idx int64 1 56k | question stringlengths 15 155 | answer stringlengths 2 29.2k ⌀ | question_cut stringlengths 15 100 | answer_cut stringlengths 2 200 ⌀ | conversation stringlengths 47 29.3k | conversation_cut stringlengths 47 301 |
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45,901 | Time series modeling with dynamic regressors in SAS vs R | While it is not built in, it is easy enough to do:
library(forecast)
fity <- auto.arima(y, xreg=x)
fitx <- auto.arima(x)
forecast(fity,h=10,xreg=forecast(fitx,h=10)$mean)
However, the prediction intervals obtained do not account for the variance in the forecasts of x. I doubt that SAS handles this either. | Time series modeling with dynamic regressors in SAS vs R | While it is not built in, it is easy enough to do:
library(forecast)
fity <- auto.arima(y, xreg=x)
fitx <- auto.arima(x)
forecast(fity,h=10,xreg=forecast(fitx,h=10)$mean)
However, the prediction inte | Time series modeling with dynamic regressors in SAS vs R
While it is not built in, it is easy enough to do:
library(forecast)
fity <- auto.arima(y, xreg=x)
fitx <- auto.arima(x)
forecast(fity,h=10,xreg=forecast(fitx,h=10)$mean)
However, the prediction intervals obtained do not account for the variance in the forecasts... | Time series modeling with dynamic regressors in SAS vs R
While it is not built in, it is easy enough to do:
library(forecast)
fity <- auto.arima(y, xreg=x)
fitx <- auto.arima(x)
forecast(fity,h=10,xreg=forecast(fitx,h=10)$mean)
However, the prediction inte |
45,902 | Is left-of-mean cdf of exponential distribution greater than that of a gamma distribution? | The answer to your monotonicity conjecture is affirmative. It admits a somewhat sneaky proof and allows us to conclude something about the Poisson distribution in the
process. This is what we explore below.
The picture
The question asks whether the cdfs decrease pointwise as $n$ increases
for each $x$ to the left of th... | Is left-of-mean cdf of exponential distribution greater than that of a gamma distribution? | The answer to your monotonicity conjecture is affirmative. It admits a somewhat sneaky proof and allows us to conclude something about the Poisson distribution in the
process. This is what we explore | Is left-of-mean cdf of exponential distribution greater than that of a gamma distribution?
The answer to your monotonicity conjecture is affirmative. It admits a somewhat sneaky proof and allows us to conclude something about the Poisson distribution in the
process. This is what we explore below.
The picture
The questi... | Is left-of-mean cdf of exponential distribution greater than that of a gamma distribution?
The answer to your monotonicity conjecture is affirmative. It admits a somewhat sneaky proof and allows us to conclude something about the Poisson distribution in the
process. This is what we explore |
45,903 | Is left-of-mean cdf of exponential distribution greater than that of a gamma distribution? | An analytical proof might be quite difficult to obtain. The CDF of a gamma distribution fixed to have mean 1 is $P(k,kx) = \frac{\gamma\left(k,kx\right)}{\Gamma\left(k\right)}$ and you want to show for $0 \le x \le 1$ and $k > 0$ that
$$
\frac{dP\left(k,kx\right)}{dk} \ge 0
$$
But this works out as being fairly horribl... | Is left-of-mean cdf of exponential distribution greater than that of a gamma distribution? | An analytical proof might be quite difficult to obtain. The CDF of a gamma distribution fixed to have mean 1 is $P(k,kx) = \frac{\gamma\left(k,kx\right)}{\Gamma\left(k\right)}$ and you want to show fo | Is left-of-mean cdf of exponential distribution greater than that of a gamma distribution?
An analytical proof might be quite difficult to obtain. The CDF of a gamma distribution fixed to have mean 1 is $P(k,kx) = \frac{\gamma\left(k,kx\right)}{\Gamma\left(k\right)}$ and you want to show for $0 \le x \le 1$ and $k > 0$... | Is left-of-mean cdf of exponential distribution greater than that of a gamma distribution?
An analytical proof might be quite difficult to obtain. The CDF of a gamma distribution fixed to have mean 1 is $P(k,kx) = \frac{\gamma\left(k,kx\right)}{\Gamma\left(k\right)}$ and you want to show fo |
45,904 | Interpreting odds ratios | The fact that these are coefficients are represented entirely by factors in R means that the Intercept is the log-odds for the event, i.e log(the proportion with event / proportion without) for subjects who all have their factor values at the lowest level. We know that of the 1615 in level 1 of the factor under scrutin... | Interpreting odds ratios | The fact that these are coefficients are represented entirely by factors in R means that the Intercept is the log-odds for the event, i.e log(the proportion with event / proportion without) for subjec | Interpreting odds ratios
The fact that these are coefficients are represented entirely by factors in R means that the Intercept is the log-odds for the event, i.e log(the proportion with event / proportion without) for subjects who all have their factor values at the lowest level. We know that of the 1615 in level 1 of... | Interpreting odds ratios
The fact that these are coefficients are represented entirely by factors in R means that the Intercept is the log-odds for the event, i.e log(the proportion with event / proportion without) for subjec |
45,905 | Interpreting odds ratios | Odds ratios are a measure of difference in rate between two groups. So, it doesn't make sense to talk about just the "odds ratio" for a single group, you have to say what you're comparing that group with.
You might find it easier to start with more fundamental quantity, odds - actually this is just another way of expre... | Interpreting odds ratios | Odds ratios are a measure of difference in rate between two groups. So, it doesn't make sense to talk about just the "odds ratio" for a single group, you have to say what you're comparing that group w | Interpreting odds ratios
Odds ratios are a measure of difference in rate between two groups. So, it doesn't make sense to talk about just the "odds ratio" for a single group, you have to say what you're comparing that group with.
You might find it easier to start with more fundamental quantity, odds - actually this is ... | Interpreting odds ratios
Odds ratios are a measure of difference in rate between two groups. So, it doesn't make sense to talk about just the "odds ratio" for a single group, you have to say what you're comparing that group w |
45,906 | Interpreting odds ratios | You can get the predicted probability of survival from a logistic regression program. In R, fitted() gives you fitted probabilities for each person. Your code would be something like:
model1 <- glm(survival~birthweight, family = binomial)
fitted(model1)
And you can extract from that the value for different birthweight... | Interpreting odds ratios | You can get the predicted probability of survival from a logistic regression program. In R, fitted() gives you fitted probabilities for each person. Your code would be something like:
model1 <- glm(su | Interpreting odds ratios
You can get the predicted probability of survival from a logistic regression program. In R, fitted() gives you fitted probabilities for each person. Your code would be something like:
model1 <- glm(survival~birthweight, family = binomial)
fitted(model1)
And you can extract from that the value ... | Interpreting odds ratios
You can get the predicted probability of survival from a logistic regression program. In R, fitted() gives you fitted probabilities for each person. Your code would be something like:
model1 <- glm(su |
45,907 | Kurtosis/4th central moment in terms of mean and variance | What you think about here is something like a philosopher's stone of statistics.
The strict answer is:
No, it is impossible to express skewness or kurtosis via the mean and variance.
@Macro gave a counterexample of distributions with different skewness and kurtosis. A question of coming up with distributions for the... | Kurtosis/4th central moment in terms of mean and variance | What you think about here is something like a philosopher's stone of statistics.
The strict answer is:
No, it is impossible to express skewness or kurtosis via the mean and variance.
@Macro gave a | Kurtosis/4th central moment in terms of mean and variance
What you think about here is something like a philosopher's stone of statistics.
The strict answer is:
No, it is impossible to express skewness or kurtosis via the mean and variance.
@Macro gave a counterexample of distributions with different skewness and ku... | Kurtosis/4th central moment in terms of mean and variance
What you think about here is something like a philosopher's stone of statistics.
The strict answer is:
No, it is impossible to express skewness or kurtosis via the mean and variance.
@Macro gave a |
45,908 | Differentiating correlation and causation using conditional probablity | Conditional Probability and Causality
The idea that you can define causation in terms of conditional probability was the 'probabilistic causality' programme in philosophy associated with e.g. Cartwright and Eels. Arguably, it failed (See Pearl for the argument). A good introductory read on the topic is here. Several... | Differentiating correlation and causation using conditional probablity | Conditional Probability and Causality
The idea that you can define causation in terms of conditional probability was the 'probabilistic causality' programme in philosophy associated with e.g. Cartwrig | Differentiating correlation and causation using conditional probablity
Conditional Probability and Causality
The idea that you can define causation in terms of conditional probability was the 'probabilistic causality' programme in philosophy associated with e.g. Cartwright and Eels. Arguably, it failed (See Pearl for ... | Differentiating correlation and causation using conditional probablity
Conditional Probability and Causality
The idea that you can define causation in terms of conditional probability was the 'probabilistic causality' programme in philosophy associated with e.g. Cartwrig |
45,909 | Differentiating correlation and causation using conditional probablity | Showing that $E_2$ increases the likelihood of $E_1$ is just another way of saying that there is a relationship and hence a nonzero correlation between the events. It does not show causation. There are no probability relationships that "show" causation. Correlation means $P(E_1 E_2)$ not equal $P(E_1) P(E_2)$ which ... | Differentiating correlation and causation using conditional probablity | Showing that $E_2$ increases the likelihood of $E_1$ is just another way of saying that there is a relationship and hence a nonzero correlation between the events. It does not show causation. There | Differentiating correlation and causation using conditional probablity
Showing that $E_2$ increases the likelihood of $E_1$ is just another way of saying that there is a relationship and hence a nonzero correlation between the events. It does not show causation. There are no probability relationships that "show" caus... | Differentiating correlation and causation using conditional probablity
Showing that $E_2$ increases the likelihood of $E_1$ is just another way of saying that there is a relationship and hence a nonzero correlation between the events. It does not show causation. There |
45,910 | How to measure usage data across cohorts/segments? | Statistically, this question seems reducible to: how can you compare two distributions to see which one is bigger? You are right to question the naive use of the mean as a blind summary of the distribution. However, there are still very many ways you could approach this. Here are a couple of options:
1) The two-sample... | How to measure usage data across cohorts/segments? | Statistically, this question seems reducible to: how can you compare two distributions to see which one is bigger? You are right to question the naive use of the mean as a blind summary of the distrib | How to measure usage data across cohorts/segments?
Statistically, this question seems reducible to: how can you compare two distributions to see which one is bigger? You are right to question the naive use of the mean as a blind summary of the distribution. However, there are still very many ways you could approach thi... | How to measure usage data across cohorts/segments?
Statistically, this question seems reducible to: how can you compare two distributions to see which one is bigger? You are right to question the naive use of the mean as a blind summary of the distrib |
45,911 | How to measure usage data across cohorts/segments? | Quick answer
Compare medians instead of means, which will be more robust to the effects of extreme values.
More details
The best way to compare the distributions of usage between your customer groups depends on what you are trying to achieve by comparing them. For example, say you have the following groups:
A: 4, 5, 6
... | How to measure usage data across cohorts/segments? | Quick answer
Compare medians instead of means, which will be more robust to the effects of extreme values.
More details
The best way to compare the distributions of usage between your customer groups | How to measure usage data across cohorts/segments?
Quick answer
Compare medians instead of means, which will be more robust to the effects of extreme values.
More details
The best way to compare the distributions of usage between your customer groups depends on what you are trying to achieve by comparing them. For exam... | How to measure usage data across cohorts/segments?
Quick answer
Compare medians instead of means, which will be more robust to the effects of extreme values.
More details
The best way to compare the distributions of usage between your customer groups |
45,912 | How to measure usage data across cohorts/segments? | It sounds like you are looking for a robust test of the difference between two measures of location. You are right that using the mean poses all sorts of problems, not least of them extreme outliers. Research in recent decades has shown that comparison of means, relying on large sample properties, is much more proble... | How to measure usage data across cohorts/segments? | It sounds like you are looking for a robust test of the difference between two measures of location. You are right that using the mean poses all sorts of problems, not least of them extreme outliers. | How to measure usage data across cohorts/segments?
It sounds like you are looking for a robust test of the difference between two measures of location. You are right that using the mean poses all sorts of problems, not least of them extreme outliers. Research in recent decades has shown that comparison of means, rely... | How to measure usage data across cohorts/segments?
It sounds like you are looking for a robust test of the difference between two measures of location. You are right that using the mean poses all sorts of problems, not least of them extreme outliers. |
45,913 | Difference between CI of ANOVA level coefficients vs t-test CI - which one is "correct"? | There is a difference between the CIs because in case of ANOVA, the estimate of the error variance is based on all observations from all groups, whereas in the separate one-sample $t$-test CI for each group, each CI uses its own error estimate based on the observations from just that single group.
Edit: Using a pooled ... | Difference between CI of ANOVA level coefficients vs t-test CI - which one is "correct"? | There is a difference between the CIs because in case of ANOVA, the estimate of the error variance is based on all observations from all groups, whereas in the separate one-sample $t$-test CI for each | Difference between CI of ANOVA level coefficients vs t-test CI - which one is "correct"?
There is a difference between the CIs because in case of ANOVA, the estimate of the error variance is based on all observations from all groups, whereas in the separate one-sample $t$-test CI for each group, each CI uses its own er... | Difference between CI of ANOVA level coefficients vs t-test CI - which one is "correct"?
There is a difference between the CIs because in case of ANOVA, the estimate of the error variance is based on all observations from all groups, whereas in the separate one-sample $t$-test CI for each |
45,914 | List of likelihood-based classification techniques | It think this has potential to become an interesting list. Maybe we should all either explain or reference how the methods use a likelihood approach.
A list of additional likelihood classification procedures:
GLMs for binomial or multinomial data (Logistic Regression, Probit Regression, other Link Functions) McCul... | List of likelihood-based classification techniques | It think this has potential to become an interesting list. Maybe we should all either explain or reference how the methods use a likelihood approach.
A list of additional likelihood classification | List of likelihood-based classification techniques
It think this has potential to become an interesting list. Maybe we should all either explain or reference how the methods use a likelihood approach.
A list of additional likelihood classification procedures:
GLMs for binomial or multinomial data (Logistic Regress... | List of likelihood-based classification techniques
It think this has potential to become an interesting list. Maybe we should all either explain or reference how the methods use a likelihood approach.
A list of additional likelihood classification |
45,915 | List of likelihood-based classification techniques | LDA and QDA are likelihood based approaches based on respectively both class-conditional densities are multivariate normal with the same covariance matrix and both class-conditional densities are multivariate normal with different covariance matrices. In a broad sense kernel discrimination can be considered likelihood... | List of likelihood-based classification techniques | LDA and QDA are likelihood based approaches based on respectively both class-conditional densities are multivariate normal with the same covariance matrix and both class-conditional densities are mult | List of likelihood-based classification techniques
LDA and QDA are likelihood based approaches based on respectively both class-conditional densities are multivariate normal with the same covariance matrix and both class-conditional densities are multivariate normal with different covariance matrices. In a broad sense... | List of likelihood-based classification techniques
LDA and QDA are likelihood based approaches based on respectively both class-conditional densities are multivariate normal with the same covariance matrix and both class-conditional densities are mult |
45,916 | Increase training performance of a neural network with low learning rate? | If time is a limiting factor, you could try reducing the number of hidden units substantially. In my experience, it's very rare to need this many hidden units. I would start with a small number (less than ten) of hidden units, and see if this gives adequate performance.
If you're more worried about local minima, perhap... | Increase training performance of a neural network with low learning rate? | If time is a limiting factor, you could try reducing the number of hidden units substantially. In my experience, it's very rare to need this many hidden units. I would start with a small number (less | Increase training performance of a neural network with low learning rate?
If time is a limiting factor, you could try reducing the number of hidden units substantially. In my experience, it's very rare to need this many hidden units. I would start with a small number (less than ten) of hidden units, and see if this giv... | Increase training performance of a neural network with low learning rate?
If time is a limiting factor, you could try reducing the number of hidden units substantially. In my experience, it's very rare to need this many hidden units. I would start with a small number (less |
45,917 | Increase training performance of a neural network with low learning rate? | Gradient descent is usually a bad optimization algorithm. Try one of the following:
stochastic gradient descent
Levenberg-Marquardt
conjugate gradient
These algorithms are usually
faster and
achieve better results
E. g. the "two spirals" problem can be solved by gradient descent in >10,000 iterations and by Levenbe... | Increase training performance of a neural network with low learning rate? | Gradient descent is usually a bad optimization algorithm. Try one of the following:
stochastic gradient descent
Levenberg-Marquardt
conjugate gradient
These algorithms are usually
faster and
achiev | Increase training performance of a neural network with low learning rate?
Gradient descent is usually a bad optimization algorithm. Try one of the following:
stochastic gradient descent
Levenberg-Marquardt
conjugate gradient
These algorithms are usually
faster and
achieve better results
E. g. the "two spirals" prob... | Increase training performance of a neural network with low learning rate?
Gradient descent is usually a bad optimization algorithm. Try one of the following:
stochastic gradient descent
Levenberg-Marquardt
conjugate gradient
These algorithms are usually
faster and
achiev |
45,918 | CCA/KCCA for more than two views | If by more than two 'views' you actually mean extending the CCA framework to k-blocks data structure, then you might be interested in
Tenenhaus, A. and Tenenhaus, M. (2011). Regularized Generalized
Canonical Correlation Analysis. Psychometrika, 76(2), 257-284.
The corresponding R package is called RGCCA. | CCA/KCCA for more than two views | If by more than two 'views' you actually mean extending the CCA framework to k-blocks data structure, then you might be interested in
Tenenhaus, A. and Tenenhaus, M. (2011). Regularized Generalized
| CCA/KCCA for more than two views
If by more than two 'views' you actually mean extending the CCA framework to k-blocks data structure, then you might be interested in
Tenenhaus, A. and Tenenhaus, M. (2011). Regularized Generalized
Canonical Correlation Analysis. Psychometrika, 76(2), 257-284.
The corresponding R p... | CCA/KCCA for more than two views
If by more than two 'views' you actually mean extending the CCA framework to k-blocks data structure, then you might be interested in
Tenenhaus, A. and Tenenhaus, M. (2011). Regularized Generalized
|
45,919 | CCA/KCCA for more than two views | This is just a guess. Is it not that CCA can be interpreted as a probabilistic model of the following form?
X | Z ~ N(A*Z,Psi)
Y | Z ~ N(B*Z,Phi)
where X is vector in first view, Y is vector in second view, and Z is latent variable which captures the relation between X and Y. Psi and Phi are covariance matrices which ... | CCA/KCCA for more than two views | This is just a guess. Is it not that CCA can be interpreted as a probabilistic model of the following form?
X | Z ~ N(A*Z,Psi)
Y | Z ~ N(B*Z,Phi)
where X is vector in first view, Y is vector in second | CCA/KCCA for more than two views
This is just a guess. Is it not that CCA can be interpreted as a probabilistic model of the following form?
X | Z ~ N(A*Z,Psi)
Y | Z ~ N(B*Z,Phi)
where X is vector in first view, Y is vector in second view, and Z is latent variable which captures the relation between X and Y. Psi and P... | CCA/KCCA for more than two views
This is just a guess. Is it not that CCA can be interpreted as a probabilistic model of the following form?
X | Z ~ N(A*Z,Psi)
Y | Z ~ N(B*Z,Phi)
where X is vector in first view, Y is vector in second |
45,920 | Effect size for Fisher's exact test? | Fisher's exact test is usually used for 2x2 tables. In such a table, you have a few choices for effect size.
One is the odds ratio, which can be calculated by hand pretty easily. If the four cells are $A_{11} A_{12} A_{21} $ and $A_{22}$ then the OR is $A_{11}*A_{22}/A_{21}*A_{12}$.
Another is the difference in propo... | Effect size for Fisher's exact test? | Fisher's exact test is usually used for 2x2 tables. In such a table, you have a few choices for effect size.
One is the odds ratio, which can be calculated by hand pretty easily. If the four cells ar | Effect size for Fisher's exact test?
Fisher's exact test is usually used for 2x2 tables. In such a table, you have a few choices for effect size.
One is the odds ratio, which can be calculated by hand pretty easily. If the four cells are $A_{11} A_{12} A_{21} $ and $A_{22}$ then the OR is $A_{11}*A_{22}/A_{21}*A_{12}$... | Effect size for Fisher's exact test?
Fisher's exact test is usually used for 2x2 tables. In such a table, you have a few choices for effect size.
One is the odds ratio, which can be calculated by hand pretty easily. If the four cells ar |
45,921 | Inverse probability of treatment weighted (IPTW) estimator for a binary outcome | You seem to be slightly misunderstanding the purpose of the weights in IPTW. You are right it would not make sense to have a fractional value for a binary outcome, but the goal of weighting here is not to get a "corrected" outcome value for each individual.
Instead, you are creating a pseudo-population the composition... | Inverse probability of treatment weighted (IPTW) estimator for a binary outcome | You seem to be slightly misunderstanding the purpose of the weights in IPTW. You are right it would not make sense to have a fractional value for a binary outcome, but the goal of weighting here is no | Inverse probability of treatment weighted (IPTW) estimator for a binary outcome
You seem to be slightly misunderstanding the purpose of the weights in IPTW. You are right it would not make sense to have a fractional value for a binary outcome, but the goal of weighting here is not to get a "corrected" outcome value for... | Inverse probability of treatment weighted (IPTW) estimator for a binary outcome
You seem to be slightly misunderstanding the purpose of the weights in IPTW. You are right it would not make sense to have a fractional value for a binary outcome, but the goal of weighting here is no |
45,922 | Inverse probability of treatment weighted (IPTW) estimator for a binary outcome | $\hat e_i$ is I believe the propensity score; i.e., the probability of $Z_i = 1 | X_i$, so treatment patients are weighted by the inverse of the propensity score, while control patients are weighted by (1- propensity score). | Inverse probability of treatment weighted (IPTW) estimator for a binary outcome | $\hat e_i$ is I believe the propensity score; i.e., the probability of $Z_i = 1 | X_i$, so treatment patients are weighted by the inverse of the propensity score, while control patients are weighted b | Inverse probability of treatment weighted (IPTW) estimator for a binary outcome
$\hat e_i$ is I believe the propensity score; i.e., the probability of $Z_i = 1 | X_i$, so treatment patients are weighted by the inverse of the propensity score, while control patients are weighted by (1- propensity score). | Inverse probability of treatment weighted (IPTW) estimator for a binary outcome
$\hat e_i$ is I believe the propensity score; i.e., the probability of $Z_i = 1 | X_i$, so treatment patients are weighted by the inverse of the propensity score, while control patients are weighted b |
45,923 | Inverse probability of treatment weighted (IPTW) estimator for a binary outcome | To expand on what Ellie said, the "inverse" part of the weighting means that if a subject has a low probability of receiving the treatment given the other covariates, they receive more representation in the IPTW "population." If your propensity model is correct (spoiler: it isn't), then the IPTW estimator is the naive ... | Inverse probability of treatment weighted (IPTW) estimator for a binary outcome | To expand on what Ellie said, the "inverse" part of the weighting means that if a subject has a low probability of receiving the treatment given the other covariates, they receive more representation | Inverse probability of treatment weighted (IPTW) estimator for a binary outcome
To expand on what Ellie said, the "inverse" part of the weighting means that if a subject has a low probability of receiving the treatment given the other covariates, they receive more representation in the IPTW "population." If your propen... | Inverse probability of treatment weighted (IPTW) estimator for a binary outcome
To expand on what Ellie said, the "inverse" part of the weighting means that if a subject has a low probability of receiving the treatment given the other covariates, they receive more representation |
45,924 | Testing two-tailed p-values using Stouffer's approach | 1) If two-sided p-values are being analyzed, you use the two-sided p-value in the calculation of the $Z_i$. The two-sided p-value is $\tilde{p}_i = p_i/2$.
2) If left-tailed p-values are used, you use $1-p_i$ instead of $p_i$ in the calculation of the $Z_i$. | Testing two-tailed p-values using Stouffer's approach | 1) If two-sided p-values are being analyzed, you use the two-sided p-value in the calculation of the $Z_i$. The two-sided p-value is $\tilde{p}_i = p_i/2$.
2) If left-tailed p-values are used, you us | Testing two-tailed p-values using Stouffer's approach
1) If two-sided p-values are being analyzed, you use the two-sided p-value in the calculation of the $Z_i$. The two-sided p-value is $\tilde{p}_i = p_i/2$.
2) If left-tailed p-values are used, you use $1-p_i$ instead of $p_i$ in the calculation of the $Z_i$. | Testing two-tailed p-values using Stouffer's approach
1) If two-sided p-values are being analyzed, you use the two-sided p-value in the calculation of the $Z_i$. The two-sided p-value is $\tilde{p}_i = p_i/2$.
2) If left-tailed p-values are used, you us |
45,925 | Calculating mutual Information | To be a little more explicit, what you are really doing is performing a double sum where you are iterating over all possible states of feature $X_i$ as well as all possible states of $C$. In your particular instance $C$ happens to be binary; that is, it has only two states (spam and ham).
As for $X_i$, it's a little u... | Calculating mutual Information | To be a little more explicit, what you are really doing is performing a double sum where you are iterating over all possible states of feature $X_i$ as well as all possible states of $C$. In your par | Calculating mutual Information
To be a little more explicit, what you are really doing is performing a double sum where you are iterating over all possible states of feature $X_i$ as well as all possible states of $C$. In your particular instance $C$ happens to be binary; that is, it has only two states (spam and ham)... | Calculating mutual Information
To be a little more explicit, what you are really doing is performing a double sum where you are iterating over all possible states of feature $X_i$ as well as all possible states of $C$. In your par |
45,926 | What causes loss of power in hypothesis testing? | There is an enormous literature on this subject; I'll just give you a quick thumbnail sketch. Let's say you're testing groups' mean differences, as in T-tests. Power will be reduced if...
...variables are measured unreliably. This will in essence "fuzz over" the differences.
...variability within groups is high. T... | What causes loss of power in hypothesis testing? | There is an enormous literature on this subject; I'll just give you a quick thumbnail sketch. Let's say you're testing groups' mean differences, as in T-tests. Power will be reduced if...
...variab | What causes loss of power in hypothesis testing?
There is an enormous literature on this subject; I'll just give you a quick thumbnail sketch. Let's say you're testing groups' mean differences, as in T-tests. Power will be reduced if...
...variables are measured unreliably. This will in essence "fuzz over" the dif... | What causes loss of power in hypothesis testing?
There is an enormous literature on this subject; I'll just give you a quick thumbnail sketch. Let's say you're testing groups' mean differences, as in T-tests. Power will be reduced if...
...variab |
45,927 | What causes loss of power in hypothesis testing? | Think of power as your ability to recognize the truthfulness of one of two competing data generating processes. It will obviously be easier when:
The data have much signal with little noise (good SNR).
The competing processes are very different one from the other (null and alternative are separated).
You have ample a... | What causes loss of power in hypothesis testing? | Think of power as your ability to recognize the truthfulness of one of two competing data generating processes. It will obviously be easier when:
The data have much signal with little noise (good SNR | What causes loss of power in hypothesis testing?
Think of power as your ability to recognize the truthfulness of one of two competing data generating processes. It will obviously be easier when:
The data have much signal with little noise (good SNR).
The competing processes are very different one from the other (null... | What causes loss of power in hypothesis testing?
Think of power as your ability to recognize the truthfulness of one of two competing data generating processes. It will obviously be easier when:
The data have much signal with little noise (good SNR |
45,928 | How to interpret 95%CI's in conjunction with significance tests for differences between group means? | The main message
Your hypothesis pertains to differences between two group means. The confidence intervals you mention pertain to the actual group means themselves.
You probably want to estimate and report the confidence interval of the difference between group means rather than confidence intervals of the group mean... | How to interpret 95%CI's in conjunction with significance tests for differences between group means? | The main message
Your hypothesis pertains to differences between two group means. The confidence intervals you mention pertain to the actual group means themselves.
You probably want to estimate and | How to interpret 95%CI's in conjunction with significance tests for differences between group means?
The main message
Your hypothesis pertains to differences between two group means. The confidence intervals you mention pertain to the actual group means themselves.
You probably want to estimate and report the confide... | How to interpret 95%CI's in conjunction with significance tests for differences between group means?
The main message
Your hypothesis pertains to differences between two group means. The confidence intervals you mention pertain to the actual group means themselves.
You probably want to estimate and |
45,929 | How to interpret 95%CI's in conjunction with significance tests for differences between group means? | 95%CI's around your individual group means (I'm assuming it's an independent group design) will overlap when the t-test is significant at 0.05 (they typically don't separate until p<0.01). The minimum distance required between the means is the size of 1 CI bar x sqrt(2). What you'll find if you calculate the CI of th... | How to interpret 95%CI's in conjunction with significance tests for differences between group means? | 95%CI's around your individual group means (I'm assuming it's an independent group design) will overlap when the t-test is significant at 0.05 (they typically don't separate until p<0.01). The minimu | How to interpret 95%CI's in conjunction with significance tests for differences between group means?
95%CI's around your individual group means (I'm assuming it's an independent group design) will overlap when the t-test is significant at 0.05 (they typically don't separate until p<0.01). The minimum distance required... | How to interpret 95%CI's in conjunction with significance tests for differences between group means?
95%CI's around your individual group means (I'm assuming it's an independent group design) will overlap when the t-test is significant at 0.05 (they typically don't separate until p<0.01). The minimu |
45,930 | How to forecast CPU demand from a time series? | Start with the forecast package in R. Both auto.arima and ets have predict and forecast methods that are useful.
Here is an example:
#Make a periodic dataset
set.seed(1)
data <- c(3,2,1,5,7,8,9,1,3,12,4,5)
data <- rep(data,5)
data <- data+seq(1,length(data)) #Add trend
data <- data+rnorm(length(data))*5 #Add noise
dat... | How to forecast CPU demand from a time series? | Start with the forecast package in R. Both auto.arima and ets have predict and forecast methods that are useful.
Here is an example:
#Make a periodic dataset
set.seed(1)
data <- c(3,2,1,5,7,8,9,1,3,1 | How to forecast CPU demand from a time series?
Start with the forecast package in R. Both auto.arima and ets have predict and forecast methods that are useful.
Here is an example:
#Make a periodic dataset
set.seed(1)
data <- c(3,2,1,5,7,8,9,1,3,12,4,5)
data <- rep(data,5)
data <- data+seq(1,length(data)) #Add trend
da... | How to forecast CPU demand from a time series?
Start with the forecast package in R. Both auto.arima and ets have predict and forecast methods that are useful.
Here is an example:
#Make a periodic dataset
set.seed(1)
data <- c(3,2,1,5,7,8,9,1,3,1 |
45,931 | How to forecast CPU demand from a time series? | What you are doing is time series analysis, and there are many packages for that. Take a look at the Task View to get you started.
Probably the simplest analysis to do (and you should always start simple) is to decompose the series into a daily effect, a trend and irregular components. Take a look at the stl function... | How to forecast CPU demand from a time series? | What you are doing is time series analysis, and there are many packages for that. Take a look at the Task View to get you started.
Probably the simplest analysis to do (and you should always start si | How to forecast CPU demand from a time series?
What you are doing is time series analysis, and there are many packages for that. Take a look at the Task View to get you started.
Probably the simplest analysis to do (and you should always start simple) is to decompose the series into a daily effect, a trend and irregul... | How to forecast CPU demand from a time series?
What you are doing is time series analysis, and there are many packages for that. Take a look at the Task View to get you started.
Probably the simplest analysis to do (and you should always start si |
45,932 | How to forecast CPU demand from a time series? | If you have reliable historical data, you can use an MCMC approach
check the following articles out,
http://lpenz.github.com/articles/df0pred-2/index.html
http://lpenz.github.com/articles/df0pred-3/index.html
He does prediction of hard drive space requirements using MCMC. | How to forecast CPU demand from a time series? | If you have reliable historical data, you can use an MCMC approach
check the following articles out,
http://lpenz.github.com/articles/df0pred-2/index.html
http://lpenz.github.com/articles/df0pred-3/i | How to forecast CPU demand from a time series?
If you have reliable historical data, you can use an MCMC approach
check the following articles out,
http://lpenz.github.com/articles/df0pred-2/index.html
http://lpenz.github.com/articles/df0pred-3/index.html
He does prediction of hard drive space requirements using MCMC. | How to forecast CPU demand from a time series?
If you have reliable historical data, you can use an MCMC approach
check the following articles out,
http://lpenz.github.com/articles/df0pred-2/index.html
http://lpenz.github.com/articles/df0pred-3/i |
45,933 | How to forecast CPU demand from a time series? | "I have 120 values showing the demand of 10 days of 12 hours each." . This is a mixed frequency problem where you might have an integrated model containing an ARIMA component describing the within day structure and a Transfer Function component ( generalization of regression ) to deal with the daily effects. These "dai... | How to forecast CPU demand from a time series? | "I have 120 values showing the demand of 10 days of 12 hours each." . This is a mixed frequency problem where you might have an integrated model containing an ARIMA component describing the within day | How to forecast CPU demand from a time series?
"I have 120 values showing the demand of 10 days of 12 hours each." . This is a mixed frequency problem where you might have an integrated model containing an ARIMA component describing the within day structure and a Transfer Function component ( generalization of regressi... | How to forecast CPU demand from a time series?
"I have 120 values showing the demand of 10 days of 12 hours each." . This is a mixed frequency problem where you might have an integrated model containing an ARIMA component describing the within day |
45,934 | How to forecast CPU demand from a time series? | From a math aspect. They finding the distribution of your data (Poisson, exponential, uniform, etc). Calculate the average to get an approximate mean. Then apply the Central Limit Theorem to find the normal distribution of samples of averages. This will let you find a good confidence interval for your estimate of that ... | How to forecast CPU demand from a time series? | From a math aspect. They finding the distribution of your data (Poisson, exponential, uniform, etc). Calculate the average to get an approximate mean. Then apply the Central Limit Theorem to find the | How to forecast CPU demand from a time series?
From a math aspect. They finding the distribution of your data (Poisson, exponential, uniform, etc). Calculate the average to get an approximate mean. Then apply the Central Limit Theorem to find the normal distribution of samples of averages. This will let you find a good... | How to forecast CPU demand from a time series?
From a math aspect. They finding the distribution of your data (Poisson, exponential, uniform, etc). Calculate the average to get an approximate mean. Then apply the Central Limit Theorem to find the |
45,935 | How to calculate skewness of data from histogram in R? | Sounds like you're looking at a published histogram and don't have the actual data?
If that is the case you could calculate a rough skewness figure by doing something like pub_his <- c(rep(10,16),rep(15,18),rep(20,27)...), picking the mid point of each bar and reading the frequency off the graph, then you'd have the da... | How to calculate skewness of data from histogram in R? | Sounds like you're looking at a published histogram and don't have the actual data?
If that is the case you could calculate a rough skewness figure by doing something like pub_his <- c(rep(10,16),rep( | How to calculate skewness of data from histogram in R?
Sounds like you're looking at a published histogram and don't have the actual data?
If that is the case you could calculate a rough skewness figure by doing something like pub_his <- c(rep(10,16),rep(15,18),rep(20,27)...), picking the mid point of each bar and read... | How to calculate skewness of data from histogram in R?
Sounds like you're looking at a published histogram and don't have the actual data?
If that is the case you could calculate a rough skewness figure by doing something like pub_his <- c(rep(10,16),rep( |
45,936 | How to calculate skewness of data from histogram in R? | In the case of variance (and indeed for the fourth central moment), the "taking the bin center" approach carries a bias.
Such bias can be corrected, via what are known as Sheppard's correction e.g. see here, which in the case of variance would subtract $\frac{1}{12}$ of the square of the bin-width from the binned estim... | How to calculate skewness of data from histogram in R? | In the case of variance (and indeed for the fourth central moment), the "taking the bin center" approach carries a bias.
Such bias can be corrected, via what are known as Sheppard's correction e.g. se | How to calculate skewness of data from histogram in R?
In the case of variance (and indeed for the fourth central moment), the "taking the bin center" approach carries a bias.
Such bias can be corrected, via what are known as Sheppard's correction e.g. see here, which in the case of variance would subtract $\frac{1}{12... | How to calculate skewness of data from histogram in R?
In the case of variance (and indeed for the fourth central moment), the "taking the bin center" approach carries a bias.
Such bias can be corrected, via what are known as Sheppard's correction e.g. se |
45,937 | What are some applications of Chinese restaurant processes? | Here are some important papers that have applied nonparametric Bayes to topic modeling for example:
Blei et al., Hierarchical Topic Models and the Nested Chinese Restaurant Process, NIPS 2003.
Teh et al., Hierarchical Dirichlet Processes, JASA 2006.
You can find tons of other papers at aclweb.org. | What are some applications of Chinese restaurant processes? | Here are some important papers that have applied nonparametric Bayes to topic modeling for example:
Blei et al., Hierarchical Topic Models and the Nested Chinese Restaurant Process, NIPS 2003.
Teh et | What are some applications of Chinese restaurant processes?
Here are some important papers that have applied nonparametric Bayes to topic modeling for example:
Blei et al., Hierarchical Topic Models and the Nested Chinese Restaurant Process, NIPS 2003.
Teh et al., Hierarchical Dirichlet Processes, JASA 2006.
You can ... | What are some applications of Chinese restaurant processes?
Here are some important papers that have applied nonparametric Bayes to topic modeling for example:
Blei et al., Hierarchical Topic Models and the Nested Chinese Restaurant Process, NIPS 2003.
Teh et |
45,938 | What are some applications of Chinese restaurant processes? | Kevin Knight's Bayesian Inference With Tears describes applications of the Chinese Restaurant Process (which he calls a "cache model") to tree substitution grammars, Chinese word segmentation, and part-of-speech tagging.
(If anyone knows the original sources for these applications, that'd be great as well.) | What are some applications of Chinese restaurant processes? | Kevin Knight's Bayesian Inference With Tears describes applications of the Chinese Restaurant Process (which he calls a "cache model") to tree substitution grammars, Chinese word segmentation, and par | What are some applications of Chinese restaurant processes?
Kevin Knight's Bayesian Inference With Tears describes applications of the Chinese Restaurant Process (which he calls a "cache model") to tree substitution grammars, Chinese word segmentation, and part-of-speech tagging.
(If anyone knows the original sources f... | What are some applications of Chinese restaurant processes?
Kevin Knight's Bayesian Inference With Tears describes applications of the Chinese Restaurant Process (which he calls a "cache model") to tree substitution grammars, Chinese word segmentation, and par |
45,939 | Critical values for Anderson-Darling test | Using Marsaglia & Marsaglia's code, and a bisection search, one can find that the 0.001 critical value is around 5.9694. This would be for 'Case 1' in the wikipedia article quoted. I am not sure how to convert to 'Case 4'. | Critical values for Anderson-Darling test | Using Marsaglia & Marsaglia's code, and a bisection search, one can find that the 0.001 critical value is around 5.9694. This would be for 'Case 1' in the wikipedia article quoted. I am not sure how t | Critical values for Anderson-Darling test
Using Marsaglia & Marsaglia's code, and a bisection search, one can find that the 0.001 critical value is around 5.9694. This would be for 'Case 1' in the wikipedia article quoted. I am not sure how to convert to 'Case 4'. | Critical values for Anderson-Darling test
Using Marsaglia & Marsaglia's code, and a bisection search, one can find that the 0.001 critical value is around 5.9694. This would be for 'Case 1' in the wikipedia article quoted. I am not sure how t |
45,940 | Critical values for Anderson-Darling test | You can use simulation (this is not a new idea, it is how Gosset/Student derived the original t table (but we have faster tools than he did)).
Generate a psuedo random sample from a normal distribution (or at least as close as the computer can come) of the sample size of interest and compute the Anderson Darling Statis... | Critical values for Anderson-Darling test | You can use simulation (this is not a new idea, it is how Gosset/Student derived the original t table (but we have faster tools than he did)).
Generate a psuedo random sample from a normal distributio | Critical values for Anderson-Darling test
You can use simulation (this is not a new idea, it is how Gosset/Student derived the original t table (but we have faster tools than he did)).
Generate a psuedo random sample from a normal distribution (or at least as close as the computer can come) of the sample size of intere... | Critical values for Anderson-Darling test
You can use simulation (this is not a new idea, it is how Gosset/Student derived the original t table (but we have faster tools than he did)).
Generate a psuedo random sample from a normal distributio |
45,941 | Stambaugh bias definition | I'm not sure you can explain this term without using some technical terms, unfortunately. I'll give it my best shot.
Some definitions first:
Bias: the difference between the expectation of an estimator and the true value of the parameter you're estimating.
OLS: Ordinary Least Squares; a method for solving a regression... | Stambaugh bias definition | I'm not sure you can explain this term without using some technical terms, unfortunately. I'll give it my best shot.
Some definitions first:
Bias: the difference between the expectation of an estimat | Stambaugh bias definition
I'm not sure you can explain this term without using some technical terms, unfortunately. I'll give it my best shot.
Some definitions first:
Bias: the difference between the expectation of an estimator and the true value of the parameter you're estimating.
OLS: Ordinary Least Squares; a metho... | Stambaugh bias definition
I'm not sure you can explain this term without using some technical terms, unfortunately. I'll give it my best shot.
Some definitions first:
Bias: the difference between the expectation of an estimat |
45,942 | Stambaugh bias definition | This is the original paper that explains the Stambaugh bias: Stambaugh (JFE1999). It examines the bias in the slope coefficient in the predictive regression of returns on past dividend yields, when the dividend yield process is highly persistent.
Let $y_t$ denote the date $t$ return and $x_t=D_t/P_t$ the date $t$ divi... | Stambaugh bias definition | This is the original paper that explains the Stambaugh bias: Stambaugh (JFE1999). It examines the bias in the slope coefficient in the predictive regression of returns on past dividend yields, when th | Stambaugh bias definition
This is the original paper that explains the Stambaugh bias: Stambaugh (JFE1999). It examines the bias in the slope coefficient in the predictive regression of returns on past dividend yields, when the dividend yield process is highly persistent.
Let $y_t$ denote the date $t$ return and $x_t=... | Stambaugh bias definition
This is the original paper that explains the Stambaugh bias: Stambaugh (JFE1999). It examines the bias in the slope coefficient in the predictive regression of returns on past dividend yields, when th |
45,943 | Can anyone explain why I have obtained an anti-predictive Support Vector Machine? | It is very probably the settings for the hyper-parameters that are the issue, leading to severe over-fitting of the data. Without proper tuning of the hyper-parameters, and SVM can perform arbitrarily badly, especially for high dimensional data (it is the tuning of the regularisation parameter that gives robustness ag... | Can anyone explain why I have obtained an anti-predictive Support Vector Machine? | It is very probably the settings for the hyper-parameters that are the issue, leading to severe over-fitting of the data. Without proper tuning of the hyper-parameters, and SVM can perform arbitraril | Can anyone explain why I have obtained an anti-predictive Support Vector Machine?
It is very probably the settings for the hyper-parameters that are the issue, leading to severe over-fitting of the data. Without proper tuning of the hyper-parameters, and SVM can perform arbitrarily badly, especially for high dimension... | Can anyone explain why I have obtained an anti-predictive Support Vector Machine?
It is very probably the settings for the hyper-parameters that are the issue, leading to severe over-fitting of the data. Without proper tuning of the hyper-parameters, and SVM can perform arbitraril |
45,944 | How to estimate a critical value of Spearman's correlation for n=100? | For values over thirty the approximation (for a two-tailed test) is
$$\frac{\Phi^{-1}\left(1-\tfrac{\alpha}{2}\right)}{\sqrt{n-1}}$$
so for example with $\alpha = 0.05$ and $n=100$ the numerator is about 1.96 and the denominator about 9.95, giving a critical value of about 0.197.
This comes from $\rho$ having approxim... | How to estimate a critical value of Spearman's correlation for n=100? | For values over thirty the approximation (for a two-tailed test) is
$$\frac{\Phi^{-1}\left(1-\tfrac{\alpha}{2}\right)}{\sqrt{n-1}}$$
so for example with $\alpha = 0.05$ and $n=100$ the numerator is a | How to estimate a critical value of Spearman's correlation for n=100?
For values over thirty the approximation (for a two-tailed test) is
$$\frac{\Phi^{-1}\left(1-\tfrac{\alpha}{2}\right)}{\sqrt{n-1}}$$
so for example with $\alpha = 0.05$ and $n=100$ the numerator is about 1.96 and the denominator about 9.95, giving a... | How to estimate a critical value of Spearman's correlation for n=100?
For values over thirty the approximation (for a two-tailed test) is
$$\frac{\Phi^{-1}\left(1-\tfrac{\alpha}{2}\right)}{\sqrt{n-1}}$$
so for example with $\alpha = 0.05$ and $n=100$ the numerator is a |
45,945 | How to estimate a critical value of Spearman's correlation for n=100? | See Wikipedia: Spearman's rank correlation coefficient#Determining significance:
"One can test for significance using
$$t = r \sqrt{\frac{n-2}{1-r^2}},$$
which is distributed approximately as Student's $t$ distribution with $n − 2$ degrees of freedom under the null hypothesis."
Here $r$ is the sample estimate of Spearm... | How to estimate a critical value of Spearman's correlation for n=100? | See Wikipedia: Spearman's rank correlation coefficient#Determining significance:
"One can test for significance using
$$t = r \sqrt{\frac{n-2}{1-r^2}},$$
which is distributed approximately as Student' | How to estimate a critical value of Spearman's correlation for n=100?
See Wikipedia: Spearman's rank correlation coefficient#Determining significance:
"One can test for significance using
$$t = r \sqrt{\frac{n-2}{1-r^2}},$$
which is distributed approximately as Student's $t$ distribution with $n − 2$ degrees of freedom... | How to estimate a critical value of Spearman's correlation for n=100?
See Wikipedia: Spearman's rank correlation coefficient#Determining significance:
"One can test for significance using
$$t = r \sqrt{\frac{n-2}{1-r^2}},$$
which is distributed approximately as Student' |
45,946 | Number of trials required from a binomial distribution to get the desired odds | I wonder what it means to be "99% sure."
The code seems to equate "dumb luck" with $p$ = 52.8% probability of wins. Let's imagine conducting $N$ trials, during which we observe $k$ wins. Suppose, for instance, $N$ = 1000 and you observe $k$ = 530 wins. That's greater than the expected number $p N$ = 528, but it's so... | Number of trials required from a binomial distribution to get the desired odds | I wonder what it means to be "99% sure."
The code seems to equate "dumb luck" with $p$ = 52.8% probability of wins. Let's imagine conducting $N$ trials, during which we observe $k$ wins. Suppose, fo | Number of trials required from a binomial distribution to get the desired odds
I wonder what it means to be "99% sure."
The code seems to equate "dumb luck" with $p$ = 52.8% probability of wins. Let's imagine conducting $N$ trials, during which we observe $k$ wins. Suppose, for instance, $N$ = 1000 and you observe $k... | Number of trials required from a binomial distribution to get the desired odds
I wonder what it means to be "99% sure."
The code seems to equate "dumb luck" with $p$ = 52.8% probability of wins. Let's imagine conducting $N$ trials, during which we observe $k$ wins. Suppose, fo |
45,947 | Number of trials required from a binomial distribution to get the desired odds | numtri[c(min(which(perwin <= 0.55)),max(which(perwin >= 0.55)))] | Number of trials required from a binomial distribution to get the desired odds | numtri[c(min(which(perwin <= 0.55)),max(which(perwin >= 0.55)))] | Number of trials required from a binomial distribution to get the desired odds
numtri[c(min(which(perwin <= 0.55)),max(which(perwin >= 0.55)))] | Number of trials required from a binomial distribution to get the desired odds
numtri[c(min(which(perwin <= 0.55)),max(which(perwin >= 0.55)))] |
45,948 | Minimization of a function by Metropolis-Hastings algorithms | You are rather looking for a simulated annealing, which is easier to understand when formulated in the original, physics way:
Having
$x$ is a state of the system
$f(x)$ is an energy of the system; energy is defined up to addition of a constant, so there is no problem with it being negative or positive -- the only cons... | Minimization of a function by Metropolis-Hastings algorithms | You are rather looking for a simulated annealing, which is easier to understand when formulated in the original, physics way:
Having
$x$ is a state of the system
$f(x)$ is an energy of the system; en | Minimization of a function by Metropolis-Hastings algorithms
You are rather looking for a simulated annealing, which is easier to understand when formulated in the original, physics way:
Having
$x$ is a state of the system
$f(x)$ is an energy of the system; energy is defined up to addition of a constant, so there is n... | Minimization of a function by Metropolis-Hastings algorithms
You are rather looking for a simulated annealing, which is easier to understand when formulated in the original, physics way:
Having
$x$ is a state of the system
$f(x)$ is an energy of the system; en |
45,949 | Minimization of a function by Metropolis-Hastings algorithms | If you want to find the global minimum of a function, simulated annealing would be the algorithm to look at, in which case there is no need to view the function as an unnormalised density of any kind and no need to transform the function. | Minimization of a function by Metropolis-Hastings algorithms | If you want to find the global minimum of a function, simulated annealing would be the algorithm to look at, in which case there is no need to view the function as an unnormalised density of any kind | Minimization of a function by Metropolis-Hastings algorithms
If you want to find the global minimum of a function, simulated annealing would be the algorithm to look at, in which case there is no need to view the function as an unnormalised density of any kind and no need to transform the function. | Minimization of a function by Metropolis-Hastings algorithms
If you want to find the global minimum of a function, simulated annealing would be the algorithm to look at, in which case there is no need to view the function as an unnormalised density of any kind |
45,950 | Minimization of a function by Metropolis-Hastings algorithms | Yes, simulated annealing is also an instance of Metropolis Hasting sampling.
Just set the unnormalized density function as $e^{-f(x)/T}$ and use symmetric proposal distribution (which also makes Metropolis Hasting sampling as Metropolis sampling).
So, the acceptance probability is $min(1, \dfrac{e^{-f(x')/T}}{e^{-f(x)/... | Minimization of a function by Metropolis-Hastings algorithms | Yes, simulated annealing is also an instance of Metropolis Hasting sampling.
Just set the unnormalized density function as $e^{-f(x)/T}$ and use symmetric proposal distribution (which also makes Metro | Minimization of a function by Metropolis-Hastings algorithms
Yes, simulated annealing is also an instance of Metropolis Hasting sampling.
Just set the unnormalized density function as $e^{-f(x)/T}$ and use symmetric proposal distribution (which also makes Metropolis Hasting sampling as Metropolis sampling).
So, the acc... | Minimization of a function by Metropolis-Hastings algorithms
Yes, simulated annealing is also an instance of Metropolis Hasting sampling.
Just set the unnormalized density function as $e^{-f(x)/T}$ and use symmetric proposal distribution (which also makes Metro |
45,951 | Inter-rater reliability using Intra-class correlation with ratings for multiple objects on multiple properties | These are distinct ways of accounting for raters or items variance in overall variance, following Shrout and Fleiss (1979) (cases 1 to 3 in Table 1):
One-way random effects model: raters are considered as sampled from a larger pool of potential raters, hence they are treated as random effects; the ICC is then interpre... | Inter-rater reliability using Intra-class correlation with ratings for multiple objects on multiple | These are distinct ways of accounting for raters or items variance in overall variance, following Shrout and Fleiss (1979) (cases 1 to 3 in Table 1):
One-way random effects model: raters are consider | Inter-rater reliability using Intra-class correlation with ratings for multiple objects on multiple properties
These are distinct ways of accounting for raters or items variance in overall variance, following Shrout and Fleiss (1979) (cases 1 to 3 in Table 1):
One-way random effects model: raters are considered as sam... | Inter-rater reliability using Intra-class correlation with ratings for multiple objects on multiple
These are distinct ways of accounting for raters or items variance in overall variance, following Shrout and Fleiss (1979) (cases 1 to 3 in Table 1):
One-way random effects model: raters are consider |
45,952 | Algorithm for choosing the number of clusters when using pam in R? | You may find an answer to a similar question useful. I have also used clValid but, as I recall, it was rather slow (at least for relatively large datasets). | Algorithm for choosing the number of clusters when using pam in R? | You may find an answer to a similar question useful. I have also used clValid but, as I recall, it was rather slow (at least for relatively large datasets). | Algorithm for choosing the number of clusters when using pam in R?
You may find an answer to a similar question useful. I have also used clValid but, as I recall, it was rather slow (at least for relatively large datasets). | Algorithm for choosing the number of clusters when using pam in R?
You may find an answer to a similar question useful. I have also used clValid but, as I recall, it was rather slow (at least for relatively large datasets). |
45,953 | Algorithm for choosing the number of clusters when using pam in R? | The fpc package provides a few clustering statistics. If you're looking for information criteria in particular, the cluster.stats method provides an information based distance. For mixture models based on clustering, the BIC is available. | Algorithm for choosing the number of clusters when using pam in R? | The fpc package provides a few clustering statistics. If you're looking for information criteria in particular, the cluster.stats method provides an information based distance. For mixture models ba | Algorithm for choosing the number of clusters when using pam in R?
The fpc package provides a few clustering statistics. If you're looking for information criteria in particular, the cluster.stats method provides an information based distance. For mixture models based on clustering, the BIC is available. | Algorithm for choosing the number of clusters when using pam in R?
The fpc package provides a few clustering statistics. If you're looking for information criteria in particular, the cluster.stats method provides an information based distance. For mixture models ba |
45,954 | Algorithm for choosing the number of clusters when using pam in R? | What about silhouette? | Algorithm for choosing the number of clusters when using pam in R? | What about silhouette? | Algorithm for choosing the number of clusters when using pam in R?
What about silhouette? | Algorithm for choosing the number of clusters when using pam in R?
What about silhouette? |
45,955 | Export/format output from pairwise.t.test to LaTeX [closed] | Does this help?
> library(xtable)
> attach(airquality)
> res <- pairwise.t.test(Ozone, Month)
> xtable(res$p.value, caption=res$method)
% latex table generated in R 2.9.2 by xtable 1.5-6 package
% Mon Aug 16 04:24:21 2010
\begin{table}[ht]
\begin{center}
\begin{tabular}{rrrrr}
\hline
& 5 & 6 & 7 & 8 \\
\hline
6 &... | Export/format output from pairwise.t.test to LaTeX [closed] | Does this help?
> library(xtable)
> attach(airquality)
> res <- pairwise.t.test(Ozone, Month)
> xtable(res$p.value, caption=res$method)
% latex table generated in R 2.9.2 by xtable 1.5-6 package
% Mon | Export/format output from pairwise.t.test to LaTeX [closed]
Does this help?
> library(xtable)
> attach(airquality)
> res <- pairwise.t.test(Ozone, Month)
> xtable(res$p.value, caption=res$method)
% latex table generated in R 2.9.2 by xtable 1.5-6 package
% Mon Aug 16 04:24:21 2010
\begin{table}[ht]
\begin{center}
\begi... | Export/format output from pairwise.t.test to LaTeX [closed]
Does this help?
> library(xtable)
> attach(airquality)
> res <- pairwise.t.test(Ozone, Month)
> xtable(res$p.value, caption=res$method)
% latex table generated in R 2.9.2 by xtable 1.5-6 package
% Mon |
45,956 | Export/format output from pairwise.t.test to LaTeX [closed] | One way that you can do the above task without using Sweave is as follows:
Write a custom export function from R that takes the pairwise.t.test object and outputs latex code.
Use \input{...} in your LaTeX document to input this file into your LaTeX document.
With regards to step 1, there are many functions that are ... | Export/format output from pairwise.t.test to LaTeX [closed] | One way that you can do the above task without using Sweave is as follows:
Write a custom export function from R that takes the pairwise.t.test object and outputs latex code.
Use \input{...} in your | Export/format output from pairwise.t.test to LaTeX [closed]
One way that you can do the above task without using Sweave is as follows:
Write a custom export function from R that takes the pairwise.t.test object and outputs latex code.
Use \input{...} in your LaTeX document to input this file into your LaTeX document.... | Export/format output from pairwise.t.test to LaTeX [closed]
One way that you can do the above task without using Sweave is as follows:
Write a custom export function from R that takes the pairwise.t.test object and outputs latex code.
Use \input{...} in your |
45,957 | Piece-wise proportional hazards model as equivalent Poisson model | It doesn't have a Poisson distribution, only a Poisson likelihood. That is, for any observed values $y$ of $Y$ the likelihood ratios $P(Y=y;\theta_1)/P(Y=y;\theta_0)$ are the same as they would be for a Poisson distribution (which is all you need for estimation and other parameter inference). The probabilities of valu... | Piece-wise proportional hazards model as equivalent Poisson model | It doesn't have a Poisson distribution, only a Poisson likelihood. That is, for any observed values $y$ of $Y$ the likelihood ratios $P(Y=y;\theta_1)/P(Y=y;\theta_0)$ are the same as they would be fo | Piece-wise proportional hazards model as equivalent Poisson model
It doesn't have a Poisson distribution, only a Poisson likelihood. That is, for any observed values $y$ of $Y$ the likelihood ratios $P(Y=y;\theta_1)/P(Y=y;\theta_0)$ are the same as they would be for a Poisson distribution (which is all you need for es... | Piece-wise proportional hazards model as equivalent Poisson model
It doesn't have a Poisson distribution, only a Poisson likelihood. That is, for any observed values $y$ of $Y$ the likelihood ratios $P(Y=y;\theta_1)/P(Y=y;\theta_0)$ are the same as they would be fo |
45,958 | Piece-wise proportional hazards model as equivalent Poisson model | One way to think about this is that, within each time interval $j$, you are modeling the Poisson parameter $\mu_{ij}$ based on the time $t_{ij}$ to the first event within interval $j$ for individual $i$, where interval $j$ starts at time $\tau_{j-1}$ and ends at $\tau_j$.
Similarly to how individuals with censored even... | Piece-wise proportional hazards model as equivalent Poisson model | One way to think about this is that, within each time interval $j$, you are modeling the Poisson parameter $\mu_{ij}$ based on the time $t_{ij}$ to the first event within interval $j$ for individual $ | Piece-wise proportional hazards model as equivalent Poisson model
One way to think about this is that, within each time interval $j$, you are modeling the Poisson parameter $\mu_{ij}$ based on the time $t_{ij}$ to the first event within interval $j$ for individual $i$, where interval $j$ starts at time $\tau_{j-1}$ and... | Piece-wise proportional hazards model as equivalent Poisson model
One way to think about this is that, within each time interval $j$, you are modeling the Poisson parameter $\mu_{ij}$ based on the time $t_{ij}$ to the first event within interval $j$ for individual $ |
45,959 | Applying Leibniz's integral rule to the Gaussian distribution's normalization condition | Nice question!
option 1
Derivatives are limits (of fractions), and moving limits inside an expectation often triggers an invocation of a theorem such as the monotone convergence theorem, Lebesgue's dominated convergence theorem, the uniformly integrable convergnce theorem or maybe even Fatou's lemma. The theorem @jbowm... | Applying Leibniz's integral rule to the Gaussian distribution's normalization condition | Nice question!
option 1
Derivatives are limits (of fractions), and moving limits inside an expectation often triggers an invocation of a theorem such as the monotone convergence theorem, Lebesgue's do | Applying Leibniz's integral rule to the Gaussian distribution's normalization condition
Nice question!
option 1
Derivatives are limits (of fractions), and moving limits inside an expectation often triggers an invocation of a theorem such as the monotone convergence theorem, Lebesgue's dominated convergence theorem, the... | Applying Leibniz's integral rule to the Gaussian distribution's normalization condition
Nice question!
option 1
Derivatives are limits (of fractions), and moving limits inside an expectation often triggers an invocation of a theorem such as the monotone convergence theorem, Lebesgue's do |
45,960 | Applying Leibniz's integral rule to the Gaussian distribution's normalization condition | Leibniz' rule can be extended to infinite regions of integration with an extra condition on the function being integrated. Let's write out the basic form:
$${d \over dy}\int_a^b f(x,y)dx = \int_a^b {df(x,y)\over dy}dx $$
To extend the bounds of integration to the infinite case, we need to have $df(x,y) / dy$ behave "w... | Applying Leibniz's integral rule to the Gaussian distribution's normalization condition | Leibniz' rule can be extended to infinite regions of integration with an extra condition on the function being integrated. Let's write out the basic form:
$${d \over dy}\int_a^b f(x,y)dx = \int_a^b { | Applying Leibniz's integral rule to the Gaussian distribution's normalization condition
Leibniz' rule can be extended to infinite regions of integration with an extra condition on the function being integrated. Let's write out the basic form:
$${d \over dy}\int_a^b f(x,y)dx = \int_a^b {df(x,y)\over dy}dx $$
To extend ... | Applying Leibniz's integral rule to the Gaussian distribution's normalization condition
Leibniz' rule can be extended to infinite regions of integration with an extra condition on the function being integrated. Let's write out the basic form:
$${d \over dy}\int_a^b f(x,y)dx = \int_a^b { |
45,961 | Can I use logistic regression when all of the regressors sum to 1? | Variables representing parts of a total, like your proportion of cell type, are called compositional-data, for more information you can peruse that tag.
But in your case the solution is simple. Your design matrix will be rank-deficient, since the sum P1 + P2 + P3 + P4 + P5 will equal the intercept. That way the interce... | Can I use logistic regression when all of the regressors sum to 1? | Variables representing parts of a total, like your proportion of cell type, are called compositional-data, for more information you can peruse that tag.
But in your case the solution is simple. Your d | Can I use logistic regression when all of the regressors sum to 1?
Variables representing parts of a total, like your proportion of cell type, are called compositional-data, for more information you can peruse that tag.
But in your case the solution is simple. Your design matrix will be rank-deficient, since the sum P1... | Can I use logistic regression when all of the regressors sum to 1?
Variables representing parts of a total, like your proportion of cell type, are called compositional-data, for more information you can peruse that tag.
But in your case the solution is simple. Your d |
45,962 | Who estimated war casualties from tightly-controlled government news sources? | You may be referring to Hugo Steinhaus. He was a Polish-Jewish mathematician, which resorted to the ingenious method you sketch to estimate the casualties of the Nazis, while in hiding during WWII. What source I got this information from, I cannot remember. It was a book, which I may have given away to someone long ago... | Who estimated war casualties from tightly-controlled government news sources? | You may be referring to Hugo Steinhaus. He was a Polish-Jewish mathematician, which resorted to the ingenious method you sketch to estimate the casualties of the Nazis, while in hiding during WWII. Wh | Who estimated war casualties from tightly-controlled government news sources?
You may be referring to Hugo Steinhaus. He was a Polish-Jewish mathematician, which resorted to the ingenious method you sketch to estimate the casualties of the Nazis, while in hiding during WWII. What source I got this information from, I c... | Who estimated war casualties from tightly-controlled government news sources?
You may be referring to Hugo Steinhaus. He was a Polish-Jewish mathematician, which resorted to the ingenious method you sketch to estimate the casualties of the Nazis, while in hiding during WWII. Wh |
45,963 | Who estimated war casualties from tightly-controlled government news sources? | Adding to the answer by @F.Tusell: The english wikipedia article on Hugo Steinhaus contains
Also while in hiding, and cut off from reliable news on the course of the war, Steinhaus devised a statistical means of estimating for himself the German casualties at the front based on sporadic obituaries published in the loc... | Who estimated war casualties from tightly-controlled government news sources? | Adding to the answer by @F.Tusell: The english wikipedia article on Hugo Steinhaus contains
Also while in hiding, and cut off from reliable news on the course of the war, Steinhaus devised a statisti | Who estimated war casualties from tightly-controlled government news sources?
Adding to the answer by @F.Tusell: The english wikipedia article on Hugo Steinhaus contains
Also while in hiding, and cut off from reliable news on the course of the war, Steinhaus devised a statistical means of estimating for himself the Ge... | Who estimated war casualties from tightly-controlled government news sources?
Adding to the answer by @F.Tusell: The english wikipedia article on Hugo Steinhaus contains
Also while in hiding, and cut off from reliable news on the course of the war, Steinhaus devised a statisti |
45,964 | Coefficient of an Interaction Term when Regressors are Independent | Next to Dave's +1 numerical example, consider an applied one, explaining wages as a function of covariates like ability, gender etc.
It is well-documented that ability and gender both have an influence on wages (i.e., $\beta_1,\beta_2$ both are nonzero), because being more able is good for your earnings and there is su... | Coefficient of an Interaction Term when Regressors are Independent | Next to Dave's +1 numerical example, consider an applied one, explaining wages as a function of covariates like ability, gender etc.
It is well-documented that ability and gender both have an influenc | Coefficient of an Interaction Term when Regressors are Independent
Next to Dave's +1 numerical example, consider an applied one, explaining wages as a function of covariates like ability, gender etc.
It is well-documented that ability and gender both have an influence on wages (i.e., $\beta_1,\beta_2$ both are nonzero)... | Coefficient of an Interaction Term when Regressors are Independent
Next to Dave's +1 numerical example, consider an applied one, explaining wages as a function of covariates like ability, gender etc.
It is well-documented that ability and gender both have an influenc |
45,965 | Coefficient of an Interaction Term when Regressors are Independent | This is not correct, and it is possible to simulate a counterexample, such as with R code.
set.seed(2022)
x1 <- c(0,1,0,1,0,1,0,1)
x2 <- c(0,0,0,0,1,1,1,1)
y <- x1 + x2 + x1*x2 + rnorm(length(x1))
summary(lm(y ~ x1*x2))
This has independent $x_1$ and $x_2$ but also results in a nonzero coefficient on their interaction... | Coefficient of an Interaction Term when Regressors are Independent | This is not correct, and it is possible to simulate a counterexample, such as with R code.
set.seed(2022)
x1 <- c(0,1,0,1,0,1,0,1)
x2 <- c(0,0,0,0,1,1,1,1)
y <- x1 + x2 + x1*x2 + rnorm(length(x1))
sum | Coefficient of an Interaction Term when Regressors are Independent
This is not correct, and it is possible to simulate a counterexample, such as with R code.
set.seed(2022)
x1 <- c(0,1,0,1,0,1,0,1)
x2 <- c(0,0,0,0,1,1,1,1)
y <- x1 + x2 + x1*x2 + rnorm(length(x1))
summary(lm(y ~ x1*x2))
This has independent $x_1$ and $... | Coefficient of an Interaction Term when Regressors are Independent
This is not correct, and it is possible to simulate a counterexample, such as with R code.
set.seed(2022)
x1 <- c(0,1,0,1,0,1,0,1)
x2 <- c(0,0,0,0,1,1,1,1)
y <- x1 + x2 + x1*x2 + rnorm(length(x1))
sum |
45,966 | conceptual understanding of quadratic regression | The individual associations of your hours and hours2 with happiness are extremely weak in your example, and nothing completely "non-mathematical" can explain this. Maybe the following plot can help illustrate how multiple regression allows the predictor hours2 to improve on predictions based solely on hours.
The value... | conceptual understanding of quadratic regression | The individual associations of your hours and hours2 with happiness are extremely weak in your example, and nothing completely "non-mathematical" can explain this. Maybe the following plot can help il | conceptual understanding of quadratic regression
The individual associations of your hours and hours2 with happiness are extremely weak in your example, and nothing completely "non-mathematical" can explain this. Maybe the following plot can help illustrate how multiple regression allows the predictor hours2 to improve... | conceptual understanding of quadratic regression
The individual associations of your hours and hours2 with happiness are extremely weak in your example, and nothing completely "non-mathematical" can explain this. Maybe the following plot can help il |
45,967 | MLE for a modified German tank problem | Given your specified distributions, the marginal density of $X$ is:
$$\begin{align}
f_X(x)
&= \int \limits_0^a \text{N}(x |\mu,\sigma^2) \cdot \text{U}(\mu|0,a) \ d \mu \\[6pt]
&= \frac{1}{a} \int \limits_0^a \frac{1}{\sigma \sqrt{2 \pi}}
\exp \bigg( -\frac{1}{2} \bigg( \frac{x-\mu}{\sigma} \bigg)^2 \bigg) \ d \mu \... | MLE for a modified German tank problem | Given your specified distributions, the marginal density of $X$ is:
$$\begin{align}
f_X(x)
&= \int \limits_0^a \text{N}(x |\mu,\sigma^2) \cdot \text{U}(\mu|0,a) \ d \mu \\[6pt]
&= \frac{1}{a} \int \l | MLE for a modified German tank problem
Given your specified distributions, the marginal density of $X$ is:
$$\begin{align}
f_X(x)
&= \int \limits_0^a \text{N}(x |\mu,\sigma^2) \cdot \text{U}(\mu|0,a) \ d \mu \\[6pt]
&= \frac{1}{a} \int \limits_0^a \frac{1}{\sigma \sqrt{2 \pi}}
\exp \bigg( -\frac{1}{2} \bigg( \frac{x... | MLE for a modified German tank problem
Given your specified distributions, the marginal density of $X$ is:
$$\begin{align}
f_X(x)
&= \int \limits_0^a \text{N}(x |\mu,\sigma^2) \cdot \text{U}(\mu|0,a) \ d \mu \\[6pt]
&= \frac{1}{a} \int \l |
45,968 | In nonlinear regression, when is MLE equivalent to least squares regression? | By definition, the least squares estimator minimises the sum of the squared distances between the actual and predicted responses. With a set of simple steps, you can show that this estimator is equivalent to the solution of a certain maximisation problem. If we let $f$ denote the nonlinear regression function and let... | In nonlinear regression, when is MLE equivalent to least squares regression? | By definition, the least squares estimator minimises the sum of the squared distances between the actual and predicted responses. With a set of simple steps, you can show that this estimator is equiv | In nonlinear regression, when is MLE equivalent to least squares regression?
By definition, the least squares estimator minimises the sum of the squared distances between the actual and predicted responses. With a set of simple steps, you can show that this estimator is equivalent to the solution of a certain maximisa... | In nonlinear regression, when is MLE equivalent to least squares regression?
By definition, the least squares estimator minimises the sum of the squared distances between the actual and predicted responses. With a set of simple steps, you can show that this estimator is equiv |
45,969 | Potential outcomes selection bias | It's really important to distinguish the observed outome, $Y_i$, and the potential outcomes, $(Y_i(1), Y_i(0))$.
The observed outcomes are, well, simply the outcome you observed for each subject.
The potential outcomes are the outcomes that you would observe if a patient was given a certain treatment.
If you have two v... | Potential outcomes selection bias | It's really important to distinguish the observed outome, $Y_i$, and the potential outcomes, $(Y_i(1), Y_i(0))$.
The observed outcomes are, well, simply the outcome you observed for each subject.
The | Potential outcomes selection bias
It's really important to distinguish the observed outome, $Y_i$, and the potential outcomes, $(Y_i(1), Y_i(0))$.
The observed outcomes are, well, simply the outcome you observed for each subject.
The potential outcomes are the outcomes that you would observe if a patient was given a ce... | Potential outcomes selection bias
It's really important to distinguish the observed outome, $Y_i$, and the potential outcomes, $(Y_i(1), Y_i(0))$.
The observed outcomes are, well, simply the outcome you observed for each subject.
The |
45,970 | Potential outcomes selection bias | Just to build on @periwinkle answer, I want to emphasise that this equation is solved by an algebraic trick by adding $E[Y(0) | D = 1]$ twice. Professors do not make this clear enough. You see that often in math actually, the use of "tricks" to solve equations (for instance adding $\cdot1$ can help solve equations).
W... | Potential outcomes selection bias | Just to build on @periwinkle answer, I want to emphasise that this equation is solved by an algebraic trick by adding $E[Y(0) | D = 1]$ twice. Professors do not make this clear enough. You see that of | Potential outcomes selection bias
Just to build on @periwinkle answer, I want to emphasise that this equation is solved by an algebraic trick by adding $E[Y(0) | D = 1]$ twice. Professors do not make this clear enough. You see that often in math actually, the use of "tricks" to solve equations (for instance adding $\c... | Potential outcomes selection bias
Just to build on @periwinkle answer, I want to emphasise that this equation is solved by an algebraic trick by adding $E[Y(0) | D = 1]$ twice. Professors do not make this clear enough. You see that of |
45,971 | Stuck on Penney's game question | Appropriate diagrams make these results intuitive -- and they can even lead to exact calculations with little effort.
Probability flows like water (or any other conserved substance). After observing a sequence $\omega$ of coin tosses, its probability is split into two "flow channels" according to the chance of heads,... | Stuck on Penney's game question | Appropriate diagrams make these results intuitive -- and they can even lead to exact calculations with little effort.
Probability flows like water (or any other conserved substance). After observing | Stuck on Penney's game question
Appropriate diagrams make these results intuitive -- and they can even lead to exact calculations with little effort.
Probability flows like water (or any other conserved substance). After observing a sequence $\omega$ of coin tosses, its probability is split into two "flow channels" a... | Stuck on Penney's game question
Appropriate diagrams make these results intuitive -- and they can even lead to exact calculations with little effort.
Probability flows like water (or any other conserved substance). After observing |
45,972 | Stuck on Penney's game question | This type of problem relates to "string-counts", which in turn relate to deterministic finite automata (DFAs) for strings (see this related question). The simplest way to understand these problems is to construct a DFA for the "language" of interest in the problem (i.e., the set of strings being counted). In the figu... | Stuck on Penney's game question | This type of problem relates to "string-counts", which in turn relate to deterministic finite automata (DFAs) for strings (see this related question). The simplest way to understand these problems is | Stuck on Penney's game question
This type of problem relates to "string-counts", which in turn relate to deterministic finite automata (DFAs) for strings (see this related question). The simplest way to understand these problems is to construct a DFA for the "language" of interest in the problem (i.e., the set of stri... | Stuck on Penney's game question
This type of problem relates to "string-counts", which in turn relate to deterministic finite automata (DFAs) for strings (see this related question). The simplest way to understand these problems is |
45,973 | How to sample $n$ observations from a multinomial distribution using binomial (or poisson) sampling? | You can do it by progressing conditionally through the categories. I'm going to work from the last category backward (for a particular reason) but it can be done in any order as long as you're consistent in how you go about it.
Equal probability case:
Sample the count in the $n$-th category, $X_n\sim\text{bin}(n,\frac{... | How to sample $n$ observations from a multinomial distribution using binomial (or poisson) sampling? | You can do it by progressing conditionally through the categories. I'm going to work from the last category backward (for a particular reason) but it can be done in any order as long as you're consist | How to sample $n$ observations from a multinomial distribution using binomial (or poisson) sampling?
You can do it by progressing conditionally through the categories. I'm going to work from the last category backward (for a particular reason) but it can be done in any order as long as you're consistent in how you go a... | How to sample $n$ observations from a multinomial distribution using binomial (or poisson) sampling?
You can do it by progressing conditionally through the categories. I'm going to work from the last category backward (for a particular reason) but it can be done in any order as long as you're consist |
45,974 | Which class to define as positive in unbalanced classification | It does not matter. It is done that way because it would be something like disease detection where most people don’t have the disease, but that’s what you want to catch. However, all of the math works out fine either way. If you made the heathy class the $1$s, your model would be outputting the probability of being hea... | Which class to define as positive in unbalanced classification | It does not matter. It is done that way because it would be something like disease detection where most people don’t have the disease, but that’s what you want to catch. However, all of the math works | Which class to define as positive in unbalanced classification
It does not matter. It is done that way because it would be something like disease detection where most people don’t have the disease, but that’s what you want to catch. However, all of the math works out fine either way. If you made the heathy class the $1... | Which class to define as positive in unbalanced classification
It does not matter. It is done that way because it would be something like disease detection where most people don’t have the disease, but that’s what you want to catch. However, all of the math works |
45,975 | Which class to define as positive in unbalanced classification | @Dave's answer is that all classification algorithms are symmetrical in regard to which class is called positive and which is called negative, or which is assigned to 0 and which to 1. This is probably true in almost all cases, but maybe one. It is true for decision trees and ensembles of decision trees since the class... | Which class to define as positive in unbalanced classification | @Dave's answer is that all classification algorithms are symmetrical in regard to which class is called positive and which is called negative, or which is assigned to 0 and which to 1. This is probabl | Which class to define as positive in unbalanced classification
@Dave's answer is that all classification algorithms are symmetrical in regard to which class is called positive and which is called negative, or which is assigned to 0 and which to 1. This is probably true in almost all cases, but maybe one. It is true for... | Which class to define as positive in unbalanced classification
@Dave's answer is that all classification algorithms are symmetrical in regard to which class is called positive and which is called negative, or which is assigned to 0 and which to 1. This is probabl |
45,976 | Robust Variance Estimation in Bayesian Meta-analysis | The reviewer is correct in the sense that this model does not properly account for correlated sampling errors (when multiple effects are computed based on the same sample of subjects, then the sampling errors of the estimates are typically correlated). By adding random effects to your model, you are modeling potential ... | Robust Variance Estimation in Bayesian Meta-analysis | The reviewer is correct in the sense that this model does not properly account for correlated sampling errors (when multiple effects are computed based on the same sample of subjects, then the samplin | Robust Variance Estimation in Bayesian Meta-analysis
The reviewer is correct in the sense that this model does not properly account for correlated sampling errors (when multiple effects are computed based on the same sample of subjects, then the sampling errors of the estimates are typically correlated). By adding rand... | Robust Variance Estimation in Bayesian Meta-analysis
The reviewer is correct in the sense that this model does not properly account for correlated sampling errors (when multiple effects are computed based on the same sample of subjects, then the samplin |
45,977 | Robust Variance Estimation in Bayesian Meta-analysis | Please check this article by brms' author: https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0173660, where they say: "...outcomes reported by the same study were explicitly modeled as correlated. In the absence of any reported correlations in the primary studies, correlations were set to r = 0.7. To in... | Robust Variance Estimation in Bayesian Meta-analysis | Please check this article by brms' author: https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0173660, where they say: "...outcomes reported by the same study were explicitly modeled as | Robust Variance Estimation in Bayesian Meta-analysis
Please check this article by brms' author: https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0173660, where they say: "...outcomes reported by the same study were explicitly modeled as correlated. In the absence of any reported correlations in the pri... | Robust Variance Estimation in Bayesian Meta-analysis
Please check this article by brms' author: https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0173660, where they say: "...outcomes reported by the same study were explicitly modeled as |
45,978 | Converting a confidence interval into a credible interval | For so called location models, such as your linear regression, anovas etc., basically for models where the outcome depends linearly on the estimated parameters, the confidence interval will be the same as the credible interval with flat prior.
If you want to know how would that credible interval look like with a differ... | Converting a confidence interval into a credible interval | For so called location models, such as your linear regression, anovas etc., basically for models where the outcome depends linearly on the estimated parameters, the confidence interval will be the sam | Converting a confidence interval into a credible interval
For so called location models, such as your linear regression, anovas etc., basically for models where the outcome depends linearly on the estimated parameters, the confidence interval will be the same as the credible interval with flat prior.
If you want to kno... | Converting a confidence interval into a credible interval
For so called location models, such as your linear regression, anovas etc., basically for models where the outcome depends linearly on the estimated parameters, the confidence interval will be the sam |
45,979 | Converting a confidence interval into a credible interval | "But what if someone were to switch from a frequentist to a Bayesian viewpoint after constructing the CI and ask themselves the question: "How confident am I (i. e. at what rate would I - given that there is someone who knows μ and will reveal it at some point - be willing to bet) that this given CI contains μ knowing ... | Converting a confidence interval into a credible interval | "But what if someone were to switch from a frequentist to a Bayesian viewpoint after constructing the CI and ask themselves the question: "How confident am I (i. e. at what rate would I - given that t | Converting a confidence interval into a credible interval
"But what if someone were to switch from a frequentist to a Bayesian viewpoint after constructing the CI and ask themselves the question: "How confident am I (i. e. at what rate would I - given that there is someone who knows μ and will reveal it at some point -... | Converting a confidence interval into a credible interval
"But what if someone were to switch from a frequentist to a Bayesian viewpoint after constructing the CI and ask themselves the question: "How confident am I (i. e. at what rate would I - given that t |
45,980 | When there are more variables than observations do shrinkage methods (such as Ridge and Lasso) always find a solution? | Yes, $p>n, \lambda=0$ case is rank-deficient. Since you already know that OLS for $p>n$ is rank-deficient, then we can see that substituting $\lambda = 0$ in your equation gives the same objective as OLS, and the proof is complete.
Yes, ridge regression works for any $\lambda >0$. The immediate demonstration is that ... | When there are more variables than observations do shrinkage methods (such as Ridge and Lasso) alway | Yes, $p>n, \lambda=0$ case is rank-deficient. Since you already know that OLS for $p>n$ is rank-deficient, then we can see that substituting $\lambda = 0$ in your equation gives the same objective as | When there are more variables than observations do shrinkage methods (such as Ridge and Lasso) always find a solution?
Yes, $p>n, \lambda=0$ case is rank-deficient. Since you already know that OLS for $p>n$ is rank-deficient, then we can see that substituting $\lambda = 0$ in your equation gives the same objective as ... | When there are more variables than observations do shrinkage methods (such as Ridge and Lasso) alway
Yes, $p>n, \lambda=0$ case is rank-deficient. Since you already know that OLS for $p>n$ is rank-deficient, then we can see that substituting $\lambda = 0$ in your equation gives the same objective as |
45,981 | How to propagate measurement uncertainty in predictors *and* responses for multidimensional, non-parametric regression (and software to do it)? | One of the more interesting choices in R is rstan, where you could code this up yourself in the Stan modeling language (which tends to be amazing in that it can produce inference for models that we used to be unable to do for a long time). However, getting started can be a little challenging and it sounds like you'd li... | How to propagate measurement uncertainty in predictors *and* responses for multidimensional, non-par | One of the more interesting choices in R is rstan, where you could code this up yourself in the Stan modeling language (which tends to be amazing in that it can produce inference for models that we us | How to propagate measurement uncertainty in predictors *and* responses for multidimensional, non-parametric regression (and software to do it)?
One of the more interesting choices in R is rstan, where you could code this up yourself in the Stan modeling language (which tends to be amazing in that it can produce inferen... | How to propagate measurement uncertainty in predictors *and* responses for multidimensional, non-par
One of the more interesting choices in R is rstan, where you could code this up yourself in the Stan modeling language (which tends to be amazing in that it can produce inference for models that we us |
45,982 | What is the purpose of having multiple neurons in each layer? | Or is each neuron learning something else entirely?
This is the purpose, although I wouldn't say they learn entirely different things since they might have some correlation. Each neuron will have its own view of the data and produces outputs according to it. It's like multiple people from different perspectives lookin... | What is the purpose of having multiple neurons in each layer? | Or is each neuron learning something else entirely?
This is the purpose, although I wouldn't say they learn entirely different things since they might have some correlation. Each neuron will have its | What is the purpose of having multiple neurons in each layer?
Or is each neuron learning something else entirely?
This is the purpose, although I wouldn't say they learn entirely different things since they might have some correlation. Each neuron will have its own view of the data and produces outputs according to it... | What is the purpose of having multiple neurons in each layer?
Or is each neuron learning something else entirely?
This is the purpose, although I wouldn't say they learn entirely different things since they might have some correlation. Each neuron will have its |
45,983 | What is the purpose of having multiple neurons in each layer? | Neural network is basically a tensor function (tensors = scalars, vectors, matrices etc.). It takes stuff in (e.g. vector of some features), compoundly apply some operations like matrix multipication or activation functions, and produces stuff out (e.g. vector of probability distribution over some classes).
The term ne... | What is the purpose of having multiple neurons in each layer? | Neural network is basically a tensor function (tensors = scalars, vectors, matrices etc.). It takes stuff in (e.g. vector of some features), compoundly apply some operations like matrix multipication | What is the purpose of having multiple neurons in each layer?
Neural network is basically a tensor function (tensors = scalars, vectors, matrices etc.). It takes stuff in (e.g. vector of some features), compoundly apply some operations like matrix multipication or activation functions, and produces stuff out (e.g. vect... | What is the purpose of having multiple neurons in each layer?
Neural network is basically a tensor function (tensors = scalars, vectors, matrices etc.). It takes stuff in (e.g. vector of some features), compoundly apply some operations like matrix multipication |
45,984 | What is the purpose of having multiple neurons in each layer? | I think I have the answer having taken some time out.
When we run a neuron, it is a glorified $z=W.T*x +b$ followed by $sigmoid(z)$
As a result, the output is just a single value in a certain range. If a layer has 100 neurons, it has 100 such features.
When we cascade and add multiple layers, the output of $L1$ is the ... | What is the purpose of having multiple neurons in each layer? | I think I have the answer having taken some time out.
When we run a neuron, it is a glorified $z=W.T*x +b$ followed by $sigmoid(z)$
As a result, the output is just a single value in a certain range. I | What is the purpose of having multiple neurons in each layer?
I think I have the answer having taken some time out.
When we run a neuron, it is a glorified $z=W.T*x +b$ followed by $sigmoid(z)$
As a result, the output is just a single value in a certain range. If a layer has 100 neurons, it has 100 such features.
When ... | What is the purpose of having multiple neurons in each layer?
I think I have the answer having taken some time out.
When we run a neuron, it is a glorified $z=W.T*x +b$ followed by $sigmoid(z)$
As a result, the output is just a single value in a certain range. I |
45,985 | What is the purpose of having multiple neurons in each layer? | Expanding upon what @gunes said, if you take a shallow network and explicitly trace out what the network's forward pass is. You can see the adding of additional nodes (within a layer) allows the network to minimise its prediction error.
Let's assume we have some Feed-Forward Neural Network (FFNN) that takes in a single... | What is the purpose of having multiple neurons in each layer? | Expanding upon what @gunes said, if you take a shallow network and explicitly trace out what the network's forward pass is. You can see the adding of additional nodes (within a layer) allows the netwo | What is the purpose of having multiple neurons in each layer?
Expanding upon what @gunes said, if you take a shallow network and explicitly trace out what the network's forward pass is. You can see the adding of additional nodes (within a layer) allows the network to minimise its prediction error.
Let's assume we have ... | What is the purpose of having multiple neurons in each layer?
Expanding upon what @gunes said, if you take a shallow network and explicitly trace out what the network's forward pass is. You can see the adding of additional nodes (within a layer) allows the netwo |
45,986 | Quantitatively, how powerful is Shapiro-Wilk or other distribution-fit tests for small sample sizes? | What can be simulated is the power of the Shapiro-Wilk test for detecting specific non-normal distributions. This depends strongly on the exact distribution you want to detect. For this reason a plethora of results can be considered, and you can find examples for the test working well and not so well. (This means that ... | Quantitatively, how powerful is Shapiro-Wilk or other distribution-fit tests for small sample sizes? | What can be simulated is the power of the Shapiro-Wilk test for detecting specific non-normal distributions. This depends strongly on the exact distribution you want to detect. For this reason a pleth | Quantitatively, how powerful is Shapiro-Wilk or other distribution-fit tests for small sample sizes?
What can be simulated is the power of the Shapiro-Wilk test for detecting specific non-normal distributions. This depends strongly on the exact distribution you want to detect. For this reason a plethora of results can ... | Quantitatively, how powerful is Shapiro-Wilk or other distribution-fit tests for small sample sizes?
What can be simulated is the power of the Shapiro-Wilk test for detecting specific non-normal distributions. This depends strongly on the exact distribution you want to detect. For this reason a pleth |
45,987 | Quantitatively, how powerful is Shapiro-Wilk or other distribution-fit tests for small sample sizes? | You are asking for the probability of a "reasonable conclusion". You can get this if and only if you give a precise enough definition of a reasonable conclusion. I too would love a procedure that reliably tells me when deviation from normality is important enough to matter, but there is a gradation from sample sizes of... | Quantitatively, how powerful is Shapiro-Wilk or other distribution-fit tests for small sample sizes? | You are asking for the probability of a "reasonable conclusion". You can get this if and only if you give a precise enough definition of a reasonable conclusion. I too would love a procedure that reli | Quantitatively, how powerful is Shapiro-Wilk or other distribution-fit tests for small sample sizes?
You are asking for the probability of a "reasonable conclusion". You can get this if and only if you give a precise enough definition of a reasonable conclusion. I too would love a procedure that reliably tells me when ... | Quantitatively, how powerful is Shapiro-Wilk or other distribution-fit tests for small sample sizes?
You are asking for the probability of a "reasonable conclusion". You can get this if and only if you give a precise enough definition of a reasonable conclusion. I too would love a procedure that reli |
45,988 | Quantitatively, how powerful is Shapiro-Wilk or other distribution-fit tests for small sample sizes? | As you allude to when you bring up the use of graphical examination for this task of assessing normality, the answer is $0\%$ $\forall$ $n$. | Quantitatively, how powerful is Shapiro-Wilk or other distribution-fit tests for small sample sizes? | As you allude to when you bring up the use of graphical examination for this task of assessing normality, the answer is $0\%$ $\forall$ $n$. | Quantitatively, how powerful is Shapiro-Wilk or other distribution-fit tests for small sample sizes?
As you allude to when you bring up the use of graphical examination for this task of assessing normality, the answer is $0\%$ $\forall$ $n$. | Quantitatively, how powerful is Shapiro-Wilk or other distribution-fit tests for small sample sizes?
As you allude to when you bring up the use of graphical examination for this task of assessing normality, the answer is $0\%$ $\forall$ $n$. |
45,989 | Calculating the area under two overlapping distribution | The distributions $X\sim\mathsf{Norm}(100, 15)$ and $Y\sim\mathsf{Norm}(110,15)$ overlap, as in your figure.
The total overlap probability is
$$P(Y \le 125)+P(X> 125)\\ = P(Y \le 125) + 1 - P(X \le 125)\\
\approx 0.048 + 0.048 = 0.096.$$
R code for figure:
hdr="Densities of NORM(100,15) and NORM(150,15)"
curve(dnorm(x... | Calculating the area under two overlapping distribution | The distributions $X\sim\mathsf{Norm}(100, 15)$ and $Y\sim\mathsf{Norm}(110,15)$ overlap, as in your figure.
The total overlap probability is
$$P(Y \le 125)+P(X> 125)\\ = P(Y \le 125) + 1 - P(X \le 12 | Calculating the area under two overlapping distribution
The distributions $X\sim\mathsf{Norm}(100, 15)$ and $Y\sim\mathsf{Norm}(110,15)$ overlap, as in your figure.
The total overlap probability is
$$P(Y \le 125)+P(X> 125)\\ = P(Y \le 125) + 1 - P(X \le 125)\\
\approx 0.048 + 0.048 = 0.096.$$
R code for figure:
hdr="D... | Calculating the area under two overlapping distribution
The distributions $X\sim\mathsf{Norm}(100, 15)$ and $Y\sim\mathsf{Norm}(110,15)$ overlap, as in your figure.
The total overlap probability is
$$P(Y \le 125)+P(X> 125)\\ = P(Y \le 125) + 1 - P(X \le 12 |
45,990 | Calculating the area under two overlapping distribution | Perhaps this is a more general solution than @BruceET's which doesn't assume normality or a preset reference point P. The OP says s/he has the PDF of the two distributions, so for example these may be:
pdf1 <- function(x, mean= 100, sd= 15) {
pdf <- (1 / (sd * sqrt(2 * pi))) * exp(-0.5 * ((x - mean)/sd)^2)
retu... | Calculating the area under two overlapping distribution | Perhaps this is a more general solution than @BruceET's which doesn't assume normality or a preset reference point P. The OP says s/he has the PDF of the two distributions, so for example these may be | Calculating the area under two overlapping distribution
Perhaps this is a more general solution than @BruceET's which doesn't assume normality or a preset reference point P. The OP says s/he has the PDF of the two distributions, so for example these may be:
pdf1 <- function(x, mean= 100, sd= 15) {
pdf <- (1 / (sd *... | Calculating the area under two overlapping distribution
Perhaps this is a more general solution than @BruceET's which doesn't assume normality or a preset reference point P. The OP says s/he has the PDF of the two distributions, so for example these may be |
45,991 | Skewness of lognormal distribution | When a variable $X$ has a Normal distribution with mean $\mu$ and standard deviation $\sigma \gt 0,$ we say that $Z=e^X$ has a Lognormal$(\mu,\sigma)$ distribution.
The laws of logarithms show that $\mu$ (an additive location parameter for the Normal family of distributions) determines the scale of $Z.$ Because the sk... | Skewness of lognormal distribution | When a variable $X$ has a Normal distribution with mean $\mu$ and standard deviation $\sigma \gt 0,$ we say that $Z=e^X$ has a Lognormal$(\mu,\sigma)$ distribution.
The laws of logarithms show that $\ | Skewness of lognormal distribution
When a variable $X$ has a Normal distribution with mean $\mu$ and standard deviation $\sigma \gt 0,$ we say that $Z=e^X$ has a Lognormal$(\mu,\sigma)$ distribution.
The laws of logarithms show that $\mu$ (an additive location parameter for the Normal family of distributions) determine... | Skewness of lognormal distribution
When a variable $X$ has a Normal distribution with mean $\mu$ and standard deviation $\sigma \gt 0,$ we say that $Z=e^X$ has a Lognormal$(\mu,\sigma)$ distribution.
The laws of logarithms show that $\ |
45,992 | Justifying the Need for Mixed Effects Models (aka. LME, MLM, etc.) | First of all, I agree with @EdM, you should first think if multilevel models in substantive terms instead of only looking for a statistical significance in model comparisons. But you may ask: how to do so? Well, asking yourself a few questions about your research hypothesis might help. Is it important to your research:... | Justifying the Need for Mixed Effects Models (aka. LME, MLM, etc.) | First of all, I agree with @EdM, you should first think if multilevel models in substantive terms instead of only looking for a statistical significance in model comparisons. But you may ask: how to d | Justifying the Need for Mixed Effects Models (aka. LME, MLM, etc.)
First of all, I agree with @EdM, you should first think if multilevel models in substantive terms instead of only looking for a statistical significance in model comparisons. But you may ask: how to do so? Well, asking yourself a few questions about you... | Justifying the Need for Mixed Effects Models (aka. LME, MLM, etc.)
First of all, I agree with @EdM, you should first think if multilevel models in substantive terms instead of only looking for a statistical significance in model comparisons. But you may ask: how to d |
45,993 | Justifying the Need for Mixed Effects Models (aka. LME, MLM, etc.) | What you are testing for is the statistical "significance" of the random effect terms. As is so often the case in statistics, that can be a good deal different from their "importance." Note this part of the answer to one of the questions that you have read:
Random effects are typically included to account for the corr... | Justifying the Need for Mixed Effects Models (aka. LME, MLM, etc.) | What you are testing for is the statistical "significance" of the random effect terms. As is so often the case in statistics, that can be a good deal different from their "importance." Note this part | Justifying the Need for Mixed Effects Models (aka. LME, MLM, etc.)
What you are testing for is the statistical "significance" of the random effect terms. As is so often the case in statistics, that can be a good deal different from their "importance." Note this part of the answer to one of the questions that you have r... | Justifying the Need for Mixed Effects Models (aka. LME, MLM, etc.)
What you are testing for is the statistical "significance" of the random effect terms. As is so often the case in statistics, that can be a good deal different from their "importance." Note this part |
45,994 | What is the intuitive difference between Wasserstein-1 distance and Wasserstein-2 distance? | The answer boils down to the difference between the distance and its squared value. Assume we use the euclidean distance, and imagine we want to transform a histogram $P_S$ whose bins are $x\in \mathbb{R}^m$ to another histogram $P_T$ with bins $y \in \mathbb{R}^n$. The $W_1$ and $W_2$ distances between the two histogr... | What is the intuitive difference between Wasserstein-1 distance and Wasserstein-2 distance? | The answer boils down to the difference between the distance and its squared value. Assume we use the euclidean distance, and imagine we want to transform a histogram $P_S$ whose bins are $x\in \mathb | What is the intuitive difference between Wasserstein-1 distance and Wasserstein-2 distance?
The answer boils down to the difference between the distance and its squared value. Assume we use the euclidean distance, and imagine we want to transform a histogram $P_S$ whose bins are $x\in \mathbb{R}^m$ to another histogram... | What is the intuitive difference between Wasserstein-1 distance and Wasserstein-2 distance?
The answer boils down to the difference between the distance and its squared value. Assume we use the euclidean distance, and imagine we want to transform a histogram $P_S$ whose bins are $x\in \mathb |
45,995 | Why GEE estimates are smaller than GLMM? | This actually depends on the link function -- eg, for a log link there is not a systematic difference, but for a logit link there is.
The reason is that the models are systematically different and the marginal likelihoods are systematically different. As the simplest example consider a logistic GLMM with a random inte... | Why GEE estimates are smaller than GLMM? | This actually depends on the link function -- eg, for a log link there is not a systematic difference, but for a logit link there is.
The reason is that the models are systematically different and the | Why GEE estimates are smaller than GLMM?
This actually depends on the link function -- eg, for a log link there is not a systematic difference, but for a logit link there is.
The reason is that the models are systematically different and the marginal likelihoods are systematically different. As the simplest example co... | Why GEE estimates are smaller than GLMM?
This actually depends on the link function -- eg, for a log link there is not a systematic difference, but for a logit link there is.
The reason is that the models are systematically different and the |
45,996 | Meaning of the value matrix in self-attention | Because Transformers are black-box models, it is hard to say, what the keys and values really are, but the motivation is that might want to retrieve something else than what is your search criterion.
Imagine something like SQL-like query: get phone numbers of people that have a similar name to "Jindrich". "Jindrich" is... | Meaning of the value matrix in self-attention | Because Transformers are black-box models, it is hard to say, what the keys and values really are, but the motivation is that might want to retrieve something else than what is your search criterion.
| Meaning of the value matrix in self-attention
Because Transformers are black-box models, it is hard to say, what the keys and values really are, but the motivation is that might want to retrieve something else than what is your search criterion.
Imagine something like SQL-like query: get phone numbers of people that ha... | Meaning of the value matrix in self-attention
Because Transformers are black-box models, it is hard to say, what the keys and values really are, but the motivation is that might want to retrieve something else than what is your search criterion.
|
45,997 | Meaning of the value matrix in self-attention | K_V takes the word (or word-part, but let's assume whole words from this discussion) in embedded space, and changes it.
Learning K_V means learning how to change this embedded representation into another embedded representation.
In a sense, what you are asking is "why should we learn how to change the embedding of the ... | Meaning of the value matrix in self-attention | K_V takes the word (or word-part, but let's assume whole words from this discussion) in embedded space, and changes it.
Learning K_V means learning how to change this embedded representation into anot | Meaning of the value matrix in self-attention
K_V takes the word (or word-part, but let's assume whole words from this discussion) in embedded space, and changes it.
Learning K_V means learning how to change this embedded representation into another embedded representation.
In a sense, what you are asking is "why shoul... | Meaning of the value matrix in self-attention
K_V takes the word (or word-part, but let's assume whole words from this discussion) in embedded space, and changes it.
Learning K_V means learning how to change this embedded representation into anot |
45,998 | Normality test for discrete values of a continuous variable | When you have many observations like the hundreds that you have, a goodness-of-fit test is going to pick up on subtle deviations that are unlikely to interest you.
You’re right: because of the discreteness of the measurements,$^{\dagger}$ your data cannot be normal, and your test is confirming that your data are not fr... | Normality test for discrete values of a continuous variable | When you have many observations like the hundreds that you have, a goodness-of-fit test is going to pick up on subtle deviations that are unlikely to interest you.
You’re right: because of the discret | Normality test for discrete values of a continuous variable
When you have many observations like the hundreds that you have, a goodness-of-fit test is going to pick up on subtle deviations that are unlikely to interest you.
You’re right: because of the discreteness of the measurements,$^{\dagger}$ your data cannot be n... | Normality test for discrete values of a continuous variable
When you have many observations like the hundreds that you have, a goodness-of-fit test is going to pick up on subtle deviations that are unlikely to interest you.
You’re right: because of the discret |
45,999 | How to show that a random factor is not needed in the model? | I have fitted a model to your data using the mixed_model function from the GLMMadaptive package without receiving any error or warning, and compared the output to that produced by glmer(with the singular fit):
(data is available here )
> library(lme4)
> library(GLMMadaptive)
> dt <- read.csv("PilotDataStacked-results.... | How to show that a random factor is not needed in the model? | I have fitted a model to your data using the mixed_model function from the GLMMadaptive package without receiving any error or warning, and compared the output to that produced by glmer(with the singu | How to show that a random factor is not needed in the model?
I have fitted a model to your data using the mixed_model function from the GLMMadaptive package without receiving any error or warning, and compared the output to that produced by glmer(with the singular fit):
(data is available here )
> library(lme4)
> libra... | How to show that a random factor is not needed in the model?
I have fitted a model to your data using the mixed_model function from the GLMMadaptive package without receiving any error or warning, and compared the output to that produced by glmer(with the singu |
46,000 | When do we use a multivariate regression? | The multivariate regression can take into account potential dependence between the two dependent (response) variables. Running two regressions separately cannot. | When do we use a multivariate regression? | The multivariate regression can take into account potential dependence between the two dependent (response) variables. Running two regressions separately cannot. | When do we use a multivariate regression?
The multivariate regression can take into account potential dependence between the two dependent (response) variables. Running two regressions separately cannot. | When do we use a multivariate regression?
The multivariate regression can take into account potential dependence between the two dependent (response) variables. Running two regressions separately cannot. |
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