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 |
|---|---|---|---|---|---|---|
37,101 | What are the consequences of not including random effects in a linear model when they should be added? | There are 2 questions here:
...the population level predictions (based on the fixed effects coefficients) are virtually identical between these two models (standard vs. mixed). Interestingly, however, the Beta coefficients are rather different...
I find this hard to understand. If there are multiple predictors, it mi... | What are the consequences of not including random effects in a linear model when they should be adde | There are 2 questions here:
...the population level predictions (based on the fixed effects coefficients) are virtually identical between these two models (standard vs. mixed). Interestingly, however | What are the consequences of not including random effects in a linear model when they should be added?
There are 2 questions here:
...the population level predictions (based on the fixed effects coefficients) are virtually identical between these two models (standard vs. mixed). Interestingly, however, the Beta coeffi... | What are the consequences of not including random effects in a linear model when they should be adde
There are 2 questions here:
...the population level predictions (based on the fixed effects coefficients) are virtually identical between these two models (standard vs. mixed). Interestingly, however |
37,102 | Can negative autocorrelation at lags 1 and 2 happen? | The following DGP, an MA($2$) process, has negative autocorrelation at lags 1 and 2:
$$
Y_t=10-.5\cdot u_{t-1}-.25\cdot u_{t-2}+u_t
$$
Here's some R code to simulate the DGP and see the ACF for yourself:
library(stats)
library(forecast) # for the Acf() function
# number of "observations"
n<-500
# initialization perio... | Can negative autocorrelation at lags 1 and 2 happen? | The following DGP, an MA($2$) process, has negative autocorrelation at lags 1 and 2:
$$
Y_t=10-.5\cdot u_{t-1}-.25\cdot u_{t-2}+u_t
$$
Here's some R code to simulate the DGP and see the ACF for yourse | Can negative autocorrelation at lags 1 and 2 happen?
The following DGP, an MA($2$) process, has negative autocorrelation at lags 1 and 2:
$$
Y_t=10-.5\cdot u_{t-1}-.25\cdot u_{t-2}+u_t
$$
Here's some R code to simulate the DGP and see the ACF for yourself:
library(stats)
library(forecast) # for the Acf() function
# nu... | Can negative autocorrelation at lags 1 and 2 happen?
The following DGP, an MA($2$) process, has negative autocorrelation at lags 1 and 2:
$$
Y_t=10-.5\cdot u_{t-1}-.25\cdot u_{t-2}+u_t
$$
Here's some R code to simulate the DGP and see the ACF for yourse |
37,103 | What's the difference between exogenous variables and independent variables? | An independent variable is defined within the context of a dependent variable. In the context of a model the independent variables are input whereas the dependent variables are the targets (Input vs Output).
An exogenous variable is a variable whose state is independent of the state of other variables in a system.
To ... | What's the difference between exogenous variables and independent variables? | An independent variable is defined within the context of a dependent variable. In the context of a model the independent variables are input whereas the dependent variables are the targets (Input vs O | What's the difference between exogenous variables and independent variables?
An independent variable is defined within the context of a dependent variable. In the context of a model the independent variables are input whereas the dependent variables are the targets (Input vs Output).
An exogenous variable is a variable... | What's the difference between exogenous variables and independent variables?
An independent variable is defined within the context of a dependent variable. In the context of a model the independent variables are input whereas the dependent variables are the targets (Input vs O |
37,104 | Regression random forest and highly skewed response distribution | One might argue that this is a classification problem with a small rounding error rather than a regression design. RF is often referred to as resilient in dealing with skewness issues but it is not invincible. In this case, chances are almost none of the positive responses would make it into each small tree being grown... | Regression random forest and highly skewed response distribution | One might argue that this is a classification problem with a small rounding error rather than a regression design. RF is often referred to as resilient in dealing with skewness issues but it is not in | Regression random forest and highly skewed response distribution
One might argue that this is a classification problem with a small rounding error rather than a regression design. RF is often referred to as resilient in dealing with skewness issues but it is not invincible. In this case, chances are almost none of the ... | Regression random forest and highly skewed response distribution
One might argue that this is a classification problem with a small rounding error rather than a regression design. RF is often referred to as resilient in dealing with skewness issues but it is not in |
37,105 | Confidence interval for xgb-forecast | So, this is the answer! (mirror)
To build confidence limits for abnormally distributed data, you first need to build a quantile regression, rather than a linear regression, as it does by default.
For this it is necessary, using the derived derivatives from the article or simply copying the code on the python, to custo... | Confidence interval for xgb-forecast | So, this is the answer! (mirror)
To build confidence limits for abnormally distributed data, you first need to build a quantile regression, rather than a linear regression, as it does by default.
For | Confidence interval for xgb-forecast
So, this is the answer! (mirror)
To build confidence limits for abnormally distributed data, you first need to build a quantile regression, rather than a linear regression, as it does by default.
For this it is necessary, using the derived derivatives from the article or simply cop... | Confidence interval for xgb-forecast
So, this is the answer! (mirror)
To build confidence limits for abnormally distributed data, you first need to build a quantile regression, rather than a linear regression, as it does by default.
For |
37,106 | How to test for goodness of fit for a logistic regression model? | You are on the right track, ROC is a common error measure for logistic regression models. More often, the Area Under The Receiver Operating Curve (AUROC) is used. The advantage is that this measure is numeric and can be compared to other validation runs / model setups of your logistic regression.
You can, for example, ... | How to test for goodness of fit for a logistic regression model? | You are on the right track, ROC is a common error measure for logistic regression models. More often, the Area Under The Receiver Operating Curve (AUROC) is used. The advantage is that this measure is | How to test for goodness of fit for a logistic regression model?
You are on the right track, ROC is a common error measure for logistic regression models. More often, the Area Under The Receiver Operating Curve (AUROC) is used. The advantage is that this measure is numeric and can be compared to other validation runs /... | How to test for goodness of fit for a logistic regression model?
You are on the right track, ROC is a common error measure for logistic regression models. More often, the Area Under The Receiver Operating Curve (AUROC) is used. The advantage is that this measure is |
37,107 | Boxplot for data with a large number of zero values | You can use violin plots and logarithmic transformation (of course you should add some constant to avoid $log(0)$) to compare the distributions and their quantiles at different levels of some factor.
For the sake of illustration please see below zero-inflated data of the number of the cod parasite (A Beginner’s Guide t... | Boxplot for data with a large number of zero values | You can use violin plots and logarithmic transformation (of course you should add some constant to avoid $log(0)$) to compare the distributions and their quantiles at different levels of some factor.
| Boxplot for data with a large number of zero values
You can use violin plots and logarithmic transformation (of course you should add some constant to avoid $log(0)$) to compare the distributions and their quantiles at different levels of some factor.
For the sake of illustration please see below zero-inflated data of ... | Boxplot for data with a large number of zero values
You can use violin plots and logarithmic transformation (of course you should add some constant to avoid $log(0)$) to compare the distributions and their quantiles at different levels of some factor.
|
37,108 | How to determine appropriate lagged features for learning systems with states? | If we want to to look at lags over a long time in the past (or features derived from them like exponential moving averages or interactions between them) then there would be a large number of feature candidates. As you correctly mentioned a grid search would be expensive, even if you want to train a simple linear regres... | How to determine appropriate lagged features for learning systems with states? | If we want to to look at lags over a long time in the past (or features derived from them like exponential moving averages or interactions between them) then there would be a large number of feature c | How to determine appropriate lagged features for learning systems with states?
If we want to to look at lags over a long time in the past (or features derived from them like exponential moving averages or interactions between them) then there would be a large number of feature candidates. As you correctly mentioned a g... | How to determine appropriate lagged features for learning systems with states?
If we want to to look at lags over a long time in the past (or features derived from them like exponential moving averages or interactions between them) then there would be a large number of feature c |
37,109 | How to determine appropriate lagged features for learning systems with states? | you could just create an instantaneous model, and you'd get OK
first-approximation results
Have you heard of Recurrent Neural Networks aka RNNs? The state parameter holds information about the past and can theoretically have infinite memory (though in practice that's not always the best configuration). Check out the... | How to determine appropriate lagged features for learning systems with states? | you could just create an instantaneous model, and you'd get OK
first-approximation results
Have you heard of Recurrent Neural Networks aka RNNs? The state parameter holds information about the past | How to determine appropriate lagged features for learning systems with states?
you could just create an instantaneous model, and you'd get OK
first-approximation results
Have you heard of Recurrent Neural Networks aka RNNs? The state parameter holds information about the past and can theoretically have infinite memo... | How to determine appropriate lagged features for learning systems with states?
you could just create an instantaneous model, and you'd get OK
first-approximation results
Have you heard of Recurrent Neural Networks aka RNNs? The state parameter holds information about the past |
37,110 | How to determine appropriate lagged features for learning systems with states? | I tend to fall back on a pretty standard answer for this: what does your theory suggest? Should rain from a month ago actually impact streamflow? A year ago? A decade? 10 minutes? Surely there is some soil research (it's a thing, I have a family member that studied it!) that gives some hints about this.
If you're simp... | How to determine appropriate lagged features for learning systems with states? | I tend to fall back on a pretty standard answer for this: what does your theory suggest? Should rain from a month ago actually impact streamflow? A year ago? A decade? 10 minutes? Surely there is some | How to determine appropriate lagged features for learning systems with states?
I tend to fall back on a pretty standard answer for this: what does your theory suggest? Should rain from a month ago actually impact streamflow? A year ago? A decade? 10 minutes? Surely there is some soil research (it's a thing, I have a fa... | How to determine appropriate lagged features for learning systems with states?
I tend to fall back on a pretty standard answer for this: what does your theory suggest? Should rain from a month ago actually impact streamflow? A year ago? A decade? 10 minutes? Surely there is some |
37,111 | Textbooks about reproducing kernel Hilbert space approach to machine learning? | The best and standard reference will be
Aronszajn, Nachman. "Theory of reproducing kernels." Transactions of
the American mathematical society 68.3 (1950): 337-404.
I am not sure how deep you know about functional analysis, different levels of functional analysis has great difference. So I will say another standar... | Textbooks about reproducing kernel Hilbert space approach to machine learning? | The best and standard reference will be
Aronszajn, Nachman. "Theory of reproducing kernels." Transactions of
the American mathematical society 68.3 (1950): 337-404.
I am not sure how deep you kno | Textbooks about reproducing kernel Hilbert space approach to machine learning?
The best and standard reference will be
Aronszajn, Nachman. "Theory of reproducing kernels." Transactions of
the American mathematical society 68.3 (1950): 337-404.
I am not sure how deep you know about functional analysis, different le... | Textbooks about reproducing kernel Hilbert space approach to machine learning?
The best and standard reference will be
Aronszajn, Nachman. "Theory of reproducing kernels." Transactions of
the American mathematical society 68.3 (1950): 337-404.
I am not sure how deep you kno |
37,112 | Should we account for the intercept term when kernelizing algorithms? | Partial answer:
Focusing on SVMs for a while, I got to this reference (pointed by @DikranMarsupial in Bias term in support vector machine):
Poggio, T., Mukherjee, S., Rifkin, R., & Rakhlin, A. (2001). Verri, A.
b. In Proceedings of the Conference on Uncertainty in Geometric
Computations.
Excerpt:
This paper is ... | Should we account for the intercept term when kernelizing algorithms? | Partial answer:
Focusing on SVMs for a while, I got to this reference (pointed by @DikranMarsupial in Bias term in support vector machine):
Poggio, T., Mukherjee, S., Rifkin, R., & Rakhlin, A. (2001) | Should we account for the intercept term when kernelizing algorithms?
Partial answer:
Focusing on SVMs for a while, I got to this reference (pointed by @DikranMarsupial in Bias term in support vector machine):
Poggio, T., Mukherjee, S., Rifkin, R., & Rakhlin, A. (2001). Verri, A.
b. In Proceedings of the Conference ... | Should we account for the intercept term when kernelizing algorithms?
Partial answer:
Focusing on SVMs for a while, I got to this reference (pointed by @DikranMarsupial in Bias term in support vector machine):
Poggio, T., Mukherjee, S., Rifkin, R., & Rakhlin, A. (2001) |
37,113 | Why is blocking necessary in experimental design if we already perform random assignment? | Well, if you have small number of experimental runs, then the random assignment could well make some variable poorly balanced between the experimental and control groups. By using blocking you avoid that.
Another idea with blocking is that it makes it possible to on purpose use inhomogeneous experimental material, be... | Why is blocking necessary in experimental design if we already perform random assignment? | Well, if you have small number of experimental runs, then the random assignment could well make some variable poorly balanced between the experimental and control groups. By using blocking you avoid | Why is blocking necessary in experimental design if we already perform random assignment?
Well, if you have small number of experimental runs, then the random assignment could well make some variable poorly balanced between the experimental and control groups. By using blocking you avoid that.
Another idea with block... | Why is blocking necessary in experimental design if we already perform random assignment?
Well, if you have small number of experimental runs, then the random assignment could well make some variable poorly balanced between the experimental and control groups. By using blocking you avoid |
37,114 | Is it ok to decrease the size of a dataset to speedup hyperparameters search? | Depends. In your case, most probably yes
The hyper-parameters do not depend too strongly on the amount of data (as long as you have "enough") but on the complexity of the data (resp. its distribution). Reducing a dataset can mean to "change" the distribution of the data caused by statistical fluctuations.
On big datase... | Is it ok to decrease the size of a dataset to speedup hyperparameters search? | Depends. In your case, most probably yes
The hyper-parameters do not depend too strongly on the amount of data (as long as you have "enough") but on the complexity of the data (resp. its distribution) | Is it ok to decrease the size of a dataset to speedup hyperparameters search?
Depends. In your case, most probably yes
The hyper-parameters do not depend too strongly on the amount of data (as long as you have "enough") but on the complexity of the data (resp. its distribution). Reducing a dataset can mean to "change" ... | Is it ok to decrease the size of a dataset to speedup hyperparameters search?
Depends. In your case, most probably yes
The hyper-parameters do not depend too strongly on the amount of data (as long as you have "enough") but on the complexity of the data (resp. its distribution) |
37,115 | Differences between linear and canonical discriminant analyses (LDA and CDA) | These are two names for the same thing.
Linear discriminant analysis (LDA) is called a lot of different names. I have seen
canonical discriminant analysis
canonical linear discriminant analysis
descriptive discriminant analysis (see What is "Descriptive Discriminant Analysis"?)
Fisher's discriminant analysis
and poss... | Differences between linear and canonical discriminant analyses (LDA and CDA) | These are two names for the same thing.
Linear discriminant analysis (LDA) is called a lot of different names. I have seen
canonical discriminant analysis
canonical linear discriminant analysis
descr | Differences between linear and canonical discriminant analyses (LDA and CDA)
These are two names for the same thing.
Linear discriminant analysis (LDA) is called a lot of different names. I have seen
canonical discriminant analysis
canonical linear discriminant analysis
descriptive discriminant analysis (see What is "... | Differences between linear and canonical discriminant analyses (LDA and CDA)
These are two names for the same thing.
Linear discriminant analysis (LDA) is called a lot of different names. I have seen
canonical discriminant analysis
canonical linear discriminant analysis
descr |
37,116 | How to express cells of a 2x2 table in terms of phi coefficient and marginal probabilities | We easily recognize every factor in the denominator of $\phi$, because $a+b=1-\mu_R$ and $a+c=1-\mu_C$. Let's therefore start with a tiny simplification to avoid writing lots of square roots:
$$\Delta=ad - bc = \phi \sqrt{\mu_R(1-\mu_R)\mu_C(1-\mu_C)}.$$
Let's find $d$:
$$\eqalign{d &= (1)d = (a+b+c+d)d = ad +bd +cd +... | How to express cells of a 2x2 table in terms of phi coefficient and marginal probabilities | We easily recognize every factor in the denominator of $\phi$, because $a+b=1-\mu_R$ and $a+c=1-\mu_C$. Let's therefore start with a tiny simplification to avoid writing lots of square roots:
$$\Delt | How to express cells of a 2x2 table in terms of phi coefficient and marginal probabilities
We easily recognize every factor in the denominator of $\phi$, because $a+b=1-\mu_R$ and $a+c=1-\mu_C$. Let's therefore start with a tiny simplification to avoid writing lots of square roots:
$$\Delta=ad - bc = \phi \sqrt{\mu_R(... | How to express cells of a 2x2 table in terms of phi coefficient and marginal probabilities
We easily recognize every factor in the denominator of $\phi$, because $a+b=1-\mu_R$ and $a+c=1-\mu_C$. Let's therefore start with a tiny simplification to avoid writing lots of square roots:
$$\Delt |
37,117 | Why are standard errors downward biased when considering weak instruments | See slides 8 and 9 of these notes. In a simplified setting,
$$y=\beta_{0}+\beta_{1}x + u$$
where $\text{Cov}(x,u) \ne 0$ but $z$ is a valid instrument for $x$, the estimated variance for $\hat{\beta_{1}}$ is the OLS estimated variance divided by the $R^2$ from the first-stage regression of $x$ on $z$. As long as $R^2 <... | Why are standard errors downward biased when considering weak instruments | See slides 8 and 9 of these notes. In a simplified setting,
$$y=\beta_{0}+\beta_{1}x + u$$
where $\text{Cov}(x,u) \ne 0$ but $z$ is a valid instrument for $x$, the estimated variance for $\hat{\beta_{ | Why are standard errors downward biased when considering weak instruments
See slides 8 and 9 of these notes. In a simplified setting,
$$y=\beta_{0}+\beta_{1}x + u$$
where $\text{Cov}(x,u) \ne 0$ but $z$ is a valid instrument for $x$, the estimated variance for $\hat{\beta_{1}}$ is the OLS estimated variance divided by ... | Why are standard errors downward biased when considering weak instruments
See slides 8 and 9 of these notes. In a simplified setting,
$$y=\beta_{0}+\beta_{1}x + u$$
where $\text{Cov}(x,u) \ne 0$ but $z$ is a valid instrument for $x$, the estimated variance for $\hat{\beta_{ |
37,118 | outlier detection: area under precision recall curve | The problem is with your example that it is possible to have zero $tp$ and zero $fp$, therefore the precision $prec = tp/(tp+fp)$ becomes undefined because we divide by zero. Because of this the PR curve only contains points for one $x$-value, and therefore the area under the PR curve becomes zero for your example.
You... | outlier detection: area under precision recall curve | The problem is with your example that it is possible to have zero $tp$ and zero $fp$, therefore the precision $prec = tp/(tp+fp)$ becomes undefined because we divide by zero. Because of this the PR cu | outlier detection: area under precision recall curve
The problem is with your example that it is possible to have zero $tp$ and zero $fp$, therefore the precision $prec = tp/(tp+fp)$ becomes undefined because we divide by zero. Because of this the PR curve only contains points for one $x$-value, and therefore the area ... | outlier detection: area under precision recall curve
The problem is with your example that it is possible to have zero $tp$ and zero $fp$, therefore the precision $prec = tp/(tp+fp)$ becomes undefined because we divide by zero. Because of this the PR cu |
37,119 | Why the focus on variance reduction for $R^2$? | There is nothing inherently wrong with measuring goodness-of-fit in a regression model with other monotonic transforms of the coefficient of determination, and indeed, there are several natural transformations that have useful interpretations. Before getting to these, it is useful to note the desirable mathematical pr... | Why the focus on variance reduction for $R^2$? | There is nothing inherently wrong with measuring goodness-of-fit in a regression model with other monotonic transforms of the coefficient of determination, and indeed, there are several natural transf | Why the focus on variance reduction for $R^2$?
There is nothing inherently wrong with measuring goodness-of-fit in a regression model with other monotonic transforms of the coefficient of determination, and indeed, there are several natural transformations that have useful interpretations. Before getting to these, it ... | Why the focus on variance reduction for $R^2$?
There is nothing inherently wrong with measuring goodness-of-fit in a regression model with other monotonic transforms of the coefficient of determination, and indeed, there are several natural transf |
37,120 | Why the focus on variance reduction for $R^2$? | Particularly for a class for non-majors, it's probably fine. Most likely your students think of standard deviation whenever you mention variance, anyway.
It also makes sense to me. The goal of regression is to reduce the variability. Sure, the variability of human height is quite large, but when you account for age and... | Why the focus on variance reduction for $R^2$? | Particularly for a class for non-majors, it's probably fine. Most likely your students think of standard deviation whenever you mention variance, anyway.
It also makes sense to me. The goal of regress | Why the focus on variance reduction for $R^2$?
Particularly for a class for non-majors, it's probably fine. Most likely your students think of standard deviation whenever you mention variance, anyway.
It also makes sense to me. The goal of regression is to reduce the variability. Sure, the variability of human height i... | Why the focus on variance reduction for $R^2$?
Particularly for a class for non-majors, it's probably fine. Most likely your students think of standard deviation whenever you mention variance, anyway.
It also makes sense to me. The goal of regress |
37,121 | Why the focus on variance reduction for $R^2$? | If $X_1,\ldots,X_n$ are independent random variables then
$$
\operatorname{var}(X_1+\cdots+X_n) = \operatorname{var}(X_1)+\cdots+\operatorname{var}(X_n).
$$
Other measures of dispersion, including standard deviation and mean absolute deviation, lack this property.
If follows that
\begin{align}
& \Big(\text{explained pa... | Why the focus on variance reduction for $R^2$? | If $X_1,\ldots,X_n$ are independent random variables then
$$
\operatorname{var}(X_1+\cdots+X_n) = \operatorname{var}(X_1)+\cdots+\operatorname{var}(X_n).
$$
Other measures of dispersion, including sta | Why the focus on variance reduction for $R^2$?
If $X_1,\ldots,X_n$ are independent random variables then
$$
\operatorname{var}(X_1+\cdots+X_n) = \operatorname{var}(X_1)+\cdots+\operatorname{var}(X_n).
$$
Other measures of dispersion, including standard deviation and mean absolute deviation, lack this property.
If follo... | Why the focus on variance reduction for $R^2$?
If $X_1,\ldots,X_n$ are independent random variables then
$$
\operatorname{var}(X_1+\cdots+X_n) = \operatorname{var}(X_1)+\cdots+\operatorname{var}(X_n).
$$
Other measures of dispersion, including sta |
37,122 | If an inverse covariance matrix is sparse, what can I say about the covariance matrix? | As already commented by Yair there is no specific sparsity condition of the inverse covariance matrix that affects the actual covariance matrix or vice versa. Anything other than trivial sparsity matrix patterns (ie. diagonal) have no guarantee that they will reflected on both a particular matrix and its inverse. Even ... | If an inverse covariance matrix is sparse, what can I say about the covariance matrix? | As already commented by Yair there is no specific sparsity condition of the inverse covariance matrix that affects the actual covariance matrix or vice versa. Anything other than trivial sparsity matr | If an inverse covariance matrix is sparse, what can I say about the covariance matrix?
As already commented by Yair there is no specific sparsity condition of the inverse covariance matrix that affects the actual covariance matrix or vice versa. Anything other than trivial sparsity matrix patterns (ie. diagonal) have n... | If an inverse covariance matrix is sparse, what can I say about the covariance matrix?
As already commented by Yair there is no specific sparsity condition of the inverse covariance matrix that affects the actual covariance matrix or vice versa. Anything other than trivial sparsity matr |
37,123 | "cumulative" vs "additive" | The cumulative error (also referred to as system error) - It's a single direction error. e.g, - If you are to measure 10 km run & your stopwatch is running 2 sec faster every minute. So at the end of the experiment to calculate error you will add 2 secs for each minute. In other words, it is a type of bias, with or wit... | "cumulative" vs "additive" | The cumulative error (also referred to as system error) - It's a single direction error. e.g, - If you are to measure 10 km run & your stopwatch is running 2 sec faster every minute. So at the end of | "cumulative" vs "additive"
The cumulative error (also referred to as system error) - It's a single direction error. e.g, - If you are to measure 10 km run & your stopwatch is running 2 sec faster every minute. So at the end of the experiment to calculate error you will add 2 secs for each minute. In other words, it is ... | "cumulative" vs "additive"
The cumulative error (also referred to as system error) - It's a single direction error. e.g, - If you are to measure 10 km run & your stopwatch is running 2 sec faster every minute. So at the end of |
37,124 | "cumulative" vs "additive" | Interestingly, this is a problem that psychologists and sociologists come across when considering theories of identity. Sam being black, male and disabled are all part of his identity and these are obviously not mutually exclusive. However the effect of them when considered together is cumulative not additive. So to ch... | "cumulative" vs "additive" | Interestingly, this is a problem that psychologists and sociologists come across when considering theories of identity. Sam being black, male and disabled are all part of his identity and these are ob | "cumulative" vs "additive"
Interestingly, this is a problem that psychologists and sociologists come across when considering theories of identity. Sam being black, male and disabled are all part of his identity and these are obviously not mutually exclusive. However the effect of them when considered together is cumula... | "cumulative" vs "additive"
Interestingly, this is a problem that psychologists and sociologists come across when considering theories of identity. Sam being black, male and disabled are all part of his identity and these are ob |
37,125 | Can intermediate rewards be used in reinforcement learning? | Is it common practice in RL to have only one reward function awarded when a task is fulfilled in the end?
This isn't quite the correct definition of a reward function. An MDP has a single reward function, $R(s,a,s'): S \times A \times S \mapsto \mathbb{R}$, where $S, A$ are the sets of states, actions in the problem. ... | Can intermediate rewards be used in reinforcement learning? | Is it common practice in RL to have only one reward function awarded when a task is fulfilled in the end?
This isn't quite the correct definition of a reward function. An MDP has a single reward func | Can intermediate rewards be used in reinforcement learning?
Is it common practice in RL to have only one reward function awarded when a task is fulfilled in the end?
This isn't quite the correct definition of a reward function. An MDP has a single reward function, $R(s,a,s'): S \times A \times S \mapsto \mathbb{R}$, w... | Can intermediate rewards be used in reinforcement learning?
Is it common practice in RL to have only one reward function awarded when a task is fulfilled in the end?
This isn't quite the correct definition of a reward function. An MDP has a single reward func |
37,126 | Can intermediate rewards be used in reinforcement learning? | I think the short version to your question is yes, it appears to be common practice to only reward an agent for full completion of a task, but be careful with your wording, as Sean pointed out in his answer that a reward function is defined for all possible combinations of states, actions, and future states.
To add to ... | Can intermediate rewards be used in reinforcement learning? | I think the short version to your question is yes, it appears to be common practice to only reward an agent for full completion of a task, but be careful with your wording, as Sean pointed out in his | Can intermediate rewards be used in reinforcement learning?
I think the short version to your question is yes, it appears to be common practice to only reward an agent for full completion of a task, but be careful with your wording, as Sean pointed out in his answer that a reward function is defined for all possible co... | Can intermediate rewards be used in reinforcement learning?
I think the short version to your question is yes, it appears to be common practice to only reward an agent for full completion of a task, but be careful with your wording, as Sean pointed out in his |
37,127 | Can intermediate rewards be used in reinforcement learning? | If you're interested in subtasks, you want to look at options. Aside from options, there is one reward function. | Can intermediate rewards be used in reinforcement learning? | If you're interested in subtasks, you want to look at options. Aside from options, there is one reward function. | Can intermediate rewards be used in reinforcement learning?
If you're interested in subtasks, you want to look at options. Aside from options, there is one reward function. | Can intermediate rewards be used in reinforcement learning?
If you're interested in subtasks, you want to look at options. Aside from options, there is one reward function. |
37,128 | Clustering and A/B testing | Absolutely, you can compare the different clusters, although it's important that you carefully consider what you infer from statistical significance. While it is indeed a very good indicator, by its very nature a threshold of $p<0.05$ will mean that $1/20$ tests will result in a false positive leaving many engineers an... | Clustering and A/B testing | Absolutely, you can compare the different clusters, although it's important that you carefully consider what you infer from statistical significance. While it is indeed a very good indicator, by its v | Clustering and A/B testing
Absolutely, you can compare the different clusters, although it's important that you carefully consider what you infer from statistical significance. While it is indeed a very good indicator, by its very nature a threshold of $p<0.05$ will mean that $1/20$ tests will result in a false positiv... | Clustering and A/B testing
Absolutely, you can compare the different clusters, although it's important that you carefully consider what you infer from statistical significance. While it is indeed a very good indicator, by its v |
37,129 | how does multicollinearity affect feature importances in random forest classifier? | Yes, multicollinearity definitely can affect variable importances in random forest models. Intuitively, it can be difficult to rank the relative importance of different variables if they have the same or similar underlying effect, which is implied by multicollinearity. That is- if we can access the underlying effect by... | how does multicollinearity affect feature importances in random forest classifier? | Yes, multicollinearity definitely can affect variable importances in random forest models. Intuitively, it can be difficult to rank the relative importance of different variables if they have the same | how does multicollinearity affect feature importances in random forest classifier?
Yes, multicollinearity definitely can affect variable importances in random forest models. Intuitively, it can be difficult to rank the relative importance of different variables if they have the same or similar underlying effect, which ... | how does multicollinearity affect feature importances in random forest classifier?
Yes, multicollinearity definitely can affect variable importances in random forest models. Intuitively, it can be difficult to rank the relative importance of different variables if they have the same |
37,130 | Statistical differences between two hourly patterns | This is an old question, but has no accepted answer, so let me offer my own.
Here is some data that, while not being exactly like yours, is close enough for our purposes.
Because the data are non-linear, I think a GAM might work well here. I'll use the mgcv library to first fit a simple gam which uses a smooth for ti... | Statistical differences between two hourly patterns | This is an old question, but has no accepted answer, so let me offer my own.
Here is some data that, while not being exactly like yours, is close enough for our purposes.
Because the data are non-lin | Statistical differences between two hourly patterns
This is an old question, but has no accepted answer, so let me offer my own.
Here is some data that, while not being exactly like yours, is close enough for our purposes.
Because the data are non-linear, I think a GAM might work well here. I'll use the mgcv library ... | Statistical differences between two hourly patterns
This is an old question, but has no accepted answer, so let me offer my own.
Here is some data that, while not being exactly like yours, is close enough for our purposes.
Because the data are non-lin |
37,131 | Statistical differences between two hourly patterns | Why don't you split into few time bands of 2h duration, say 00:04, 04:06, etc. and for each band you apply a two-sample t-test for each band. You didn't mention how many patients for each group, but if they are only few a t-test should do the work. Then you will get a p-value and a confidence interval for each time ban... | Statistical differences between two hourly patterns | Why don't you split into few time bands of 2h duration, say 00:04, 04:06, etc. and for each band you apply a two-sample t-test for each band. You didn't mention how many patients for each group, but i | Statistical differences between two hourly patterns
Why don't you split into few time bands of 2h duration, say 00:04, 04:06, etc. and for each band you apply a two-sample t-test for each band. You didn't mention how many patients for each group, but if they are only few a t-test should do the work. Then you will get a... | Statistical differences between two hourly patterns
Why don't you split into few time bands of 2h duration, say 00:04, 04:06, etc. and for each band you apply a two-sample t-test for each band. You didn't mention how many patients for each group, but i |
37,132 | How to impute a missing categorical predictor variable for a random forest model? | I think you need an unsupervised imputing method. That is one which do not use the target values for imputation. If you only have few prediction feature vectors, it may be difficult to uncover a data structure. Instead you could mix your predictions with already imputed training feature vectors and use this structure t... | How to impute a missing categorical predictor variable for a random forest model? | I think you need an unsupervised imputing method. That is one which do not use the target values for imputation. If you only have few prediction feature vectors, it may be difficult to uncover a data | How to impute a missing categorical predictor variable for a random forest model?
I think you need an unsupervised imputing method. That is one which do not use the target values for imputation. If you only have few prediction feature vectors, it may be difficult to uncover a data structure. Instead you could mix your ... | How to impute a missing categorical predictor variable for a random forest model?
I think you need an unsupervised imputing method. That is one which do not use the target values for imputation. If you only have few prediction feature vectors, it may be difficult to uncover a data |
37,133 | Truncated trivariate normal - conditional expectation | By definition if $P(A)>0$
$$E(X|A)=\frac{E(X1_A)}{p(A)}$$
so
$$E(X_1|a<X_2<b)=\frac{E(X_1 1_{a<X_2<b})}{p(a<X_2<b)}
=\frac{\int_a^b \int x_1 f(x_1,x_2) dx_1 dx_2}{p(a<X_2<b)}$$
similarity define
$A=\{X_2\in (a,b)\}$ and $B=\{X_3\in (a,b)\}$
$$E(X_1|a<X_2<b,a<X_2<b)=E(X_1|AB)=
\frac{E(X_1 1_{AB})}{p(AB)}=\frac{E(X_1 1_... | Truncated trivariate normal - conditional expectation | By definition if $P(A)>0$
$$E(X|A)=\frac{E(X1_A)}{p(A)}$$
so
$$E(X_1|a<X_2<b)=\frac{E(X_1 1_{a<X_2<b})}{p(a<X_2<b)}
=\frac{\int_a^b \int x_1 f(x_1,x_2) dx_1 dx_2}{p(a<X_2<b)}$$
similarity define
$A=\ | Truncated trivariate normal - conditional expectation
By definition if $P(A)>0$
$$E(X|A)=\frac{E(X1_A)}{p(A)}$$
so
$$E(X_1|a<X_2<b)=\frac{E(X_1 1_{a<X_2<b})}{p(a<X_2<b)}
=\frac{\int_a^b \int x_1 f(x_1,x_2) dx_1 dx_2}{p(a<X_2<b)}$$
similarity define
$A=\{X_2\in (a,b)\}$ and $B=\{X_3\in (a,b)\}$
$$E(X_1|a<X_2<b,a<X_2<b)... | Truncated trivariate normal - conditional expectation
By definition if $P(A)>0$
$$E(X|A)=\frac{E(X1_A)}{p(A)}$$
so
$$E(X_1|a<X_2<b)=\frac{E(X_1 1_{a<X_2<b})}{p(a<X_2<b)}
=\frac{\int_a^b \int x_1 f(x_1,x_2) dx_1 dx_2}{p(a<X_2<b)}$$
similarity define
$A=\ |
37,134 | Truncated trivariate normal - conditional expectation | Let's address the questions in turn.
The first one concerns the bivariate Normal distribution of $(X_1,X_2).$ This is determined by its mean $(\mu_1,\mu_2),$ the variances $\sigma_1\gt 0$ and $\sigma_2\gt 0,$ and the correlation coefficient $\rho = \rho_{12}.$ The theory of least-squares regression in the bivariate No... | Truncated trivariate normal - conditional expectation | Let's address the questions in turn.
The first one concerns the bivariate Normal distribution of $(X_1,X_2).$ This is determined by its mean $(\mu_1,\mu_2),$ the variances $\sigma_1\gt 0$ and $\sigma | Truncated trivariate normal - conditional expectation
Let's address the questions in turn.
The first one concerns the bivariate Normal distribution of $(X_1,X_2).$ This is determined by its mean $(\mu_1,\mu_2),$ the variances $\sigma_1\gt 0$ and $\sigma_2\gt 0,$ and the correlation coefficient $\rho = \rho_{12}.$ The ... | Truncated trivariate normal - conditional expectation
Let's address the questions in turn.
The first one concerns the bivariate Normal distribution of $(X_1,X_2).$ This is determined by its mean $(\mu_1,\mu_2),$ the variances $\sigma_1\gt 0$ and $\sigma |
37,135 | Why do we want low autocorrelation for MCMC convergence? | There's two things going on here that both lead to wanting to low autocorrelation, but from slightly different angles.
First is that if you have some sort of sampler (i.e. Metropolis Hasting, Gibbs sampler, whatever), you would like to have very little autocorrelation in the samples. This can be explained very easily ... | Why do we want low autocorrelation for MCMC convergence? | There's two things going on here that both lead to wanting to low autocorrelation, but from slightly different angles.
First is that if you have some sort of sampler (i.e. Metropolis Hasting, Gibbs s | Why do we want low autocorrelation for MCMC convergence?
There's two things going on here that both lead to wanting to low autocorrelation, but from slightly different angles.
First is that if you have some sort of sampler (i.e. Metropolis Hasting, Gibbs sampler, whatever), you would like to have very little autocorre... | Why do we want low autocorrelation for MCMC convergence?
There's two things going on here that both lead to wanting to low autocorrelation, but from slightly different angles.
First is that if you have some sort of sampler (i.e. Metropolis Hasting, Gibbs s |
37,136 | Sampling distribution of sample trimmed (truncated) mean | No analytical formula is known for the expected minimum of $n$ normal variables when $n>5$.
Meanwhile, the trimmed mean in the background of the question has expectation $−1/(n−1)$ times the expectation of that minimum. So no analytical formula is known for the expected trimmed mean when $n>5$. This suggests that there... | Sampling distribution of sample trimmed (truncated) mean | No analytical formula is known for the expected minimum of $n$ normal variables when $n>5$.
Meanwhile, the trimmed mean in the background of the question has expectation $−1/(n−1)$ times the expectati | Sampling distribution of sample trimmed (truncated) mean
No analytical formula is known for the expected minimum of $n$ normal variables when $n>5$.
Meanwhile, the trimmed mean in the background of the question has expectation $−1/(n−1)$ times the expectation of that minimum. So no analytical formula is known for the e... | Sampling distribution of sample trimmed (truncated) mean
No analytical formula is known for the expected minimum of $n$ normal variables when $n>5$.
Meanwhile, the trimmed mean in the background of the question has expectation $−1/(n−1)$ times the expectati |
37,137 | Why is a lognormal distribution a good fit for server response times? | You might be interested in reading the paper
Vern Paxson. Empirically-Derived Analytic Models of
Wide-Area TCP Connections. IEEE/ACM Transactions on Networking, 1994.
which is available online here. From the abstract:
We analyze 3 million TCP connections that occurred during
15 wide-area traffic traces. The tr... | Why is a lognormal distribution a good fit for server response times? | You might be interested in reading the paper
Vern Paxson. Empirically-Derived Analytic Models of
Wide-Area TCP Connections. IEEE/ACM Transactions on Networking, 1994.
which is available online he | Why is a lognormal distribution a good fit for server response times?
You might be interested in reading the paper
Vern Paxson. Empirically-Derived Analytic Models of
Wide-Area TCP Connections. IEEE/ACM Transactions on Networking, 1994.
which is available online here. From the abstract:
We analyze 3 million TCP c... | Why is a lognormal distribution a good fit for server response times?
You might be interested in reading the paper
Vern Paxson. Empirically-Derived Analytic Models of
Wide-Area TCP Connections. IEEE/ACM Transactions on Networking, 1994.
which is available online he |
37,138 | Why is a lognormal distribution a good fit for server response times? | Say $X_1, \ldots X_n \overset{iid}{\sim} \text{something}$. You don't know the distribution but you don't need to. By the central limit theorem $\bar{X} \to \mathcal{N}$. Don't worry about the parameters. Then $\exp(\bar{X}) \to \text{lognormal}$. Last part: $Y_1 = \exp(\frac{\sum_i X_i}{n}) = \left[\exp(\sum_i X_i)\ri... | Why is a lognormal distribution a good fit for server response times? | Say $X_1, \ldots X_n \overset{iid}{\sim} \text{something}$. You don't know the distribution but you don't need to. By the central limit theorem $\bar{X} \to \mathcal{N}$. Don't worry about the paramet | Why is a lognormal distribution a good fit for server response times?
Say $X_1, \ldots X_n \overset{iid}{\sim} \text{something}$. You don't know the distribution but you don't need to. By the central limit theorem $\bar{X} \to \mathcal{N}$. Don't worry about the parameters. Then $\exp(\bar{X}) \to \text{lognormal}$. La... | Why is a lognormal distribution a good fit for server response times?
Say $X_1, \ldots X_n \overset{iid}{\sim} \text{something}$. You don't know the distribution but you don't need to. By the central limit theorem $\bar{X} \to \mathcal{N}$. Don't worry about the paramet |
37,139 | MANOVA as protection against Type I errors | Requiring a significant MANOVA or ANOVA before conducting individual t-tests can help protect against Type I error, but is not generally sufficient to provide strong Type I error control. For example, if you only conduct the individual tests when the MANOVA is significant, that controls the familywise Type I error rate... | MANOVA as protection against Type I errors | Requiring a significant MANOVA or ANOVA before conducting individual t-tests can help protect against Type I error, but is not generally sufficient to provide strong Type I error control. For example, | MANOVA as protection against Type I errors
Requiring a significant MANOVA or ANOVA before conducting individual t-tests can help protect against Type I error, but is not generally sufficient to provide strong Type I error control. For example, if you only conduct the individual tests when the MANOVA is significant, tha... | MANOVA as protection against Type I errors
Requiring a significant MANOVA or ANOVA before conducting individual t-tests can help protect against Type I error, but is not generally sufficient to provide strong Type I error control. For example, |
37,140 | Fair coin testing | If you didn't actually test the coin after the first set of tosses, or make the choice to toss the second set based on the first, then yes, you should be able to simply combine them into one large sample.
If your behavior was in any way contingent on what happened in the first set, then it affects the properties of th... | Fair coin testing | If you didn't actually test the coin after the first set of tosses, or make the choice to toss the second set based on the first, then yes, you should be able to simply combine them into one large sa | Fair coin testing
If you didn't actually test the coin after the first set of tosses, or make the choice to toss the second set based on the first, then yes, you should be able to simply combine them into one large sample.
If your behavior was in any way contingent on what happened in the first set, then it affects th... | Fair coin testing
If you didn't actually test the coin after the first set of tosses, or make the choice to toss the second set based on the first, then yes, you should be able to simply combine them into one large sa |
37,141 | Cramer's $\phi $ for three-way contingency tables | There really isn't a straightforward generalization to Cramer's V, in the same way that Pearson's $\phi$ isn't defined for $2 x 2 .... 2$ tables. This is because there are multiple null models to be selecting from, so a single collapsed relationship statistic is not meaningful.
As an example, say you have a large $\ch... | Cramer's $\phi $ for three-way contingency tables | There really isn't a straightforward generalization to Cramer's V, in the same way that Pearson's $\phi$ isn't defined for $2 x 2 .... 2$ tables. This is because there are multiple null models to be s | Cramer's $\phi $ for three-way contingency tables
There really isn't a straightforward generalization to Cramer's V, in the same way that Pearson's $\phi$ isn't defined for $2 x 2 .... 2$ tables. This is because there are multiple null models to be selecting from, so a single collapsed relationship statistic is not mea... | Cramer's $\phi $ for three-way contingency tables
There really isn't a straightforward generalization to Cramer's V, in the same way that Pearson's $\phi$ isn't defined for $2 x 2 .... 2$ tables. This is because there are multiple null models to be s |
37,142 | Gibbs Sampler output: how many Markov chains? | This two-block Gibbs sampler is the only generic case when sub-chains remain Markov chains per se, because $(X_1^{(n)})$ is generated via the kernel
$$K(x_1,x_1^\prime)=\int f_2(x_2|x_1)f_1(x_1^\prime|x_2)\,\text{d}x_2$$
See our MCMC book for more details, but this is a case of interleaving property that also guarantee... | Gibbs Sampler output: how many Markov chains? | This two-block Gibbs sampler is the only generic case when sub-chains remain Markov chains per se, because $(X_1^{(n)})$ is generated via the kernel
$$K(x_1,x_1^\prime)=\int f_2(x_2|x_1)f_1(x_1^\prime | Gibbs Sampler output: how many Markov chains?
This two-block Gibbs sampler is the only generic case when sub-chains remain Markov chains per se, because $(X_1^{(n)})$ is generated via the kernel
$$K(x_1,x_1^\prime)=\int f_2(x_2|x_1)f_1(x_1^\prime|x_2)\,\text{d}x_2$$
See our MCMC book for more details, but this is a cas... | Gibbs Sampler output: how many Markov chains?
This two-block Gibbs sampler is the only generic case when sub-chains remain Markov chains per se, because $(X_1^{(n)})$ is generated via the kernel
$$K(x_1,x_1^\prime)=\int f_2(x_2|x_1)f_1(x_1^\prime |
37,143 | Frequency jump detection | Since it seems that you have a time series here, I would recommend you to check my relevant answer for some ideas (time series clustering, entropy measures, anomaly detection) as well as links to further information. In addition, I would also consider the Fourier transformation approach.
UPDATE (based on discussion wit... | Frequency jump detection | Since it seems that you have a time series here, I would recommend you to check my relevant answer for some ideas (time series clustering, entropy measures, anomaly detection) as well as links to furt | Frequency jump detection
Since it seems that you have a time series here, I would recommend you to check my relevant answer for some ideas (time series clustering, entropy measures, anomaly detection) as well as links to further information. In addition, I would also consider the Fourier transformation approach.
UPDATE... | Frequency jump detection
Since it seems that you have a time series here, I would recommend you to check my relevant answer for some ideas (time series clustering, entropy measures, anomaly detection) as well as links to furt |
37,144 | Frequency jump detection | What an interesting data set. I imagine your specific type of data do not represent 500 independent events simply... co-occurring, then returning to 0 of these events occurring for years on end. Similar to disease outbreaks, there is (probably) a triggering event that changes the state of the world to one in which suc... | Frequency jump detection | What an interesting data set. I imagine your specific type of data do not represent 500 independent events simply... co-occurring, then returning to 0 of these events occurring for years on end. Simi | Frequency jump detection
What an interesting data set. I imagine your specific type of data do not represent 500 independent events simply... co-occurring, then returning to 0 of these events occurring for years on end. Similar to disease outbreaks, there is (probably) a triggering event that changes the state of the ... | Frequency jump detection
What an interesting data set. I imagine your specific type of data do not represent 500 independent events simply... co-occurring, then returning to 0 of these events occurring for years on end. Simi |
37,145 | Random Forest partial plot for a binary predictor | In general partial plots are the average of a series of hypothetical predictions.
For continuous variables, partialPlot selects a series of n.pt values along the variable of interest. It creates a test data set identical to the training data, and sequentially sets the variable of interest for all observations to a sel... | Random Forest partial plot for a binary predictor | In general partial plots are the average of a series of hypothetical predictions.
For continuous variables, partialPlot selects a series of n.pt values along the variable of interest. It creates a te | Random Forest partial plot for a binary predictor
In general partial plots are the average of a series of hypothetical predictions.
For continuous variables, partialPlot selects a series of n.pt values along the variable of interest. It creates a test data set identical to the training data, and sequentially sets the ... | Random Forest partial plot for a binary predictor
In general partial plots are the average of a series of hypothetical predictions.
For continuous variables, partialPlot selects a series of n.pt values along the variable of interest. It creates a te |
37,146 | When KL Divergence and KS test will show inconsistent results? | Set aside Kullback-Leibler divergence for a moment and consider the following: it's perfectly possible for the Kolmogorov-Smirnov p-value to be small and for the corresponding Kolomogorov-Smirnov distance to be small.
Specifically, that can easily happen with large sample sizes, where even small differences are still l... | When KL Divergence and KS test will show inconsistent results? | Set aside Kullback-Leibler divergence for a moment and consider the following: it's perfectly possible for the Kolmogorov-Smirnov p-value to be small and for the corresponding Kolomogorov-Smirnov dist | When KL Divergence and KS test will show inconsistent results?
Set aside Kullback-Leibler divergence for a moment and consider the following: it's perfectly possible for the Kolmogorov-Smirnov p-value to be small and for the corresponding Kolomogorov-Smirnov distance to be small.
Specifically, that can easily happen wi... | When KL Divergence and KS test will show inconsistent results?
Set aside Kullback-Leibler divergence for a moment and consider the following: it's perfectly possible for the Kolmogorov-Smirnov p-value to be small and for the corresponding Kolomogorov-Smirnov dist |
37,147 | Gibbs Sampler contradiction proof | \begin{align*}\mathbb{P}(X_{n+1} \in A_k | X_n \in A_k) &=\mathbb{E}[\mathbb{I}_{A_k}(X_{n+1}) | X_n \in A_k]\\
&= \mathbb{E}[\mathbb{E}[\mathbb{I}_{A_k}(X_{n+1}) | X_n \in A_k,Y_1,...,Y_{k-1}] | X_n \in A_k]\\
&= \mathbb{E}[\mathbb{P}(X_{n+1} \in A_k | X_n \in A_k,Y_1,...,Y_{k-1}) | X_n \in A_k]\\
&= \mathbb{E}[\mathb... | Gibbs Sampler contradiction proof | \begin{align*}\mathbb{P}(X_{n+1} \in A_k | X_n \in A_k) &=\mathbb{E}[\mathbb{I}_{A_k}(X_{n+1}) | X_n \in A_k]\\
&= \mathbb{E}[\mathbb{E}[\mathbb{I}_{A_k}(X_{n+1}) | X_n \in A_k,Y_1,...,Y_{k-1}] | X_n | Gibbs Sampler contradiction proof
\begin{align*}\mathbb{P}(X_{n+1} \in A_k | X_n \in A_k) &=\mathbb{E}[\mathbb{I}_{A_k}(X_{n+1}) | X_n \in A_k]\\
&= \mathbb{E}[\mathbb{E}[\mathbb{I}_{A_k}(X_{n+1}) | X_n \in A_k,Y_1,...,Y_{k-1}] | X_n \in A_k]\\
&= \mathbb{E}[\mathbb{P}(X_{n+1} \in A_k | X_n \in A_k,Y_1,...,Y_{k-1}) | X... | Gibbs Sampler contradiction proof
\begin{align*}\mathbb{P}(X_{n+1} \in A_k | X_n \in A_k) &=\mathbb{E}[\mathbb{I}_{A_k}(X_{n+1}) | X_n \in A_k]\\
&= \mathbb{E}[\mathbb{E}[\mathbb{I}_{A_k}(X_{n+1}) | X_n \in A_k,Y_1,...,Y_{k-1}] | X_n |
37,148 | Addressing "NOTE: Results may be misleading due to involvement in interactions" warning with Tukey post-hoc comparisons in lsmeans R package | My view is that the $F$ test of statistical significance of the interaction effect is less important than the subjective nature of the interaction, as evidenced by the plot. The plot tells me that it is reasonably sensible to compare the overall averages of Depression and Top, but it'd be silly to compare those average... | Addressing "NOTE: Results may be misleading due to involvement in interactions" warning with Tukey p | My view is that the $F$ test of statistical significance of the interaction effect is less important than the subjective nature of the interaction, as evidenced by the plot. The plot tells me that it | Addressing "NOTE: Results may be misleading due to involvement in interactions" warning with Tukey post-hoc comparisons in lsmeans R package
My view is that the $F$ test of statistical significance of the interaction effect is less important than the subjective nature of the interaction, as evidenced by the plot. The p... | Addressing "NOTE: Results may be misleading due to involvement in interactions" warning with Tukey p
My view is that the $F$ test of statistical significance of the interaction effect is less important than the subjective nature of the interaction, as evidenced by the plot. The plot tells me that it |
37,149 | How to get the variance of the residual variance in a simple linear regression model | With:
$\frac{\sum e_i^2}{\sigma ^2}\sim \chi^2_{n-2} $
and knowing that $var(\chi^2_{n-2}=2(n−2)$
I can get that $var[\frac{\sum e_i^2}{\sigma ^2}]=2(n−2)$ dividing for $(n−2)^2$ and multipliying for $\sigma^4$ I get $var[\frac{\sum e_i^2}{(n-2)}]=\frac{2\sigma^4}{n-2}=var[S^2_R]$. I applied that $a^2 \cdot Var(x)=... | How to get the variance of the residual variance in a simple linear regression model | With:
$\frac{\sum e_i^2}{\sigma ^2}\sim \chi^2_{n-2} $
and knowing that $var(\chi^2_{n-2}=2(n−2)$
I can get that $var[\frac{\sum e_i^2}{\sigma ^2}]=2(n−2)$ dividing for $(n−2)^2$ and multipliying | How to get the variance of the residual variance in a simple linear regression model
With:
$\frac{\sum e_i^2}{\sigma ^2}\sim \chi^2_{n-2} $
and knowing that $var(\chi^2_{n-2}=2(n−2)$
I can get that $var[\frac{\sum e_i^2}{\sigma ^2}]=2(n−2)$ dividing for $(n−2)^2$ and multipliying for $\sigma^4$ I get $var[\frac{\su... | How to get the variance of the residual variance in a simple linear regression model
With:
$\frac{\sum e_i^2}{\sigma ^2}\sim \chi^2_{n-2} $
and knowing that $var(\chi^2_{n-2}=2(n−2)$
I can get that $var[\frac{\sum e_i^2}{\sigma ^2}]=2(n−2)$ dividing for $(n−2)^2$ and multipliying |
37,150 | Is $X_{(1)} + X_{(n)}$ a good estimator for $\theta$? | Since this is for self study, I've decided to make this intentionally terse. First, when $\theta = 1$, show that
$$
(X_{(1)}, X_{(n)} - X_{(1)},1 - X_{(n)}) \sim \operatorname{Dirichlet}(1, n-1, 1).
$$
More generally, you might show
$$
(X_{(1)}, X_{(2)} - X_{(1)}, \ldots, X_{(n)} - X_{(n-1)}, 1 - X_{(n)}) \sim \operat... | Is $X_{(1)} + X_{(n)}$ a good estimator for $\theta$? | Since this is for self study, I've decided to make this intentionally terse. First, when $\theta = 1$, show that
$$
(X_{(1)}, X_{(n)} - X_{(1)},1 - X_{(n)}) \sim \operatorname{Dirichlet}(1, n-1, 1).
| Is $X_{(1)} + X_{(n)}$ a good estimator for $\theta$?
Since this is for self study, I've decided to make this intentionally terse. First, when $\theta = 1$, show that
$$
(X_{(1)}, X_{(n)} - X_{(1)},1 - X_{(n)}) \sim \operatorname{Dirichlet}(1, n-1, 1).
$$
More generally, you might show
$$
(X_{(1)}, X_{(2)} - X_{(1)}, ... | Is $X_{(1)} + X_{(n)}$ a good estimator for $\theta$?
Since this is for self study, I've decided to make this intentionally terse. First, when $\theta = 1$, show that
$$
(X_{(1)}, X_{(n)} - X_{(1)},1 - X_{(n)}) \sim \operatorname{Dirichlet}(1, n-1, 1).
|
37,151 | Limits on conditional expectation with normal margins and specified (Pearson) correlation | I think there are no bounds. This conclusion relies on the following construction, which is simplest to describe for arbitrary continuous distributions. As we go along, conditions will be added until we are in the case of Normal marginals.
So, let $X$ be any continuous random variable with distribution function $F$. ... | Limits on conditional expectation with normal margins and specified (Pearson) correlation | I think there are no bounds. This conclusion relies on the following construction, which is simplest to describe for arbitrary continuous distributions. As we go along, conditions will be added unti | Limits on conditional expectation with normal margins and specified (Pearson) correlation
I think there are no bounds. This conclusion relies on the following construction, which is simplest to describe for arbitrary continuous distributions. As we go along, conditions will be added until we are in the case of Normal... | Limits on conditional expectation with normal margins and specified (Pearson) correlation
I think there are no bounds. This conclusion relies on the following construction, which is simplest to describe for arbitrary continuous distributions. As we go along, conditions will be added unti |
37,152 | Limits on conditional expectation with normal margins and specified (Pearson) correlation | If I understand your question correctly the answer depends on the "actual bivariate dependence relationship (the copula)" used.
Well there exist bounds on the value a copula can take right? So why not use the comonotonicity copula and countermonotonicity copula to establish the limits.
Source: Thorsten Schmidt - Copin... | Limits on conditional expectation with normal margins and specified (Pearson) correlation | If I understand your question correctly the answer depends on the "actual bivariate dependence relationship (the copula)" used.
Well there exist bounds on the value a copula can take right? So why not | Limits on conditional expectation with normal margins and specified (Pearson) correlation
If I understand your question correctly the answer depends on the "actual bivariate dependence relationship (the copula)" used.
Well there exist bounds on the value a copula can take right? So why not use the comonotonicity copula... | Limits on conditional expectation with normal margins and specified (Pearson) correlation
If I understand your question correctly the answer depends on the "actual bivariate dependence relationship (the copula)" used.
Well there exist bounds on the value a copula can take right? So why not |
37,153 | How to efficiently compute Theil-Sen estimator? | According to wikipedia, it can be calculated exactly in O(n log(n)).
Wikipedia points to no less than six papers detailing different deterministic or randomized algorithms with $O(n\log n)$ performance, right in the section where they mention the existence of such algorithms (as well as mentioning an even faster one ... | How to efficiently compute Theil-Sen estimator? | According to wikipedia, it can be calculated exactly in O(n log(n)).
Wikipedia points to no less than six papers detailing different deterministic or randomized algorithms with $O(n\log n)$ performa | How to efficiently compute Theil-Sen estimator?
According to wikipedia, it can be calculated exactly in O(n log(n)).
Wikipedia points to no less than six papers detailing different deterministic or randomized algorithms with $O(n\log n)$ performance, right in the section where they mention the existence of such algor... | How to efficiently compute Theil-Sen estimator?
According to wikipedia, it can be calculated exactly in O(n log(n)).
Wikipedia points to no less than six papers detailing different deterministic or randomized algorithms with $O(n\log n)$ performa |
37,154 | How to efficiently compute Theil-Sen estimator? | The R-package robslopes contains a C++ implementation based on the algorithm by Dillencourt et. al (1992) and Matousek et. al (1998). See https://cran.r-project.org/web/packages/robslopes/index.html | How to efficiently compute Theil-Sen estimator? | The R-package robslopes contains a C++ implementation based on the algorithm by Dillencourt et. al (1992) and Matousek et. al (1998). See https://cran.r-project.org/web/packages/robslopes/index.html | How to efficiently compute Theil-Sen estimator?
The R-package robslopes contains a C++ implementation based on the algorithm by Dillencourt et. al (1992) and Matousek et. al (1998). See https://cran.r-project.org/web/packages/robslopes/index.html | How to efficiently compute Theil-Sen estimator?
The R-package robslopes contains a C++ implementation based on the algorithm by Dillencourt et. al (1992) and Matousek et. al (1998). See https://cran.r-project.org/web/packages/robslopes/index.html |
37,155 | How to determine moving window size? | I agree with whuber. You should have some methodology, for example bootstrapping and stability criterion (that is perturb your data a little bit and check that your estimates do not change too much), or better sharp theoretical results, to help you decide if you have enough samples to compute your estimates correctly. ... | How to determine moving window size? | I agree with whuber. You should have some methodology, for example bootstrapping and stability criterion (that is perturb your data a little bit and check that your estimates do not change too much), | How to determine moving window size?
I agree with whuber. You should have some methodology, for example bootstrapping and stability criterion (that is perturb your data a little bit and check that your estimates do not change too much), or better sharp theoretical results, to help you decide if you have enough samples ... | How to determine moving window size?
I agree with whuber. You should have some methodology, for example bootstrapping and stability criterion (that is perturb your data a little bit and check that your estimates do not change too much), |
37,156 | How to determine moving window size? | Generally one picks the size of a sliding window that captures enough of information. Pick it too big, you will get more irrelevant information (loss of resolution). Pick too small, you will loose details.
You can see this following way. Suppose you have some real-valued function as a mixture of sinusoids with differen... | How to determine moving window size? | Generally one picks the size of a sliding window that captures enough of information. Pick it too big, you will get more irrelevant information (loss of resolution). Pick too small, you will loose det | How to determine moving window size?
Generally one picks the size of a sliding window that captures enough of information. Pick it too big, you will get more irrelevant information (loss of resolution). Pick too small, you will loose details.
You can see this following way. Suppose you have some real-valued function as... | How to determine moving window size?
Generally one picks the size of a sliding window that captures enough of information. Pick it too big, you will get more irrelevant information (loss of resolution). Pick too small, you will loose det |
37,157 | How to determine moving window size? | I've done some thinking about this in a different context and came up with an approach that seemed reasonable intuitively, although I have a compsci rather than stats background.
The motivation for a smaller window size is increased sensitivity to changes in the underlying process from which you are sampling. I'll cal... | How to determine moving window size? | I've done some thinking about this in a different context and came up with an approach that seemed reasonable intuitively, although I have a compsci rather than stats background.
The motivation for a | How to determine moving window size?
I've done some thinking about this in a different context and came up with an approach that seemed reasonable intuitively, although I have a compsci rather than stats background.
The motivation for a smaller window size is increased sensitivity to changes in the underlying process f... | How to determine moving window size?
I've done some thinking about this in a different context and came up with an approach that seemed reasonable intuitively, although I have a compsci rather than stats background.
The motivation for a |
37,158 | Stationary function | Stationarity is a concept defined for stochastic processes. Since we look at the process as random function then we can extend the definition of stationarity to functions. I.e a stationary function is a realisation of stationary process. This extension is quite informal though.
Stationarity for a process means that th... | Stationary function | Stationarity is a concept defined for stochastic processes. Since we look at the process as random function then we can extend the definition of stationarity to functions. I.e a stationary function is | Stationary function
Stationarity is a concept defined for stochastic processes. Since we look at the process as random function then we can extend the definition of stationarity to functions. I.e a stationary function is a realisation of stationary process. This extension is quite informal though.
Stationarity for a p... | Stationary function
Stationarity is a concept defined for stochastic processes. Since we look at the process as random function then we can extend the definition of stationarity to functions. I.e a stationary function is |
37,159 | Support vector regression versus kernel ridge regression | As expected: it depends on what you want. In terms of generalization performance, typically the performance differences are minor.
That said, minimizing the $l_1$-norm has the extremely attractive feature of yielding sparse solutions (the support vectors are a subset of the training set). When doing ridge regression, j... | Support vector regression versus kernel ridge regression | As expected: it depends on what you want. In terms of generalization performance, typically the performance differences are minor.
That said, minimizing the $l_1$-norm has the extremely attractive fea | Support vector regression versus kernel ridge regression
As expected: it depends on what you want. In terms of generalization performance, typically the performance differences are minor.
That said, minimizing the $l_1$-norm has the extremely attractive feature of yielding sparse solutions (the support vectors are a su... | Support vector regression versus kernel ridge regression
As expected: it depends on what you want. In terms of generalization performance, typically the performance differences are minor.
That said, minimizing the $l_1$-norm has the extremely attractive fea |
37,160 | K-means as a limit case of EM algorithm for Gaussian mixtures with covariances $\epsilon^2 I$ going to $0$ | Is it true that up to some constant and scalar multiplication:
$\lim_{\sigma \to 0} Q((\pi, \mu, \Sigma), (\pi, \mu, \Sigma)^{\text{old}}) = -J$?
This is not the case since – as you observed yourself – the limit diverges.
However, if we first transform $Q$ and then take the limit, we converge to the k-means objecti... | K-means as a limit case of EM algorithm for Gaussian mixtures with covariances $\epsilon^2 I$ going | Is it true that up to some constant and scalar multiplication:
$\lim_{\sigma \to 0} Q((\pi, \mu, \Sigma), (\pi, \mu, \Sigma)^{\text{old}}) = -J$?
This is not the case since – as you observed yours | K-means as a limit case of EM algorithm for Gaussian mixtures with covariances $\epsilon^2 I$ going to $0$
Is it true that up to some constant and scalar multiplication:
$\lim_{\sigma \to 0} Q((\pi, \mu, \Sigma), (\pi, \mu, \Sigma)^{\text{old}}) = -J$?
This is not the case since – as you observed yourself – the lim... | K-means as a limit case of EM algorithm for Gaussian mixtures with covariances $\epsilon^2 I$ going
Is it true that up to some constant and scalar multiplication:
$\lim_{\sigma \to 0} Q((\pi, \mu, \Sigma), (\pi, \mu, \Sigma)^{\text{old}}) = -J$?
This is not the case since – as you observed yours |
37,161 | Truncated Gamma distribution parameter estimation | Maximum Likelihood Estimation (MLE) works remarkably well, even for fairly small datasets. For truncation at an upper limit of $U$ and lower limit of $L$, simply divide the Gamma likelihood of any data value $x$ by the total probability of the interval $[L,U]$ to obtain the likelihood for the truncated distribution.
H... | Truncated Gamma distribution parameter estimation | Maximum Likelihood Estimation (MLE) works remarkably well, even for fairly small datasets. For truncation at an upper limit of $U$ and lower limit of $L$, simply divide the Gamma likelihood of any da | Truncated Gamma distribution parameter estimation
Maximum Likelihood Estimation (MLE) works remarkably well, even for fairly small datasets. For truncation at an upper limit of $U$ and lower limit of $L$, simply divide the Gamma likelihood of any data value $x$ by the total probability of the interval $[L,U]$ to obtai... | Truncated Gamma distribution parameter estimation
Maximum Likelihood Estimation (MLE) works remarkably well, even for fairly small datasets. For truncation at an upper limit of $U$ and lower limit of $L$, simply divide the Gamma likelihood of any da |
37,162 | Truncated Gamma distribution parameter estimation | First it is more convenient to truncate gamma distribution, utilising the direct method of truncation
G(x) = (F(x,a,b) - F( zmin, a,b))/ (F(zmax,a,b) - F( zmin, a,b)). F are the gamma cumulative function and not (x-zmin).((b-zmin) to truncate in
zmin it is te left bound ary
zmax the right boundary
So, the transforma... | Truncated Gamma distribution parameter estimation | First it is more convenient to truncate gamma distribution, utilising the direct method of truncation
G(x) = (F(x,a,b) - F( zmin, a,b))/ (F(zmax,a,b) - F( zmin, a,b)). F are the gamma cumulative funct | Truncated Gamma distribution parameter estimation
First it is more convenient to truncate gamma distribution, utilising the direct method of truncation
G(x) = (F(x,a,b) - F( zmin, a,b))/ (F(zmax,a,b) - F( zmin, a,b)). F are the gamma cumulative function and not (x-zmin).((b-zmin) to truncate in
zmin it is te left bou... | Truncated Gamma distribution parameter estimation
First it is more convenient to truncate gamma distribution, utilising the direct method of truncation
G(x) = (F(x,a,b) - F( zmin, a,b))/ (F(zmax,a,b) - F( zmin, a,b)). F are the gamma cumulative funct |
37,163 | When to use zero-inflated poisson regression and negative binomial distribution | I suspect that your problem may be that the default behavior of predict.glm isn't what you think it is.
Specifically, predict used on a glm object will by default gives a response on the scale of the linear predictors, not the response.
This is quite clearly stated in the help (?predict.glm) but seems to trip people u... | When to use zero-inflated poisson regression and negative binomial distribution | I suspect that your problem may be that the default behavior of predict.glm isn't what you think it is.
Specifically, predict used on a glm object will by default gives a response on the scale of the | When to use zero-inflated poisson regression and negative binomial distribution
I suspect that your problem may be that the default behavior of predict.glm isn't what you think it is.
Specifically, predict used on a glm object will by default gives a response on the scale of the linear predictors, not the response.
Th... | When to use zero-inflated poisson regression and negative binomial distribution
I suspect that your problem may be that the default behavior of predict.glm isn't what you think it is.
Specifically, predict used on a glm object will by default gives a response on the scale of the |
37,164 | How to apply a Gaussian radial basis function kernel PCA to nonlinear data? | The first problem seems to be that the sign of gamma is wrong (it should be negative: $-15$, as in the definition of the kernel, not as in your code). Alternatively, use exp(-gamma * mat_sq_dists).
The second problem is that you clobber the eigenvectors with your invocation of zip's when you sort the list. The $i$-th e... | How to apply a Gaussian radial basis function kernel PCA to nonlinear data? | The first problem seems to be that the sign of gamma is wrong (it should be negative: $-15$, as in the definition of the kernel, not as in your code). Alternatively, use exp(-gamma * mat_sq_dists).
Th | How to apply a Gaussian radial basis function kernel PCA to nonlinear data?
The first problem seems to be that the sign of gamma is wrong (it should be negative: $-15$, as in the definition of the kernel, not as in your code). Alternatively, use exp(-gamma * mat_sq_dists).
The second problem is that you clobber the eig... | How to apply a Gaussian radial basis function kernel PCA to nonlinear data?
The first problem seems to be that the sign of gamma is wrong (it should be negative: $-15$, as in the definition of the kernel, not as in your code). Alternatively, use exp(-gamma * mat_sq_dists).
Th |
37,165 | Good papers with reproducible analysis requiring only the basics | At the Universit of Goettingen they started a Wiki collecting various studies and their replications: http://replication.uni-goettingen.de/ | Good papers with reproducible analysis requiring only the basics | At the Universit of Goettingen they started a Wiki collecting various studies and their replications: http://replication.uni-goettingen.de/ | Good papers with reproducible analysis requiring only the basics
At the Universit of Goettingen they started a Wiki collecting various studies and their replications: http://replication.uni-goettingen.de/ | Good papers with reproducible analysis requiring only the basics
At the Universit of Goettingen they started a Wiki collecting various studies and their replications: http://replication.uni-goettingen.de/ |
37,166 | Is the population of blue-eyed Martians decreasing? | This answer describes three ways to handle the varying sample sizes appropriately: a Generalized Linear Model and two weighted Ordinary Least Squares regressions. In this case all three work well. In general, when some proportions are near $0$ or $1$, the GLM is better.
Because the sample sizes are so small compared... | Is the population of blue-eyed Martians decreasing? | This answer describes three ways to handle the varying sample sizes appropriately: a Generalized Linear Model and two weighted Ordinary Least Squares regressions. In this case all three work well. I | Is the population of blue-eyed Martians decreasing?
This answer describes three ways to handle the varying sample sizes appropriately: a Generalized Linear Model and two weighted Ordinary Least Squares regressions. In this case all three work well. In general, when some proportions are near $0$ or $1$, the GLM is bet... | Is the population of blue-eyed Martians decreasing?
This answer describes three ways to handle the varying sample sizes appropriately: a Generalized Linear Model and two weighted Ordinary Least Squares regressions. In this case all three work well. I |
37,167 | Follow-up question: When should you center your data & when should you standardize? | Suppose a model of the form
$$\mathbb{E}(Y) = f(\beta_0 + \beta_1 x_1 + \cdots + \beta_d x_d)$$
with parameters $(\beta_0, \beta_1, \ldots, \beta_d)$ is fit to data $((x_{i1}, x_{i2}, \ldots, x_{id}, y_i))$ by optimizing some measure of discrepancy between the $y_i$ and the corresponding $\mathrm{x}_i$, as is done (for... | Follow-up question: When should you center your data & when should you standardize? | Suppose a model of the form
$$\mathbb{E}(Y) = f(\beta_0 + \beta_1 x_1 + \cdots + \beta_d x_d)$$
with parameters $(\beta_0, \beta_1, \ldots, \beta_d)$ is fit to data $((x_{i1}, x_{i2}, \ldots, x_{id}, | Follow-up question: When should you center your data & when should you standardize?
Suppose a model of the form
$$\mathbb{E}(Y) = f(\beta_0 + \beta_1 x_1 + \cdots + \beta_d x_d)$$
with parameters $(\beta_0, \beta_1, \ldots, \beta_d)$ is fit to data $((x_{i1}, x_{i2}, \ldots, x_{id}, y_i))$ by optimizing some measure of... | Follow-up question: When should you center your data & when should you standardize?
Suppose a model of the form
$$\mathbb{E}(Y) = f(\beta_0 + \beta_1 x_1 + \cdots + \beta_d x_d)$$
with parameters $(\beta_0, \beta_1, \ldots, \beta_d)$ is fit to data $((x_{i1}, x_{i2}, \ldots, x_{id}, |
37,168 | Multi-class classification via all pairwise classifications with LDA | This question is not restricted to LDA, but can be asked about any binary classifier that is used in a multi-class setting by making all pairwise comparisons. The question is how to combine all pairwise classifications into one final classification.
The simplest approach is as follows. Each of the $\frac{K(K-1)}{2}$ pa... | Multi-class classification via all pairwise classifications with LDA | This question is not restricted to LDA, but can be asked about any binary classifier that is used in a multi-class setting by making all pairwise comparisons. The question is how to combine all pairwi | Multi-class classification via all pairwise classifications with LDA
This question is not restricted to LDA, but can be asked about any binary classifier that is used in a multi-class setting by making all pairwise comparisons. The question is how to combine all pairwise classifications into one final classification.
T... | Multi-class classification via all pairwise classifications with LDA
This question is not restricted to LDA, but can be asked about any binary classifier that is used in a multi-class setting by making all pairwise comparisons. The question is how to combine all pairwi |
37,169 | Proper Number of Clicks for Conversion Rate Testing | Paul. A conversion rate is defined as:
$\textrm{Conversion rate} = r =\frac{\textrm{Number of goal achievements}}{\textrm{Visits}} = \frac{s}{n}$.
Assuming that the number of goal achievements is basically the number of success $s$ out of the number of trials $v$ (rather than the number of events per unit time or space... | Proper Number of Clicks for Conversion Rate Testing | Paul. A conversion rate is defined as:
$\textrm{Conversion rate} = r =\frac{\textrm{Number of goal achievements}}{\textrm{Visits}} = \frac{s}{n}$.
Assuming that the number of goal achievements is basi | Proper Number of Clicks for Conversion Rate Testing
Paul. A conversion rate is defined as:
$\textrm{Conversion rate} = r =\frac{\textrm{Number of goal achievements}}{\textrm{Visits}} = \frac{s}{n}$.
Assuming that the number of goal achievements is basically the number of success $s$ out of the number of trials $v$ (rat... | Proper Number of Clicks for Conversion Rate Testing
Paul. A conversion rate is defined as:
$\textrm{Conversion rate} = r =\frac{\textrm{Number of goal achievements}}{\textrm{Visits}} = \frac{s}{n}$.
Assuming that the number of goal achievements is basi |
37,170 | Ordinal Logistic Regression with a Different Link Function | I think we first have to ask whether it's necessary to use proportional odds logistic regression to approximate a cumulative relative risk, e.g. the relative risk of reporting a higher outcome. The probabilistic formulation of the proportional odds model relies on observing arbitrary bins of a latent logistic random va... | Ordinal Logistic Regression with a Different Link Function | I think we first have to ask whether it's necessary to use proportional odds logistic regression to approximate a cumulative relative risk, e.g. the relative risk of reporting a higher outcome. The pr | Ordinal Logistic Regression with a Different Link Function
I think we first have to ask whether it's necessary to use proportional odds logistic regression to approximate a cumulative relative risk, e.g. the relative risk of reporting a higher outcome. The probabilistic formulation of the proportional odds model relies... | Ordinal Logistic Regression with a Different Link Function
I think we first have to ask whether it's necessary to use proportional odds logistic regression to approximate a cumulative relative risk, e.g. the relative risk of reporting a higher outcome. The pr |
37,171 | Ordinal Logistic Regression with a Different Link Function | Let's address your two questions separately:
Is the "rare outcome assumption" for an OR to approximate a relative risk still true in ordinal logistic regression?
Not really. You said yourself that your outcomes are evenly spread throughout the four categories, so no category is going to be particularly rare.
If so, is ... | Ordinal Logistic Regression with a Different Link Function | Let's address your two questions separately:
Is the "rare outcome assumption" for an OR to approximate a relative risk still true in ordinal logistic regression?
Not really. You said yourself that you | Ordinal Logistic Regression with a Different Link Function
Let's address your two questions separately:
Is the "rare outcome assumption" for an OR to approximate a relative risk still true in ordinal logistic regression?
Not really. You said yourself that your outcomes are evenly spread throughout the four categories, ... | Ordinal Logistic Regression with a Different Link Function
Let's address your two questions separately:
Is the "rare outcome assumption" for an OR to approximate a relative risk still true in ordinal logistic regression?
Not really. You said yourself that you |
37,172 | Does Box-Cox parameter estimation count towards parameters for AIC? | Write $p_\lambda(x)$ for the Box-Cox transformation of $x$ with parameter $\lambda$, $-\infty\lt\lambda\lt\infty$. The full model for data $(x_i,y_i)$ where the responses $(y_i)$ are viewed as a realization of a random vector $(Y_i)$ is described in the question as
$$\mathbb{E}(p_{\lambda_y}(Y_i)) = a + b\, p_{\lambda... | Does Box-Cox parameter estimation count towards parameters for AIC? | Write $p_\lambda(x)$ for the Box-Cox transformation of $x$ with parameter $\lambda$, $-\infty\lt\lambda\lt\infty$. The full model for data $(x_i,y_i)$ where the responses $(y_i)$ are viewed as a real | Does Box-Cox parameter estimation count towards parameters for AIC?
Write $p_\lambda(x)$ for the Box-Cox transformation of $x$ with parameter $\lambda$, $-\infty\lt\lambda\lt\infty$. The full model for data $(x_i,y_i)$ where the responses $(y_i)$ are viewed as a realization of a random vector $(Y_i)$ is described in t... | Does Box-Cox parameter estimation count towards parameters for AIC?
Write $p_\lambda(x)$ for the Box-Cox transformation of $x$ with parameter $\lambda$, $-\infty\lt\lambda\lt\infty$. The full model for data $(x_i,y_i)$ where the responses $(y_i)$ are viewed as a real |
37,173 | Does Box-Cox parameter estimation count towards parameters for AIC? | Why are you transforming the data?
What scale are you asking your questions on? If it isn't the transformed scale, then there is the issue of parameterization.
An example might help. Suppose some response $Y \sim \log N(\mu, \sigma)$, and you want to compare $Y$ across two independent populations. Suppose further th... | Does Box-Cox parameter estimation count towards parameters for AIC? | Why are you transforming the data?
What scale are you asking your questions on? If it isn't the transformed scale, then there is the issue of parameterization.
An example might help. Suppose some re | Does Box-Cox parameter estimation count towards parameters for AIC?
Why are you transforming the data?
What scale are you asking your questions on? If it isn't the transformed scale, then there is the issue of parameterization.
An example might help. Suppose some response $Y \sim \log N(\mu, \sigma)$, and you want to... | Does Box-Cox parameter estimation count towards parameters for AIC?
Why are you transforming the data?
What scale are you asking your questions on? If it isn't the transformed scale, then there is the issue of parameterization.
An example might help. Suppose some re |
37,174 | Internal validation via bootstrap: What ROC curve to present? | You are making the assumption that the ROC curve is informative and leads to good decisions. Neither is true. I have yet to see an ROC curve that provided useful insight. It also has a large ink:information ratio. The $c$-index (concordance probability) is a good measure of predictive discrimination. I would like ... | Internal validation via bootstrap: What ROC curve to present? | You are making the assumption that the ROC curve is informative and leads to good decisions. Neither is true. I have yet to see an ROC curve that provided useful insight. It also has a large ink:in | Internal validation via bootstrap: What ROC curve to present?
You are making the assumption that the ROC curve is informative and leads to good decisions. Neither is true. I have yet to see an ROC curve that provided useful insight. It also has a large ink:information ratio. The $c$-index (concordance probability) ... | Internal validation via bootstrap: What ROC curve to present?
You are making the assumption that the ROC curve is informative and leads to good decisions. Neither is true. I have yet to see an ROC curve that provided useful insight. It also has a large ink:in |
37,175 | Internal validation via bootstrap: What ROC curve to present? | You raised a very good question that I was wondering for a long time. Perhaps it depends on your results to make a decision how to report. For most situations, authors would like to report a raw/apparent AUC (ie. step #1 in your question) despite over-optimism or not, and then report the bootstrap optimism corrected AU... | Internal validation via bootstrap: What ROC curve to present? | You raised a very good question that I was wondering for a long time. Perhaps it depends on your results to make a decision how to report. For most situations, authors would like to report a raw/appar | Internal validation via bootstrap: What ROC curve to present?
You raised a very good question that I was wondering for a long time. Perhaps it depends on your results to make a decision how to report. For most situations, authors would like to report a raw/apparent AUC (ie. step #1 in your question) despite over-optimi... | Internal validation via bootstrap: What ROC curve to present?
You raised a very good question that I was wondering for a long time. Perhaps it depends on your results to make a decision how to report. For most situations, authors would like to report a raw/appar |
37,176 | Internal validation via bootstrap: What ROC curve to present? | There are many details missing your question - however it appears to me that you are not talking about test set all. If you intend to demonstrate the generalizability of your model (which is primary use case for an ROC curve), you are expected to present the ROC derived from a test set, not validation or internal valid... | Internal validation via bootstrap: What ROC curve to present? | There are many details missing your question - however it appears to me that you are not talking about test set all. If you intend to demonstrate the generalizability of your model (which is primary u | Internal validation via bootstrap: What ROC curve to present?
There are many details missing your question - however it appears to me that you are not talking about test set all. If you intend to demonstrate the generalizability of your model (which is primary use case for an ROC curve), you are expected to present the... | Internal validation via bootstrap: What ROC curve to present?
There are many details missing your question - however it appears to me that you are not talking about test set all. If you intend to demonstrate the generalizability of your model (which is primary u |
37,177 | Rare event logistic regression bias correction | They define $\tau$ & $\bar{y}$ too: $\tau$ is the fraction of 1's in the population; $\bar{y}$ is the observed fraction of 1's in the sample (based on prior information).
You'd typically use prior correction when you've sampled based on the outcome; which I'd guess you haven't here. But if you have, then $\bar{y}=\fra... | Rare event logistic regression bias correction | They define $\tau$ & $\bar{y}$ too: $\tau$ is the fraction of 1's in the population; $\bar{y}$ is the observed fraction of 1's in the sample (based on prior information).
You'd typically use prior co | Rare event logistic regression bias correction
They define $\tau$ & $\bar{y}$ too: $\tau$ is the fraction of 1's in the population; $\bar{y}$ is the observed fraction of 1's in the sample (based on prior information).
You'd typically use prior correction when you've sampled based on the outcome; which I'd guess you ha... | Rare event logistic regression bias correction
They define $\tau$ & $\bar{y}$ too: $\tau$ is the fraction of 1's in the population; $\bar{y}$ is the observed fraction of 1's in the sample (based on prior information).
You'd typically use prior co |
37,178 | How to make the rare events corrections described in King and Zeng (2001)? | The logistf() function do not implement rare event logistic regression, that is done by the relogit() function in the Zelig package, on CRAN. You should test that one! | How to make the rare events corrections described in King and Zeng (2001)? | The logistf() function do not implement rare event logistic regression, that is done by the relogit() function in the Zelig package, on CRAN. You should test that one! | How to make the rare events corrections described in King and Zeng (2001)?
The logistf() function do not implement rare event logistic regression, that is done by the relogit() function in the Zelig package, on CRAN. You should test that one! | How to make the rare events corrections described in King and Zeng (2001)?
The logistf() function do not implement rare event logistic regression, that is done by the relogit() function in the Zelig package, on CRAN. You should test that one! |
37,179 | How to make the rare events corrections described in King and Zeng (2001)? | I realised that my comparisons of fitted and actual proportions in the first graph, top right-hand corner, are not the best way to assess model fit, since in the big data I can caclulate proportions for ABC categories, but with the model fit where all four variables are included, proportions are predicted for each ABCD... | How to make the rare events corrections described in King and Zeng (2001)? | I realised that my comparisons of fitted and actual proportions in the first graph, top right-hand corner, are not the best way to assess model fit, since in the big data I can caclulate proportions f | How to make the rare events corrections described in King and Zeng (2001)?
I realised that my comparisons of fitted and actual proportions in the first graph, top right-hand corner, are not the best way to assess model fit, since in the big data I can caclulate proportions for ABC categories, but with the model fit whe... | How to make the rare events corrections described in King and Zeng (2001)?
I realised that my comparisons of fitted and actual proportions in the first graph, top right-hand corner, are not the best way to assess model fit, since in the big data I can caclulate proportions f |
37,180 | When/why does the central tendency of a resampling simulation markedly differ from the observed value? | Any nonlinear statistic (a non-linear combination of linear statistics such as sample means) has a small sample bias. Cohen's $d$ is obviously no exception: it is essentially
$$
d=\frac{m_1 - m_2}{\sqrt{m_3-m_4^2}}
$$
which is fairly non-linear, at least as far as the terms in the denominator go.
Each of the moments ca... | When/why does the central tendency of a resampling simulation markedly differ from the observed valu | Any nonlinear statistic (a non-linear combination of linear statistics such as sample means) has a small sample bias. Cohen's $d$ is obviously no exception: it is essentially
$$
d=\frac{m_1 - m_2}{\sq | When/why does the central tendency of a resampling simulation markedly differ from the observed value?
Any nonlinear statistic (a non-linear combination of linear statistics such as sample means) has a small sample bias. Cohen's $d$ is obviously no exception: it is essentially
$$
d=\frac{m_1 - m_2}{\sqrt{m_3-m_4^2}}
$$... | When/why does the central tendency of a resampling simulation markedly differ from the observed valu
Any nonlinear statistic (a non-linear combination of linear statistics such as sample means) has a small sample bias. Cohen's $d$ is obviously no exception: it is essentially
$$
d=\frac{m_1 - m_2}{\sq |
37,181 | p-value and the base rate fallacy | The positive predictive value (PPV; the probability that a drug actually working, given that we rejected the null hypothesis that it had no effect—i.e. the probability that we made a true rejection) is sensitive to the base rate of cancer drugs that actually work.
Consider the $2\times2$ table below, where testing posi... | p-value and the base rate fallacy | The positive predictive value (PPV; the probability that a drug actually working, given that we rejected the null hypothesis that it had no effect—i.e. the probability that we made a true rejection) i | p-value and the base rate fallacy
The positive predictive value (PPV; the probability that a drug actually working, given that we rejected the null hypothesis that it had no effect—i.e. the probability that we made a true rejection) is sensitive to the base rate of cancer drugs that actually work.
Consider the $2\times... | p-value and the base rate fallacy
The positive predictive value (PPV; the probability that a drug actually working, given that we rejected the null hypothesis that it had no effect—i.e. the probability that we made a true rejection) i |
37,182 | How to perform hypothesis testing for comparing different classifiers | In general layman's terms (and not just for this problem),
Null Hypothesis $H_0$: no change or difference (i.e. the classifiers have the same performance, however you define it)
Alternative Hypothesis: there is some sort of difference in performance
For your classifier performance comparison problem, I recommend read... | How to perform hypothesis testing for comparing different classifiers | In general layman's terms (and not just for this problem),
Null Hypothesis $H_0$: no change or difference (i.e. the classifiers have the same performance, however you define it)
Alternative Hypothesi | How to perform hypothesis testing for comparing different classifiers
In general layman's terms (and not just for this problem),
Null Hypothesis $H_0$: no change or difference (i.e. the classifiers have the same performance, however you define it)
Alternative Hypothesis: there is some sort of difference in performance... | How to perform hypothesis testing for comparing different classifiers
In general layman's terms (and not just for this problem),
Null Hypothesis $H_0$: no change or difference (i.e. the classifiers have the same performance, however you define it)
Alternative Hypothesi |
37,183 | How to perform hypothesis testing for comparing different classifiers | One-way ANOVA followed by post hoc tests using Tukey-Kramer method for multiple comparison analysis is one possible approach.
As a result various plots are generated where in each graph, the mean of the classifier performance measure and an interval (95% confidence interval) are clearly represented. Two means are signi... | How to perform hypothesis testing for comparing different classifiers | One-way ANOVA followed by post hoc tests using Tukey-Kramer method for multiple comparison analysis is one possible approach.
As a result various plots are generated where in each graph, the mean of t | How to perform hypothesis testing for comparing different classifiers
One-way ANOVA followed by post hoc tests using Tukey-Kramer method for multiple comparison analysis is one possible approach.
As a result various plots are generated where in each graph, the mean of the classifier performance measure and an interval ... | How to perform hypothesis testing for comparing different classifiers
One-way ANOVA followed by post hoc tests using Tukey-Kramer method for multiple comparison analysis is one possible approach.
As a result various plots are generated where in each graph, the mean of t |
37,184 | How to perform hypothesis testing for comparing different classifiers | I would not do an ANOVA because your experimental design corresponds to a one way within subjects (the algorithms are tested on identical test-set folds). Such an ANOVA has a sphericity assumption which you cannot assume is met by your data.
But this is not a problem anyway. What you really need are those post-hoc test... | How to perform hypothesis testing for comparing different classifiers | I would not do an ANOVA because your experimental design corresponds to a one way within subjects (the algorithms are tested on identical test-set folds). Such an ANOVA has a sphericity assumption whi | How to perform hypothesis testing for comparing different classifiers
I would not do an ANOVA because your experimental design corresponds to a one way within subjects (the algorithms are tested on identical test-set folds). Such an ANOVA has a sphericity assumption which you cannot assume is met by your data.
But this... | How to perform hypothesis testing for comparing different classifiers
I would not do an ANOVA because your experimental design corresponds to a one way within subjects (the algorithms are tested on identical test-set folds). Such an ANOVA has a sphericity assumption whi |
37,185 | How do I implement a deep autoencoder? | Basically, you want to use layer-wise approach to train your deep autoencoder. You want to train one layer at a time, and then eventually do fine-tuning on all the layers.
You can follow this stanford UFLDL tutorial. It is a great tutorial for deep learning (have stacked autoencoder; not built from RBM. But it should ... | How do I implement a deep autoencoder? | Basically, you want to use layer-wise approach to train your deep autoencoder. You want to train one layer at a time, and then eventually do fine-tuning on all the layers.
You can follow this stanfor | How do I implement a deep autoencoder?
Basically, you want to use layer-wise approach to train your deep autoencoder. You want to train one layer at a time, and then eventually do fine-tuning on all the layers.
You can follow this stanford UFLDL tutorial. It is a great tutorial for deep learning (have stacked autoenco... | How do I implement a deep autoencoder?
Basically, you want to use layer-wise approach to train your deep autoencoder. You want to train one layer at a time, and then eventually do fine-tuning on all the layers.
You can follow this stanfor |
37,186 | Why it is better to use the cumulative distribution to compute distances? | We all know the equation for the PDF of a Gaussian distribution, right?
$$
f_X(x\vert\mu,\sigma^2) = \dfrac{1}{\sqrt{2\pi\sigma^2}}\exp\bigg[{-\dfrac{1}{2}\bigg(\dfrac{x-\mu}{\sigma}\bigg)^2}\bigg]
$$
However, this also is a valid equation for the PDF of a Gaussian distribution.
$$
g_X(x\vert\mu,\sigma^2) = \begin{cas... | Why it is better to use the cumulative distribution to compute distances? | We all know the equation for the PDF of a Gaussian distribution, right?
$$
f_X(x\vert\mu,\sigma^2) = \dfrac{1}{\sqrt{2\pi\sigma^2}}\exp\bigg[{-\dfrac{1}{2}\bigg(\dfrac{x-\mu}{\sigma}\bigg)^2}\bigg]
$$ | Why it is better to use the cumulative distribution to compute distances?
We all know the equation for the PDF of a Gaussian distribution, right?
$$
f_X(x\vert\mu,\sigma^2) = \dfrac{1}{\sqrt{2\pi\sigma^2}}\exp\bigg[{-\dfrac{1}{2}\bigg(\dfrac{x-\mu}{\sigma}\bigg)^2}\bigg]
$$
However, this also is a valid equation for th... | Why it is better to use the cumulative distribution to compute distances?
We all know the equation for the PDF of a Gaussian distribution, right?
$$
f_X(x\vert\mu,\sigma^2) = \dfrac{1}{\sqrt{2\pi\sigma^2}}\exp\bigg[{-\dfrac{1}{2}\bigg(\dfrac{x-\mu}{\sigma}\bigg)^2}\bigg]
$$ |
37,187 | Why it is better to use the cumulative distribution to compute distances? | Others have already pointed out that a PDF can be modified arbitrarily on a set of probability measure zero, and this still gives a valid PDF for the random variable. That is true, but it is somewhat of an artificial answer to your question. In such cases, for almost all random variables we deal with in practice, the... | Why it is better to use the cumulative distribution to compute distances? | Others have already pointed out that a PDF can be modified arbitrarily on a set of probability measure zero, and this still gives a valid PDF for the random variable. That is true, but it is somewhat | Why it is better to use the cumulative distribution to compute distances?
Others have already pointed out that a PDF can be modified arbitrarily on a set of probability measure zero, and this still gives a valid PDF for the random variable. That is true, but it is somewhat of an artificial answer to your question. In... | Why it is better to use the cumulative distribution to compute distances?
Others have already pointed out that a PDF can be modified arbitrarily on a set of probability measure zero, and this still gives a valid PDF for the random variable. That is true, but it is somewhat |
37,188 | Conditioning on independent random variables | Given the information in the question, we have a sample of $n$ i.i.d normals (which also means that their joint distribution is also normal), each following $N(\mu, \sigma^2)$. Therefore $\bar X \sim N(\mu, \sigma^2/n)$.
One can easily calculate that $\operatorname{Cov}(X_1, \bar X) = \sigma^2/n$. So their correlation ... | Conditioning on independent random variables | Given the information in the question, we have a sample of $n$ i.i.d normals (which also means that their joint distribution is also normal), each following $N(\mu, \sigma^2)$. Therefore $\bar X \sim | Conditioning on independent random variables
Given the information in the question, we have a sample of $n$ i.i.d normals (which also means that their joint distribution is also normal), each following $N(\mu, \sigma^2)$. Therefore $\bar X \sim N(\mu, \sigma^2/n)$.
One can easily calculate that $\operatorname{Cov}(X_1,... | Conditioning on independent random variables
Given the information in the question, we have a sample of $n$ i.i.d normals (which also means that their joint distribution is also normal), each following $N(\mu, \sigma^2)$. Therefore $\bar X \sim |
37,189 | derivation of predictive distribution of Gaussian Process | See for example Murphyin page 110-111 Chapter 4.3 Inference in jointly Gaussian distributions. What you are looking for in Theorem 4.3.1, which uses the Matrix Inversion Lemma to compute the posterior conditional probabilities. Replacing $x_1$ with $u_{*}$ and $x_2$ with $u$, $\Sigma_{11}$ with $K_{x^*}$, $\Sigma_{22}$... | derivation of predictive distribution of Gaussian Process | See for example Murphyin page 110-111 Chapter 4.3 Inference in jointly Gaussian distributions. What you are looking for in Theorem 4.3.1, which uses the Matrix Inversion Lemma to compute the posterior | derivation of predictive distribution of Gaussian Process
See for example Murphyin page 110-111 Chapter 4.3 Inference in jointly Gaussian distributions. What you are looking for in Theorem 4.3.1, which uses the Matrix Inversion Lemma to compute the posterior conditional probabilities. Replacing $x_1$ with $u_{*}$ and $... | derivation of predictive distribution of Gaussian Process
See for example Murphyin page 110-111 Chapter 4.3 Inference in jointly Gaussian distributions. What you are looking for in Theorem 4.3.1, which uses the Matrix Inversion Lemma to compute the posterior |
37,190 | How to design experiments for Market Research (with a twist)? | One approach to your problem is using a stratified sample. One purpose of stratification is making sure certain domains (groups) of the population are represented in the sample, which otherwise would be represented too sparsely for valid inference, e.g. due to small selection probability.
For example, if "Native Americ... | How to design experiments for Market Research (with a twist)? | One approach to your problem is using a stratified sample. One purpose of stratification is making sure certain domains (groups) of the population are represented in the sample, which otherwise would | How to design experiments for Market Research (with a twist)?
One approach to your problem is using a stratified sample. One purpose of stratification is making sure certain domains (groups) of the population are represented in the sample, which otherwise would be represented too sparsely for valid inference, e.g. due ... | How to design experiments for Market Research (with a twist)?
One approach to your problem is using a stratified sample. One purpose of stratification is making sure certain domains (groups) of the population are represented in the sample, which otherwise would |
37,191 | Can I use Wilcoxon Signed-Rank Test to test pairs of data in a time series? | One major concern is whether there's serial dependence in the differences, due to the observations being over time. The test assumes independence and if that doesn't hold, it could be badly affected. [The rest of my answer is predicated on independence being sufficiently close to true that the null distribution of the ... | Can I use Wilcoxon Signed-Rank Test to test pairs of data in a time series? | One major concern is whether there's serial dependence in the differences, due to the observations being over time. The test assumes independence and if that doesn't hold, it could be badly affected. | Can I use Wilcoxon Signed-Rank Test to test pairs of data in a time series?
One major concern is whether there's serial dependence in the differences, due to the observations being over time. The test assumes independence and if that doesn't hold, it could be badly affected. [The rest of my answer is predicated on inde... | Can I use Wilcoxon Signed-Rank Test to test pairs of data in a time series?
One major concern is whether there's serial dependence in the differences, due to the observations being over time. The test assumes independence and if that doesn't hold, it could be badly affected. |
37,192 | Can I use Wilcoxon Signed-Rank Test to test pairs of data in a time series? | I have also been wondering about this. It turns out that this question has cropped up a few times in the recent past:
Is Wilcoxon Signed-Rank Test the right test to use?
Can I use wilcoxon signed rank test for time series data
@Glen_b makes the point that autocorrelation in the data (e.g. the tendency for readings c... | Can I use Wilcoxon Signed-Rank Test to test pairs of data in a time series? | I have also been wondering about this. It turns out that this question has cropped up a few times in the recent past:
Is Wilcoxon Signed-Rank Test the right test to use?
Can I use wilcoxon signed ra | Can I use Wilcoxon Signed-Rank Test to test pairs of data in a time series?
I have also been wondering about this. It turns out that this question has cropped up a few times in the recent past:
Is Wilcoxon Signed-Rank Test the right test to use?
Can I use wilcoxon signed rank test for time series data
@Glen_b makes ... | Can I use Wilcoxon Signed-Rank Test to test pairs of data in a time series?
I have also been wondering about this. It turns out that this question has cropped up a few times in the recent past:
Is Wilcoxon Signed-Rank Test the right test to use?
Can I use wilcoxon signed ra |
37,193 | What method is simulating pvalues from re sampling from the data | It seems to me that Ellis could be referring to as many as three distinct ideas here. First he says something about creating "simulated data generated by a model under the null hypothesis of no relation." I would call this a form of parametric bootstrapping. Then he says that this would be "probably based on resampling... | What method is simulating pvalues from re sampling from the data | It seems to me that Ellis could be referring to as many as three distinct ideas here. First he says something about creating "simulated data generated by a model under the null hypothesis of no relati | What method is simulating pvalues from re sampling from the data
It seems to me that Ellis could be referring to as many as three distinct ideas here. First he says something about creating "simulated data generated by a model under the null hypothesis of no relation." I would call this a form of parametric bootstrappi... | What method is simulating pvalues from re sampling from the data
It seems to me that Ellis could be referring to as many as three distinct ideas here. First he says something about creating "simulated data generated by a model under the null hypothesis of no relati |
37,194 | Specify a Zero-inflated (Hurdle) Gamma Model in JAGS/BUGS | I figured out the answer, with help from Martyn Plummer. My code uses the inverse link for the gamma model (and no inverse of the predictors). Also, this code requires the 'glm' module for JAGS.
model{
# For the ones trick
C <- 10000
# for every observation
for(i in 1:N){
# define the logistic regression... | Specify a Zero-inflated (Hurdle) Gamma Model in JAGS/BUGS | I figured out the answer, with help from Martyn Plummer. My code uses the inverse link for the gamma model (and no inverse of the predictors). Also, this code requires the 'glm' module for JAGS.
model | Specify a Zero-inflated (Hurdle) Gamma Model in JAGS/BUGS
I figured out the answer, with help from Martyn Plummer. My code uses the inverse link for the gamma model (and no inverse of the predictors). Also, this code requires the 'glm' module for JAGS.
model{
# For the ones trick
C <- 10000
# for every observat... | Specify a Zero-inflated (Hurdle) Gamma Model in JAGS/BUGS
I figured out the answer, with help from Martyn Plummer. My code uses the inverse link for the gamma model (and no inverse of the predictors). Also, this code requires the 'glm' module for JAGS.
model |
37,195 | G-test statistic and KL divergence | People use inconsistent language with the KL divergence. Sometimes "the divergence of $Q$ from $P$" means $KL(P \| Q)$; sometimes it means $KL(Q \| P)$.
$KL(\text{true} \| \text{approximation})$ indeed has a nice information-theoretic interpretation as the inefficiency due to encoding the true distribution with a code ... | G-test statistic and KL divergence | People use inconsistent language with the KL divergence. Sometimes "the divergence of $Q$ from $P$" means $KL(P \| Q)$; sometimes it means $KL(Q \| P)$.
$KL(\text{true} \| \text{approximation})$ indee | G-test statistic and KL divergence
People use inconsistent language with the KL divergence. Sometimes "the divergence of $Q$ from $P$" means $KL(P \| Q)$; sometimes it means $KL(Q \| P)$.
$KL(\text{true} \| \text{approximation})$ indeed has a nice information-theoretic interpretation as the inefficiency due to encoding... | G-test statistic and KL divergence
People use inconsistent language with the KL divergence. Sometimes "the divergence of $Q$ from $P$" means $KL(P \| Q)$; sometimes it means $KL(Q \| P)$.
$KL(\text{true} \| \text{approximation})$ indee |
37,196 | A Bayesian perspective on omitted-variable bias (and other covariate-selection bias problems) | In general, Bayesian estimation is not very concerned with unbiasedness of estimators since the model is always misspecified. There definitely exist proofs about conditions for unbiased estimation in Bayesian frameworks. I just don't think practitioners care very much about that and try to avoid using fitting procedure... | A Bayesian perspective on omitted-variable bias (and other covariate-selection bias problems) | In general, Bayesian estimation is not very concerned with unbiasedness of estimators since the model is always misspecified. There definitely exist proofs about conditions for unbiased estimation in | A Bayesian perspective on omitted-variable bias (and other covariate-selection bias problems)
In general, Bayesian estimation is not very concerned with unbiasedness of estimators since the model is always misspecified. There definitely exist proofs about conditions for unbiased estimation in Bayesian frameworks. I jus... | A Bayesian perspective on omitted-variable bias (and other covariate-selection bias problems)
In general, Bayesian estimation is not very concerned with unbiasedness of estimators since the model is always misspecified. There definitely exist proofs about conditions for unbiased estimation in |
37,197 | A Bayesian perspective on omitted-variable bias (and other covariate-selection bias problems) | It's not properly true that Bayesian models are always misspecified!
Try by yourself... You will realize that even with a wrong prior you can find conditions for having an unbiased posterior estimator. | A Bayesian perspective on omitted-variable bias (and other covariate-selection bias problems) | It's not properly true that Bayesian models are always misspecified!
Try by yourself... You will realize that even with a wrong prior you can find conditions for having an unbiased posterior estimator | A Bayesian perspective on omitted-variable bias (and other covariate-selection bias problems)
It's not properly true that Bayesian models are always misspecified!
Try by yourself... You will realize that even with a wrong prior you can find conditions for having an unbiased posterior estimator. | A Bayesian perspective on omitted-variable bias (and other covariate-selection bias problems)
It's not properly true that Bayesian models are always misspecified!
Try by yourself... You will realize that even with a wrong prior you can find conditions for having an unbiased posterior estimator |
37,198 | How to select cut-point for making classifications table for logistic regression? | Setting these cut points should really be done in the context of some descicion making process. I'll give you an example that you might be able to generalize to your context.
Let's say I build a model that estimates the probability a person has event Y occur in the future, given their score on X today. I then estimate... | How to select cut-point for making classifications table for logistic regression? | Setting these cut points should really be done in the context of some descicion making process. I'll give you an example that you might be able to generalize to your context.
Let's say I build a mode | How to select cut-point for making classifications table for logistic regression?
Setting these cut points should really be done in the context of some descicion making process. I'll give you an example that you might be able to generalize to your context.
Let's say I build a model that estimates the probability a per... | How to select cut-point for making classifications table for logistic regression?
Setting these cut points should really be done in the context of some descicion making process. I'll give you an example that you might be able to generalize to your context.
Let's say I build a mode |
37,199 | How to select cut-point for making classifications table for logistic regression? | For example there is a R package ROCR which contains many valuable functions to evaluate a decision concerning cutt-off points. It might very well be that there is a range of values which are optimal in certain sense.
Also you can build decision based on cost function / loss function. For example consider False Positiv... | How to select cut-point for making classifications table for logistic regression? | For example there is a R package ROCR which contains many valuable functions to evaluate a decision concerning cutt-off points. It might very well be that there is a range of values which are optimal | How to select cut-point for making classifications table for logistic regression?
For example there is a R package ROCR which contains many valuable functions to evaluate a decision concerning cutt-off points. It might very well be that there is a range of values which are optimal in certain sense.
Also you can build d... | How to select cut-point for making classifications table for logistic regression?
For example there is a R package ROCR which contains many valuable functions to evaluate a decision concerning cutt-off points. It might very well be that there is a range of values which are optimal |
37,200 | How do I show that $(\hat{\beta_1}-\beta_1)$ and $ \bar{u}$ are uncorrelated, i.e. that $E[(\hat{\beta_1}-\beta_1) \bar{u}] = 0$? | Strategy
It can be illuminating to move back and forth among three points of view: the statistical one (viewing $x_i$ and $y_i$ as data), a geometrical one (where least squares solutions are just projections in suitable Euclidean spaces), and an algebraic one (manipulating symbols representing matrices or linear transf... | How do I show that $(\hat{\beta_1}-\beta_1)$ and $ \bar{u}$ are uncorrelated, i.e. that $E[(\hat{\be | Strategy
It can be illuminating to move back and forth among three points of view: the statistical one (viewing $x_i$ and $y_i$ as data), a geometrical one (where least squares solutions are just proj | How do I show that $(\hat{\beta_1}-\beta_1)$ and $ \bar{u}$ are uncorrelated, i.e. that $E[(\hat{\beta_1}-\beta_1) \bar{u}] = 0$?
Strategy
It can be illuminating to move back and forth among three points of view: the statistical one (viewing $x_i$ and $y_i$ as data), a geometrical one (where least squares solutions are... | How do I show that $(\hat{\beta_1}-\beta_1)$ and $ \bar{u}$ are uncorrelated, i.e. that $E[(\hat{\be
Strategy
It can be illuminating to move back and forth among three points of view: the statistical one (viewing $x_i$ and $y_i$ as data), a geometrical one (where least squares solutions are just proj |
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