression mo | How are partial regression slopes calculated in multiple regression?
To avoid blackening the place, I will not use bold symbols -but the answer will be carried out in matrix form. Vectors are column vectors, a prime will denote the transpose.
Let a linear regression model
$$y = X_1b_1 + X_2b_2 + u_A \qquad [A]$$
The no... | How are partial regression slopes calculated in multiple regression?
To avoid blackening the place, I will not use bold symbols -but the answer will be carried out in matrix form. Vectors are column vectors, a prime will denote the transpose.
Let a linear regression mo |
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