idx int64 1 56k | question stringlengths 15 155 | answer stringlengths 2 29.2k ⌀ | question_cut stringlengths 15 100 | answer_cut stringlengths 2 200 ⌀ | conversation stringlengths 47 29.3k | conversation_cut stringlengths 47 301 |
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42,201 | Formula for confidence intervals for small samples and unknown population standard deviation | Here are some good notes on standard deviation and the standard error of the mean here.
The Wackerly et al text computes small sample confidence intervals in section 8.8 (page 430) you can see their formula here.
Confidence interval: $\bar{Y} \pm t_{\alpha/2} * \frac{S}{\sqrt{n}}$
Where $\bar{y}$ = $\frac{1}{n}$$\sum{\... | Formula for confidence intervals for small samples and unknown population standard deviation | Here are some good notes on standard deviation and the standard error of the mean here.
The Wackerly et al text computes small sample confidence intervals in section 8.8 (page 430) you can see their f | Formula for confidence intervals for small samples and unknown population standard deviation
Here are some good notes on standard deviation and the standard error of the mean here.
The Wackerly et al text computes small sample confidence intervals in section 8.8 (page 430) you can see their formula here.
Confidence int... | Formula for confidence intervals for small samples and unknown population standard deviation
Here are some good notes on standard deviation and the standard error of the mean here.
The Wackerly et al text computes small sample confidence intervals in section 8.8 (page 430) you can see their f |
42,202 | Moments of Laplace distribution | Here is a quick check using a symbolic algebra package ...
Let $X \sim \text{Laplace}(\mu, \sigma)$ with pdf $f(x)$:
Then, the first 4 raw moments $E[X^i]$ are given by:
where I am using the Expect function from the mathStatica package for Mathematica.
It is worth noting that the $3^\text{rd}$ and $4^\text{th}$ raw ... | Moments of Laplace distribution | Here is a quick check using a symbolic algebra package ...
Let $X \sim \text{Laplace}(\mu, \sigma)$ with pdf $f(x)$:
Then, the first 4 raw moments $E[X^i]$ are given by:
where I am using the Expect | Moments of Laplace distribution
Here is a quick check using a symbolic algebra package ...
Let $X \sim \text{Laplace}(\mu, \sigma)$ with pdf $f(x)$:
Then, the first 4 raw moments $E[X^i]$ are given by:
where I am using the Expect function from the mathStatica package for Mathematica.
It is worth noting that the $3^\... | Moments of Laplace distribution
Here is a quick check using a symbolic algebra package ...
Let $X \sim \text{Laplace}(\mu, \sigma)$ with pdf $f(x)$:
Then, the first 4 raw moments $E[X^i]$ are given by:
where I am using the Expect |
42,203 | Moments of Laplace distribution | It's been awhile and looks like this hasn't been answered. I'll provide one and hopefully we can mark this as correct. I'll answer in order the questions asked using the parameterization of the wikipedia page
$$f(x\mid\mu,b)= \frac{1}{2b} \exp \left( -\frac{|x-\mu|}{b} \right), x\in \mathbb{R}. $$
For the case $\mu=0$... | Moments of Laplace distribution | It's been awhile and looks like this hasn't been answered. I'll provide one and hopefully we can mark this as correct. I'll answer in order the questions asked using the parameterization of the wikipe | Moments of Laplace distribution
It's been awhile and looks like this hasn't been answered. I'll provide one and hopefully we can mark this as correct. I'll answer in order the questions asked using the parameterization of the wikipedia page
$$f(x\mid\mu,b)= \frac{1}{2b} \exp \left( -\frac{|x-\mu|}{b} \right), x\in \mat... | Moments of Laplace distribution
It's been awhile and looks like this hasn't been answered. I'll provide one and hopefully we can mark this as correct. I'll answer in order the questions asked using the parameterization of the wikipe |
42,204 | What to do with almost-continuous variable in regression? | I'd say interact continuous age with a dummy "continuous age is available", and categorical age with a dummy "continuous age is not available". That way you'll be using as much of the information you have as possible.
Of course if the effect of age is something you'd like to be able to summarize with just one point est... | What to do with almost-continuous variable in regression? | I'd say interact continuous age with a dummy "continuous age is available", and categorical age with a dummy "continuous age is not available". That way you'll be using as much of the information you | What to do with almost-continuous variable in regression?
I'd say interact continuous age with a dummy "continuous age is available", and categorical age with a dummy "continuous age is not available". That way you'll be using as much of the information you have as possible.
Of course if the effect of age is something ... | What to do with almost-continuous variable in regression?
I'd say interact continuous age with a dummy "continuous age is available", and categorical age with a dummy "continuous age is not available". That way you'll be using as much of the information you |
42,205 | What to do with almost-continuous variable in regression? | You can incorporate this in the Bayesian framework by specifying a prior distribution for the age variable. And for the posterior, you have:
$$p(\theta|DI)\propto p(\theta|I)p(D|\theta I)$$
Now you simply take $D\equiv (18+)$ for example. This is no more difficult "in-principle" compared to when you actually do know ... | What to do with almost-continuous variable in regression? | You can incorporate this in the Bayesian framework by specifying a prior distribution for the age variable. And for the posterior, you have:
$$p(\theta|DI)\propto p(\theta|I)p(D|\theta I)$$
Now you s | What to do with almost-continuous variable in regression?
You can incorporate this in the Bayesian framework by specifying a prior distribution for the age variable. And for the posterior, you have:
$$p(\theta|DI)\propto p(\theta|I)p(D|\theta I)$$
Now you simply take $D\equiv (18+)$ for example. This is no more diffi... | What to do with almost-continuous variable in regression?
You can incorporate this in the Bayesian framework by specifying a prior distribution for the age variable. And for the posterior, you have:
$$p(\theta|DI)\propto p(\theta|I)p(D|\theta I)$$
Now you s |
42,206 | What to do with almost-continuous variable in regression? | You can treat age as an interval censored variable. Some survival routines do this in a straight forward way for the response variable, if age is a predictor then I don't know if there are ready made tools available. But you could still do it using maximum liklihood. | What to do with almost-continuous variable in regression? | You can treat age as an interval censored variable. Some survival routines do this in a straight forward way for the response variable, if age is a predictor then I don't know if there are ready made | What to do with almost-continuous variable in regression?
You can treat age as an interval censored variable. Some survival routines do this in a straight forward way for the response variable, if age is a predictor then I don't know if there are ready made tools available. But you could still do it using maximum lik... | What to do with almost-continuous variable in regression?
You can treat age as an interval censored variable. Some survival routines do this in a straight forward way for the response variable, if age is a predictor then I don't know if there are ready made |
42,207 | Probability for finding a double-as-likely event | Partition the outcomes by the frequency of occurrences $x$ of the "double outcome", $0 \le x \le t$. Conditional on this number, the distribution of the remaining $t-x$ outcomes is multinomial across $n-1$ equiprobable bins. Let $p(t-x, n-1, x)$ be the chance that no bin out of $n-1$ equally likely ones receives more... | Probability for finding a double-as-likely event | Partition the outcomes by the frequency of occurrences $x$ of the "double outcome", $0 \le x \le t$. Conditional on this number, the distribution of the remaining $t-x$ outcomes is multinomial across | Probability for finding a double-as-likely event
Partition the outcomes by the frequency of occurrences $x$ of the "double outcome", $0 \le x \le t$. Conditional on this number, the distribution of the remaining $t-x$ outcomes is multinomial across $n-1$ equiprobable bins. Let $p(t-x, n-1, x)$ be the chance that no b... | Probability for finding a double-as-likely event
Partition the outcomes by the frequency of occurrences $x$ of the "double outcome", $0 \le x \le t$. Conditional on this number, the distribution of the remaining $t-x$ outcomes is multinomial across |
42,208 | Probability for finding a double-as-likely event | I agree with some comments, in that the Poisson approximation sounds nice here (not a 'crude' approximation). It should be asympotically exact, and it seems the most reasonable thing to do, as an exact analytic solutions seems difficult.
As an intermediate alternative, (if you really need it) I suggest I fisrt order co... | Probability for finding a double-as-likely event | I agree with some comments, in that the Poisson approximation sounds nice here (not a 'crude' approximation). It should be asympotically exact, and it seems the most reasonable thing to do, as an exac | Probability for finding a double-as-likely event
I agree with some comments, in that the Poisson approximation sounds nice here (not a 'crude' approximation). It should be asympotically exact, and it seems the most reasonable thing to do, as an exact analytic solutions seems difficult.
As an intermediate alternative, (... | Probability for finding a double-as-likely event
I agree with some comments, in that the Poisson approximation sounds nice here (not a 'crude' approximation). It should be asympotically exact, and it seems the most reasonable thing to do, as an exac |
42,209 | Probability for finding a double-as-likely event | Just a word of explanation: Part out of curiosity, part for lack of a better more theoretical method, i approached the problem in a completely empirical/inductive way. I'm aware that there is the risk of getting stuck in a dead end without gaining much insight, but i thought, i'll just present what i got so far anyway,... | Probability for finding a double-as-likely event | Just a word of explanation: Part out of curiosity, part for lack of a better more theoretical method, i approached the problem in a completely empirical/inductive way. I'm aware that there is the risk | Probability for finding a double-as-likely event
Just a word of explanation: Part out of curiosity, part for lack of a better more theoretical method, i approached the problem in a completely empirical/inductive way. I'm aware that there is the risk of getting stuck in a dead end without gaining much insight, but i tho... | Probability for finding a double-as-likely event
Just a word of explanation: Part out of curiosity, part for lack of a better more theoretical method, i approached the problem in a completely empirical/inductive way. I'm aware that there is the risk |
42,210 | Improving accuracy of a binary classification when the target is unbalanced | The problem is more with the choice of the accuracy scoring rule. Make sure that the ultimate goal is classification as opposed to prediction. The proportion classified correctly is a discontinuous improper scoring rule. An improper scoring rule is one that is optimized by a bogus model. With an improper scoring ru... | Improving accuracy of a binary classification when the target is unbalanced | The problem is more with the choice of the accuracy scoring rule. Make sure that the ultimate goal is classification as opposed to prediction. The proportion classified correctly is a discontinuous | Improving accuracy of a binary classification when the target is unbalanced
The problem is more with the choice of the accuracy scoring rule. Make sure that the ultimate goal is classification as opposed to prediction. The proportion classified correctly is a discontinuous improper scoring rule. An improper scoring ... | Improving accuracy of a binary classification when the target is unbalanced
The problem is more with the choice of the accuracy scoring rule. Make sure that the ultimate goal is classification as opposed to prediction. The proportion classified correctly is a discontinuous |
42,211 | Improving accuracy of a binary classification when the target is unbalanced | Regarding decision trees, I would suggest the following. Assume that you have 10 training examples from class $C_1$ and 90 training examples from class $C_2$. You can use an ensemble of $N$ decision trees, where each tree is trained on 10 examples from $C_1$ and 10 randomly chosen examples from $C_2$. The decision of t... | Improving accuracy of a binary classification when the target is unbalanced | Regarding decision trees, I would suggest the following. Assume that you have 10 training examples from class $C_1$ and 90 training examples from class $C_2$. You can use an ensemble of $N$ decision t | Improving accuracy of a binary classification when the target is unbalanced
Regarding decision trees, I would suggest the following. Assume that you have 10 training examples from class $C_1$ and 90 training examples from class $C_2$. You can use an ensemble of $N$ decision trees, where each tree is trained on 10 examp... | Improving accuracy of a binary classification when the target is unbalanced
Regarding decision trees, I would suggest the following. Assume that you have 10 training examples from class $C_1$ and 90 training examples from class $C_2$. You can use an ensemble of $N$ decision t |
42,212 | Improving accuracy of a binary classification when the target is unbalanced | Based on the output you shared, Maximum # of branches from a node is set at 2. It's possible that raising that limit would give you more options for branches, especially if SAS can take continuous variables and break them up into categories. It's data dredgy, but that's the game we're in, and as long as you crossvali... | Improving accuracy of a binary classification when the target is unbalanced | Based on the output you shared, Maximum # of branches from a node is set at 2. It's possible that raising that limit would give you more options for branches, especially if SAS can take continuous va | Improving accuracy of a binary classification when the target is unbalanced
Based on the output you shared, Maximum # of branches from a node is set at 2. It's possible that raising that limit would give you more options for branches, especially if SAS can take continuous variables and break them up into categories. ... | Improving accuracy of a binary classification when the target is unbalanced
Based on the output you shared, Maximum # of branches from a node is set at 2. It's possible that raising that limit would give you more options for branches, especially if SAS can take continuous va |
42,213 | Improving accuracy of a binary classification when the target is unbalanced | If you are using tree-based methods, you can play around with the splitting criterion. For example, at each step, choose the split that gives the highest weighted accuracy (the average of the two classes' accuracies).
This can be used as the basis for a random forest too, which should give you a good classifier.
I once... | Improving accuracy of a binary classification when the target is unbalanced | If you are using tree-based methods, you can play around with the splitting criterion. For example, at each step, choose the split that gives the highest weighted accuracy (the average of the two clas | Improving accuracy of a binary classification when the target is unbalanced
If you are using tree-based methods, you can play around with the splitting criterion. For example, at each step, choose the split that gives the highest weighted accuracy (the average of the two classes' accuracies).
This can be used as the ba... | Improving accuracy of a binary classification when the target is unbalanced
If you are using tree-based methods, you can play around with the splitting criterion. For example, at each step, choose the split that gives the highest weighted accuracy (the average of the two clas |
42,214 | Effect size of Cochran's Q | I have found two measures of effect size in the literature for Cochran's $Q$ test of $b$ blocks (subjects) and $k$ treatments (groups):
Serlin, Carr and Marascuillo's (2007) maximum-corrected measure of effect size ($\eta^{2}_{Q}$), which is given by:
$$\eta^{2}_{Q} = \frac{Q}{b(k-1)},$$
where $0\le\eta^{2}_{Q}\le 1$.
... | Effect size of Cochran's Q | I have found two measures of effect size in the literature for Cochran's $Q$ test of $b$ blocks (subjects) and $k$ treatments (groups):
Serlin, Carr and Marascuillo's (2007) maximum-corrected measure | Effect size of Cochran's Q
I have found two measures of effect size in the literature for Cochran's $Q$ test of $b$ blocks (subjects) and $k$ treatments (groups):
Serlin, Carr and Marascuillo's (2007) maximum-corrected measure of effect size ($\eta^{2}_{Q}$), which is given by:
$$\eta^{2}_{Q} = \frac{Q}{b(k-1)},$$
wher... | Effect size of Cochran's Q
I have found two measures of effect size in the literature for Cochran's $Q$ test of $b$ blocks (subjects) and $k$ treatments (groups):
Serlin, Carr and Marascuillo's (2007) maximum-corrected measure |
42,215 | Effect size of Cochran's Q | I found this paper with Google but I cannot access it, so I don't really know what it is about really:
Berry KJ, Johnston JE, Mielke PW Jr.
An alternative measure of effect size
for Cochran's Q test for related
proportions. Percept Mot Skills.
2007 Jun;104(3 Pt 2):1236-42.
I initially thought that using pairw... | Effect size of Cochran's Q | I found this paper with Google but I cannot access it, so I don't really know what it is about really:
Berry KJ, Johnston JE, Mielke PW Jr.
An alternative measure of effect size
for Cochran's Q t | Effect size of Cochran's Q
I found this paper with Google but I cannot access it, so I don't really know what it is about really:
Berry KJ, Johnston JE, Mielke PW Jr.
An alternative measure of effect size
for Cochran's Q test for related
proportions. Percept Mot Skills.
2007 Jun;104(3 Pt 2):1236-42.
I initial... | Effect size of Cochran's Q
I found this paper with Google but I cannot access it, so I don't really know what it is about really:
Berry KJ, Johnston JE, Mielke PW Jr.
An alternative measure of effect size
for Cochran's Q t |
42,216 | Binomial data analysis with all 0 responses for some treatment groups | The problem with zeroes, is that the data do not rule out arbitrarily small proportions. So your prior information must be assessed more carefully, because in this case it still matters. Details which are irrelevant when the prior information is "swamped" by the data can be important. In this type of problem, the po... | Binomial data analysis with all 0 responses for some treatment groups | The problem with zeroes, is that the data do not rule out arbitrarily small proportions. So your prior information must be assessed more carefully, because in this case it still matters. Details whi | Binomial data analysis with all 0 responses for some treatment groups
The problem with zeroes, is that the data do not rule out arbitrarily small proportions. So your prior information must be assessed more carefully, because in this case it still matters. Details which are irrelevant when the prior information is "s... | Binomial data analysis with all 0 responses for some treatment groups
The problem with zeroes, is that the data do not rule out arbitrarily small proportions. So your prior information must be assessed more carefully, because in this case it still matters. Details whi |
42,217 | Binomial data analysis with all 0 responses for some treatment groups | I believe that this is an experiment where it is safe to assume a monotone relationship: for a longer exposition time the infection probability can not be smaller. So you can run monotone/isotonic regression.
You can even incorporate into your model that the infection probability at time=0 is 0. | Binomial data analysis with all 0 responses for some treatment groups | I believe that this is an experiment where it is safe to assume a monotone relationship: for a longer exposition time the infection probability can not be smaller. So you can run monotone/isotonic reg | Binomial data analysis with all 0 responses for some treatment groups
I believe that this is an experiment where it is safe to assume a monotone relationship: for a longer exposition time the infection probability can not be smaller. So you can run monotone/isotonic regression.
You can even incorporate into your model ... | Binomial data analysis with all 0 responses for some treatment groups
I believe that this is an experiment where it is safe to assume a monotone relationship: for a longer exposition time the infection probability can not be smaller. So you can run monotone/isotonic reg |
42,218 | Binomial data analysis with all 0 responses for some treatment groups | You could try exact logistic regression with proc logistic, but then you cannot specify random effects somewhere in your model which you probably do now as you're using proc mixed. You'd have to switch to fixed effects but you could keep the binomial error distribution. | Binomial data analysis with all 0 responses for some treatment groups | You could try exact logistic regression with proc logistic, but then you cannot specify random effects somewhere in your model which you probably do now as you're using proc mixed. You'd have to switc | Binomial data analysis with all 0 responses for some treatment groups
You could try exact logistic regression with proc logistic, but then you cannot specify random effects somewhere in your model which you probably do now as you're using proc mixed. You'd have to switch to fixed effects but you could keep the binomial... | Binomial data analysis with all 0 responses for some treatment groups
You could try exact logistic regression with proc logistic, but then you cannot specify random effects somewhere in your model which you probably do now as you're using proc mixed. You'd have to switc |
42,219 | Remeasuring "bad" values | If the probability of a bad measurement is small than the probability of having two bad measurements out of three will be very small, thus neglecting the outlying one among the three will usually leave you with two valid measurements.
I would, however, record all the values measured, even other measurements on the same... | Remeasuring "bad" values | If the probability of a bad measurement is small than the probability of having two bad measurements out of three will be very small, thus neglecting the outlying one among the three will usually leav | Remeasuring "bad" values
If the probability of a bad measurement is small than the probability of having two bad measurements out of three will be very small, thus neglecting the outlying one among the three will usually leave you with two valid measurements.
I would, however, record all the values measured, even other... | Remeasuring "bad" values
If the probability of a bad measurement is small than the probability of having two bad measurements out of three will be very small, thus neglecting the outlying one among the three will usually leav |
42,220 | Is there a method to find what is a good sample size for a VAR-model? | The usual way of estimating VAR(p) model for $n$-dimensional vector $X_t=(X_{1t},...,X_{nt})$ is using OLS for each equation:
\begin{align}
X_{it}=\theta_{0i}+\sum_{s=1}^p\sum_{j=1}^n\theta_{sj}X_{j,t-s}+\varepsilon_{it}
\end{align}
So the answer is yes. For each equation you will need to estimate $np+1$ parameters, so... | Is there a method to find what is a good sample size for a VAR-model? | The usual way of estimating VAR(p) model for $n$-dimensional vector $X_t=(X_{1t},...,X_{nt})$ is using OLS for each equation:
\begin{align}
X_{it}=\theta_{0i}+\sum_{s=1}^p\sum_{j=1}^n\theta_{sj}X_{j,t | Is there a method to find what is a good sample size for a VAR-model?
The usual way of estimating VAR(p) model for $n$-dimensional vector $X_t=(X_{1t},...,X_{nt})$ is using OLS for each equation:
\begin{align}
X_{it}=\theta_{0i}+\sum_{s=1}^p\sum_{j=1}^n\theta_{sj}X_{j,t-s}+\varepsilon_{it}
\end{align}
So the answer is ... | Is there a method to find what is a good sample size for a VAR-model?
The usual way of estimating VAR(p) model for $n$-dimensional vector $X_t=(X_{1t},...,X_{nt})$ is using OLS for each equation:
\begin{align}
X_{it}=\theta_{0i}+\sum_{s=1}^p\sum_{j=1}^n\theta_{sj}X_{j,t |
42,221 | Limiting distribution of a squared sum of random variables | If $X_i$ and $Y_j$ are dependent for $i=j$, but independent for $i\neq j$ we have an iid sample from bivariate distribution $Z_i=(X_i,Y_i)$. Then central limit theorem gives us
\begin{align}
\sqrt{n}\left(\frac{1}{n}\sum_{i=1}^nZ_i -EZ_1\right)\xrightarrow{D}N(0,\Sigma)
\end{align}
with $\Sigma=cov(Z_1)$ and $\xrighta... | Limiting distribution of a squared sum of random variables | If $X_i$ and $Y_j$ are dependent for $i=j$, but independent for $i\neq j$ we have an iid sample from bivariate distribution $Z_i=(X_i,Y_i)$. Then central limit theorem gives us
\begin{align}
\sqrt{n} | Limiting distribution of a squared sum of random variables
If $X_i$ and $Y_j$ are dependent for $i=j$, but independent for $i\neq j$ we have an iid sample from bivariate distribution $Z_i=(X_i,Y_i)$. Then central limit theorem gives us
\begin{align}
\sqrt{n}\left(\frac{1}{n}\sum_{i=1}^nZ_i -EZ_1\right)\xrightarrow{D}N... | Limiting distribution of a squared sum of random variables
If $X_i$ and $Y_j$ are dependent for $i=j$, but independent for $i\neq j$ we have an iid sample from bivariate distribution $Z_i=(X_i,Y_i)$. Then central limit theorem gives us
\begin{align}
\sqrt{n} |
42,222 | How can I make a continuous distribution out of simulation results in R? | It sounds like what you're describing is a bootstrap simulation in order to estimate the distribution of a statistic (the relative frequencies).
The package I'd suggest you to look into is the boot package:
functions and datasets for
bootstrapping from the book "Bootstrap
Methods and Their Applications" by A.
C.... | How can I make a continuous distribution out of simulation results in R? | It sounds like what you're describing is a bootstrap simulation in order to estimate the distribution of a statistic (the relative frequencies).
The package I'd suggest you to look into is the boot pa | How can I make a continuous distribution out of simulation results in R?
It sounds like what you're describing is a bootstrap simulation in order to estimate the distribution of a statistic (the relative frequencies).
The package I'd suggest you to look into is the boot package:
functions and datasets for
bootstrapp... | How can I make a continuous distribution out of simulation results in R?
It sounds like what you're describing is a bootstrap simulation in order to estimate the distribution of a statistic (the relative frequencies).
The package I'd suggest you to look into is the boot pa |
42,223 | How can I make a continuous distribution out of simulation results in R? | Sounds like you want something like a Kernel Density Estimate of the distribution. In R I think you want density function. | How can I make a continuous distribution out of simulation results in R? | Sounds like you want something like a Kernel Density Estimate of the distribution. In R I think you want density function. | How can I make a continuous distribution out of simulation results in R?
Sounds like you want something like a Kernel Density Estimate of the distribution. In R I think you want density function. | How can I make a continuous distribution out of simulation results in R?
Sounds like you want something like a Kernel Density Estimate of the distribution. In R I think you want density function. |
42,224 | What options are there to combine different distance functions? | I can think of three:
Combine them in a linear manner ($d=d_1+\alpha d_2$) and find best $\alpha$ by some optimization, let's say minimizing CV error for kNN or minimizing silhouette for clustering.
Train separate classifiers / cluster the data few times based on both distances and then blend the results. This may not... | What options are there to combine different distance functions? | I can think of three:
Combine them in a linear manner ($d=d_1+\alpha d_2$) and find best $\alpha$ by some optimization, let's say minimizing CV error for kNN or minimizing silhouette for clustering.
| What options are there to combine different distance functions?
I can think of three:
Combine them in a linear manner ($d=d_1+\alpha d_2$) and find best $\alpha$ by some optimization, let's say minimizing CV error for kNN or minimizing silhouette for clustering.
Train separate classifiers / cluster the data few times ... | What options are there to combine different distance functions?
I can think of three:
Combine them in a linear manner ($d=d_1+\alpha d_2$) and find best $\alpha$ by some optimization, let's say minimizing CV error for kNN or minimizing silhouette for clustering.
|
42,225 | Assessing linearity in a mixed effects model | Not really an answer, but I was interested in trying it out...
I assume that the pattern is not easily recognisable just by plotting? So I tried to make up some data that might behave this way:
set.seed(69)
id<- rep(1:20, each=6)
x<-rep(1:6, 20)
y<-jitter(x+id/5, factor=5) + jitter(sin(x), factor=5)
df1<-data.frame(id,... | Assessing linearity in a mixed effects model | Not really an answer, but I was interested in trying it out...
I assume that the pattern is not easily recognisable just by plotting? So I tried to make up some data that might behave this way:
set.se | Assessing linearity in a mixed effects model
Not really an answer, but I was interested in trying it out...
I assume that the pattern is not easily recognisable just by plotting? So I tried to make up some data that might behave this way:
set.seed(69)
id<- rep(1:20, each=6)
x<-rep(1:6, 20)
y<-jitter(x+id/5, factor=5) +... | Assessing linearity in a mixed effects model
Not really an answer, but I was interested in trying it out...
I assume that the pattern is not easily recognisable just by plotting? So I tried to make up some data that might behave this way:
set.se |
42,226 | A measure to describe the distribution of a dendrogram | See this SO question: https://stackoverflow.com/questions/2218395/how-do-you-compare-the-similarity-between-two-dendrograms-in-r | A measure to describe the distribution of a dendrogram | See this SO question: https://stackoverflow.com/questions/2218395/how-do-you-compare-the-similarity-between-two-dendrograms-in-r | A measure to describe the distribution of a dendrogram
See this SO question: https://stackoverflow.com/questions/2218395/how-do-you-compare-the-similarity-between-two-dendrograms-in-r | A measure to describe the distribution of a dendrogram
See this SO question: https://stackoverflow.com/questions/2218395/how-do-you-compare-the-similarity-between-two-dendrograms-in-r |
42,227 | Model suggestion | Not easy at all. This starts to sound like the sort of thing that Jamie Robins and colleagues have done a lot of work on. To quote the start of the abstract of one of their papers:
"In observational studies with exposures or treatments that vary over time, standard approaches for adjustment of confounding are biased wh... | Model suggestion | Not easy at all. This starts to sound like the sort of thing that Jamie Robins and colleagues have done a lot of work on. To quote the start of the abstract of one of their papers:
"In observational s | Model suggestion
Not easy at all. This starts to sound like the sort of thing that Jamie Robins and colleagues have done a lot of work on. To quote the start of the abstract of one of their papers:
"In observational studies with exposures or treatments that vary over time, standard approaches for adjustment of confound... | Model suggestion
Not easy at all. This starts to sound like the sort of thing that Jamie Robins and colleagues have done a lot of work on. To quote the start of the abstract of one of their papers:
"In observational s |
42,228 | Model suggestion | You have clearly stated a part of your model:
C depends on B, in that values of B above a threshold will change C. The change in C will furthermore reduce B in the next measurement.
By "next measurement" I understand you mean next in time. Let's index time as $t = 0, 1, 2, \ldots$. Then the dependence of C on B sou... | Model suggestion | You have clearly stated a part of your model:
C depends on B, in that values of B above a threshold will change C. The change in C will furthermore reduce B in the next measurement.
By "next measure | Model suggestion
You have clearly stated a part of your model:
C depends on B, in that values of B above a threshold will change C. The change in C will furthermore reduce B in the next measurement.
By "next measurement" I understand you mean next in time. Let's index time as $t = 0, 1, 2, \ldots$. Then the depende... | Model suggestion
You have clearly stated a part of your model:
C depends on B, in that values of B above a threshold will change C. The change in C will furthermore reduce B in the next measurement.
By "next measure |
42,229 | Model suggestion | Your problem is one of multi-collinear regressors (since B and C are correlated). I would suggest that you look at the answers to the question: Dealing with correlated regressors.
The following paper may also be relevant in your context: Using principal components for estimating logistic regression with high-dimension... | Model suggestion | Your problem is one of multi-collinear regressors (since B and C are correlated). I would suggest that you look at the answers to the question: Dealing with correlated regressors.
The following paper | Model suggestion
Your problem is one of multi-collinear regressors (since B and C are correlated). I would suggest that you look at the answers to the question: Dealing with correlated regressors.
The following paper may also be relevant in your context: Using principal components for estimating logistic regression wi... | Model suggestion
Your problem is one of multi-collinear regressors (since B and C are correlated). I would suggest that you look at the answers to the question: Dealing with correlated regressors.
The following paper |
42,230 | Bootstrapped regression with total data or bootstrap with matched data? | There is a wrinkle that you need to worry about. In the case of matching, you are throwing away observations (i.e., those that aren't matched and don't make it into your analysis) and some might be replicated. These decisions aren't random; they are a function of covariates. As a result, creating confidence intervals i... | Bootstrapped regression with total data or bootstrap with matched data? | There is a wrinkle that you need to worry about. In the case of matching, you are throwing away observations (i.e., those that aren't matched and don't make it into your analysis) and some might be re | Bootstrapped regression with total data or bootstrap with matched data?
There is a wrinkle that you need to worry about. In the case of matching, you are throwing away observations (i.e., those that aren't matched and don't make it into your analysis) and some might be replicated. These decisions aren't random; they ar... | Bootstrapped regression with total data or bootstrap with matched data?
There is a wrinkle that you need to worry about. In the case of matching, you are throwing away observations (i.e., those that aren't matched and don't make it into your analysis) and some might be re |
42,231 | How can I work around "lumpiness" in simulated maximum likelihood estimation? | It sounds like you need to use a more robust optimization algorithm that can handle local minima. Particle swarm methods work quite well in this case. Or you could try other evolutionary optimization methods or simulated annealing. | How can I work around "lumpiness" in simulated maximum likelihood estimation? | It sounds like you need to use a more robust optimization algorithm that can handle local minima. Particle swarm methods work quite well in this case. Or you could try other evolutionary optimization | How can I work around "lumpiness" in simulated maximum likelihood estimation?
It sounds like you need to use a more robust optimization algorithm that can handle local minima. Particle swarm methods work quite well in this case. Or you could try other evolutionary optimization methods or simulated annealing. | How can I work around "lumpiness" in simulated maximum likelihood estimation?
It sounds like you need to use a more robust optimization algorithm that can handle local minima. Particle swarm methods work quite well in this case. Or you could try other evolutionary optimization |
42,232 | How can I work around "lumpiness" in simulated maximum likelihood estimation? | Your likelihood function is non-concave (i.e. the Hessian matrix of your likelihood function is not SDN). From this it follows that
You will only find a local maximae to your likelihood function (no garantuee of global optimality)
This maxima will always depend on your choice of starting point.
Your maximization proce... | How can I work around "lumpiness" in simulated maximum likelihood estimation? | Your likelihood function is non-concave (i.e. the Hessian matrix of your likelihood function is not SDN). From this it follows that
You will only find a local maximae to your likelihood function (no | How can I work around "lumpiness" in simulated maximum likelihood estimation?
Your likelihood function is non-concave (i.e. the Hessian matrix of your likelihood function is not SDN). From this it follows that
You will only find a local maximae to your likelihood function (no garantuee of global optimality)
This maxim... | How can I work around "lumpiness" in simulated maximum likelihood estimation?
Your likelihood function is non-concave (i.e. the Hessian matrix of your likelihood function is not SDN). From this it follows that
You will only find a local maximae to your likelihood function (no |
42,233 | How can I work around "lumpiness" in simulated maximum likelihood estimation? | You could avoid the problem altogether by simply estimating
W = alphaH * H + alphaM * M + alphaL * L + X * beta
using 2sls. The fact that H,M, and L are discrete doesn't violate any of the assumptions of 2sls. Of course, using maximum likelihood will produce more efficient estimates, but it relies on more assumptions. ... | How can I work around "lumpiness" in simulated maximum likelihood estimation? | You could avoid the problem altogether by simply estimating
W = alphaH * H + alphaM * M + alphaL * L + X * beta
using 2sls. The fact that H,M, and L are discrete doesn't violate any of the assumptions | How can I work around "lumpiness" in simulated maximum likelihood estimation?
You could avoid the problem altogether by simply estimating
W = alphaH * H + alphaM * M + alphaL * L + X * beta
using 2sls. The fact that H,M, and L are discrete doesn't violate any of the assumptions of 2sls. Of course, using maximum likelih... | How can I work around "lumpiness" in simulated maximum likelihood estimation?
You could avoid the problem altogether by simply estimating
W = alphaH * H + alphaM * M + alphaL * L + X * beta
using 2sls. The fact that H,M, and L are discrete doesn't violate any of the assumptions |
42,234 | Using bootstrap for glm coefficients variance estimation (in R) | Have you thought about using simulate in the arm package? Gelman & Hill have some nice chapters on this in their book. | Using bootstrap for glm coefficients variance estimation (in R) | Have you thought about using simulate in the arm package? Gelman & Hill have some nice chapters on this in their book. | Using bootstrap for glm coefficients variance estimation (in R)
Have you thought about using simulate in the arm package? Gelman & Hill have some nice chapters on this in their book. | Using bootstrap for glm coefficients variance estimation (in R)
Have you thought about using simulate in the arm package? Gelman & Hill have some nice chapters on this in their book. |
42,235 | Using bootstrap for glm coefficients variance estimation (in R) | Yes, you are right. What boot does is that it just generates new training sets by drawing with replacement from the original set. So about 2/3 of the original objects are present in each of the new sets, still the size is the same, so it does not influence model building. | Using bootstrap for glm coefficients variance estimation (in R) | Yes, you are right. What boot does is that it just generates new training sets by drawing with replacement from the original set. So about 2/3 of the original objects are present in each of the new se | Using bootstrap for glm coefficients variance estimation (in R)
Yes, you are right. What boot does is that it just generates new training sets by drawing with replacement from the original set. So about 2/3 of the original objects are present in each of the new sets, still the size is the same, so it does not influence... | Using bootstrap for glm coefficients variance estimation (in R)
Yes, you are right. What boot does is that it just generates new training sets by drawing with replacement from the original set. So about 2/3 of the original objects are present in each of the new se |
42,236 | Appropriate link function for 2AFC data? | It doesn't just seem like it will have consequences, it will have large consequences. Fit that second function to the data you put in your last question on this. It goes dramatically negative as it approaches 0.5.
Perhaps more importantly, you also need to consider what the different equations mean for how one interp... | Appropriate link function for 2AFC data? | It doesn't just seem like it will have consequences, it will have large consequences. Fit that second function to the data you put in your last question on this. It goes dramatically negative as it | Appropriate link function for 2AFC data?
It doesn't just seem like it will have consequences, it will have large consequences. Fit that second function to the data you put in your last question on this. It goes dramatically negative as it approaches 0.5.
Perhaps more importantly, you also need to consider what the di... | Appropriate link function for 2AFC data?
It doesn't just seem like it will have consequences, it will have large consequences. Fit that second function to the data you put in your last question on this. It goes dramatically negative as it |
42,237 | Donut-like Distribution in Cartesian Coordinates | Converting a 2D density $f_{r,\theta}$ from polar coordinates $(r,\theta)$ to Cartesian coordinates $(x,y)$ where $r(x,y)^2 = x^2+y^2$ and $\tan{\theta(x,y)}=y/x$ turns out to be simple, because the reference (Lebesgue) measure merely changes from $r\,\mathrm dr\,\mathrm d\theta$ to $\mathrm dx\,\mathrm dy.$ Therefore... | Donut-like Distribution in Cartesian Coordinates | Converting a 2D density $f_{r,\theta}$ from polar coordinates $(r,\theta)$ to Cartesian coordinates $(x,y)$ where $r(x,y)^2 = x^2+y^2$ and $\tan{\theta(x,y)}=y/x$ turns out to be simple, because the r | Donut-like Distribution in Cartesian Coordinates
Converting a 2D density $f_{r,\theta}$ from polar coordinates $(r,\theta)$ to Cartesian coordinates $(x,y)$ where $r(x,y)^2 = x^2+y^2$ and $\tan{\theta(x,y)}=y/x$ turns out to be simple, because the reference (Lebesgue) measure merely changes from $r\,\mathrm dr\,\mathrm... | Donut-like Distribution in Cartesian Coordinates
Converting a 2D density $f_{r,\theta}$ from polar coordinates $(r,\theta)$ to Cartesian coordinates $(x,y)$ where $r(x,y)^2 = x^2+y^2$ and $\tan{\theta(x,y)}=y/x$ turns out to be simple, because the r |
42,238 | Flipping an unfair coin until there are more heads | Consolidation of my comments:
You stop the first time you have one more Heads than Tails, so you are correct that the probability you stop after an even number of flips is $0$.
So let's consider the probability of stopping after $2k+1$ flips. After $2k$ flips you want the same number of Heads and Tails, without ever h... | Flipping an unfair coin until there are more heads | Consolidation of my comments:
You stop the first time you have one more Heads than Tails, so you are correct that the probability you stop after an even number of flips is $0$.
So let's consider the | Flipping an unfair coin until there are more heads
Consolidation of my comments:
You stop the first time you have one more Heads than Tails, so you are correct that the probability you stop after an even number of flips is $0$.
So let's consider the probability of stopping after $2k+1$ flips. After $2k$ flips you want... | Flipping an unfair coin until there are more heads
Consolidation of my comments:
You stop the first time you have one more Heads than Tails, so you are correct that the probability you stop after an even number of flips is $0$.
So let's consider the |
42,239 | Flipping an unfair coin until there are more heads | I found another solution on Quora which ingeniously avoids the labour of finding out the PMF.
$\displaystyle \mathbb E[X] = p\cdot \mathbb E[H|X] + (1-p)\cdot \mathbb E[T|X] \tag{1}\label 1$
where,
$\mathbb E[T|X]$ denotes the expected number of flips given that the first flip has been a tail.
$\mathbb E[H|X]$ denotes... | Flipping an unfair coin until there are more heads | I found another solution on Quora which ingeniously avoids the labour of finding out the PMF.
$\displaystyle \mathbb E[X] = p\cdot \mathbb E[H|X] + (1-p)\cdot \mathbb E[T|X] \tag{1}\label 1$
where,
$ | Flipping an unfair coin until there are more heads
I found another solution on Quora which ingeniously avoids the labour of finding out the PMF.
$\displaystyle \mathbb E[X] = p\cdot \mathbb E[H|X] + (1-p)\cdot \mathbb E[T|X] \tag{1}\label 1$
where,
$\mathbb E[T|X]$ denotes the expected number of flips given that the f... | Flipping an unfair coin until there are more heads
I found another solution on Quora which ingeniously avoids the labour of finding out the PMF.
$\displaystyle \mathbb E[X] = p\cdot \mathbb E[H|X] + (1-p)\cdot \mathbb E[T|X] \tag{1}\label 1$
where,
$ |
42,240 | How does the Brier Score break down to (Reliability - Resolution + Uncertainty)? | Brier Score decomposition relies on a foundational concept in statistics called the partition of sums of squares. The basic idea is that we have a sums of squares over any series, we can break that series into arbitrary groups, calculate the sums of squares within each group, calculate the sums of squares between each ... | How does the Brier Score break down to (Reliability - Resolution + Uncertainty)? | Brier Score decomposition relies on a foundational concept in statistics called the partition of sums of squares. The basic idea is that we have a sums of squares over any series, we can break that se | How does the Brier Score break down to (Reliability - Resolution + Uncertainty)?
Brier Score decomposition relies on a foundational concept in statistics called the partition of sums of squares. The basic idea is that we have a sums of squares over any series, we can break that series into arbitrary groups, calculate t... | How does the Brier Score break down to (Reliability - Resolution + Uncertainty)?
Brier Score decomposition relies on a foundational concept in statistics called the partition of sums of squares. The basic idea is that we have a sums of squares over any series, we can break that se |
42,241 | How does the Brier Score break down to (Reliability - Resolution + Uncertainty)? | The Brier score (BS) is a measure of the accuracy of probabilistic predictions. It is calculated by taking the mean squared error between the predicted probabilities and the true outcomes.
The first equation you provided is the general form of the Brier score, which takes into account all of the predicted probabilities... | How does the Brier Score break down to (Reliability - Resolution + Uncertainty)? | The Brier score (BS) is a measure of the accuracy of probabilistic predictions. It is calculated by taking the mean squared error between the predicted probabilities and the true outcomes.
The first e | How does the Brier Score break down to (Reliability - Resolution + Uncertainty)?
The Brier score (BS) is a measure of the accuracy of probabilistic predictions. It is calculated by taking the mean squared error between the predicted probabilities and the true outcomes.
The first equation you provided is the general for... | How does the Brier Score break down to (Reliability - Resolution + Uncertainty)?
The Brier score (BS) is a measure of the accuracy of probabilistic predictions. It is calculated by taking the mean squared error between the predicted probabilities and the true outcomes.
The first e |
42,242 | What is the statistical model for a multi-label problem? | Let's generalise your example by supposing that we have $K$ types of animal/object. As you correctly point out, if we are dealing with observations where these types are mutually exclusive then we would have $K$ possible outcomes and so we would use some kind of multinomial model with $K$ categories. However, if thes... | What is the statistical model for a multi-label problem? | Let's generalise your example by supposing that we have $K$ types of animal/object. As you correctly point out, if we are dealing with observations where these types are mutually exclusive then we wo | What is the statistical model for a multi-label problem?
Let's generalise your example by supposing that we have $K$ types of animal/object. As you correctly point out, if we are dealing with observations where these types are mutually exclusive then we would have $K$ possible outcomes and so we would use some kind of... | What is the statistical model for a multi-label problem?
Let's generalise your example by supposing that we have $K$ types of animal/object. As you correctly point out, if we are dealing with observations where these types are mutually exclusive then we wo |
42,243 | What is the statistical model for a multi-label problem? | You can think of the multinomial (aka multinoulli) distribution used in multinomial classification as a multivariate discrete distribution obtained in two steps:
assign a Bernoulli marginal distribution to each of the labels;
use a very specific copula function to model the dependence between the marginals; the copula... | What is the statistical model for a multi-label problem? | You can think of the multinomial (aka multinoulli) distribution used in multinomial classification as a multivariate discrete distribution obtained in two steps:
assign a Bernoulli marginal distribut | What is the statistical model for a multi-label problem?
You can think of the multinomial (aka multinoulli) distribution used in multinomial classification as a multivariate discrete distribution obtained in two steps:
assign a Bernoulli marginal distribution to each of the labels;
use a very specific copula function ... | What is the statistical model for a multi-label problem?
You can think of the multinomial (aka multinoulli) distribution used in multinomial classification as a multivariate discrete distribution obtained in two steps:
assign a Bernoulli marginal distribut |
42,244 | A Kinder Egg Problem | You could potentially approach this as an inference from an occupancy problem, depending on the sampling method. For simplicity, let's assume that there are $N$ types of toys and your sampling method gives you an IID sample of $n$ toys that are equiprobable over the different types. Let $K_n$ denote the number of dis... | A Kinder Egg Problem | You could potentially approach this as an inference from an occupancy problem, depending on the sampling method. For simplicity, let's assume that there are $N$ types of toys and your sampling method | A Kinder Egg Problem
You could potentially approach this as an inference from an occupancy problem, depending on the sampling method. For simplicity, let's assume that there are $N$ types of toys and your sampling method gives you an IID sample of $n$ toys that are equiprobable over the different types. Let $K_n$ den... | A Kinder Egg Problem
You could potentially approach this as an inference from an occupancy problem, depending on the sampling method. For simplicity, let's assume that there are $N$ types of toys and your sampling method |
42,245 | Are $U=\frac{2X_1^2}{(X_2+X_3)^2}$ and $V=\frac{2(X_2-X_3)^2}{2X_1^2+(X_2+X_3)^2}$ independent? | Let $X=X_1,$ $Y=(X_2+X_3)/\sqrt2,$ and $Z=(X_2-X_3)/\sqrt2.$ As in your question, it is apparent that these are iid standard Normal. Moreover,
$$U = \frac{X^2}{Y^2}\ \text{ and }\ V = 2\frac{Z^2}{X^2 + Y^2}.$$
Consider, then, how $X/Y$ and $X^2+Y^2$ are related. The latter is the squared distance from the origin whil... | Are $U=\frac{2X_1^2}{(X_2+X_3)^2}$ and $V=\frac{2(X_2-X_3)^2}{2X_1^2+(X_2+X_3)^2}$ independent? | Let $X=X_1,$ $Y=(X_2+X_3)/\sqrt2,$ and $Z=(X_2-X_3)/\sqrt2.$ As in your question, it is apparent that these are iid standard Normal. Moreover,
$$U = \frac{X^2}{Y^2}\ \text{ and }\ V = 2\frac{Z^2}{X^2 | Are $U=\frac{2X_1^2}{(X_2+X_3)^2}$ and $V=\frac{2(X_2-X_3)^2}{2X_1^2+(X_2+X_3)^2}$ independent?
Let $X=X_1,$ $Y=(X_2+X_3)/\sqrt2,$ and $Z=(X_2-X_3)/\sqrt2.$ As in your question, it is apparent that these are iid standard Normal. Moreover,
$$U = \frac{X^2}{Y^2}\ \text{ and }\ V = 2\frac{Z^2}{X^2 + Y^2}.$$
Consider, the... | Are $U=\frac{2X_1^2}{(X_2+X_3)^2}$ and $V=\frac{2(X_2-X_3)^2}{2X_1^2+(X_2+X_3)^2}$ independent?
Let $X=X_1,$ $Y=(X_2+X_3)/\sqrt2,$ and $Z=(X_2-X_3)/\sqrt2.$ As in your question, it is apparent that these are iid standard Normal. Moreover,
$$U = \frac{X^2}{Y^2}\ \text{ and }\ V = 2\frac{Z^2}{X^2 |
42,246 | Calculate $E [ Z_{t-1}| X_{t-1}]$ in an ARMA process | For the Gaussian ARMA model we can derive the conditional mean and variance using standard results for conditional moments for the multivariate normal distribution. This requires use of the auto-correlation function for the ARMA model. You can find details of how to compute the autocorrelation function for an ARMA mo... | Calculate $E [ Z_{t-1}| X_{t-1}]$ in an ARMA process | For the Gaussian ARMA model we can derive the conditional mean and variance using standard results for conditional moments for the multivariate normal distribution. This requires use of the auto-corr | Calculate $E [ Z_{t-1}| X_{t-1}]$ in an ARMA process
For the Gaussian ARMA model we can derive the conditional mean and variance using standard results for conditional moments for the multivariate normal distribution. This requires use of the auto-correlation function for the ARMA model. You can find details of how t... | Calculate $E [ Z_{t-1}| X_{t-1}]$ in an ARMA process
For the Gaussian ARMA model we can derive the conditional mean and variance using standard results for conditional moments for the multivariate normal distribution. This requires use of the auto-corr |
42,247 | Why do most ML papers totally ignore the variance of the validation error? | The current trend in machine learning research is to train huge models. Let me quote one article
At OpenAI, an important machine-learning think tank, researchers recently designed and trained a much-lauded deep-learning language system called GPT-3 at the cost of more than $4 million. Even though they made a mistake w... | Why do most ML papers totally ignore the variance of the validation error? | The current trend in machine learning research is to train huge models. Let me quote one article
At OpenAI, an important machine-learning think tank, researchers recently designed and trained a much- | Why do most ML papers totally ignore the variance of the validation error?
The current trend in machine learning research is to train huge models. Let me quote one article
At OpenAI, an important machine-learning think tank, researchers recently designed and trained a much-lauded deep-learning language system called G... | Why do most ML papers totally ignore the variance of the validation error?
The current trend in machine learning research is to train huge models. Let me quote one article
At OpenAI, an important machine-learning think tank, researchers recently designed and trained a much- |
42,248 | Confused: Why is lme4 changing techniques from Wald F tests to Wald Chisquare? | It's not
Anova(conflictcon1, type = 3, Test = 'F')
but rather
Anova(conflictcon1, type = 3, test.statistic = 'F') | Confused: Why is lme4 changing techniques from Wald F tests to Wald Chisquare? | It's not
Anova(conflictcon1, type = 3, Test = 'F')
but rather
Anova(conflictcon1, type = 3, test.statistic = 'F') | Confused: Why is lme4 changing techniques from Wald F tests to Wald Chisquare?
It's not
Anova(conflictcon1, type = 3, Test = 'F')
but rather
Anova(conflictcon1, type = 3, test.statistic = 'F') | Confused: Why is lme4 changing techniques from Wald F tests to Wald Chisquare?
It's not
Anova(conflictcon1, type = 3, Test = 'F')
but rather
Anova(conflictcon1, type = 3, test.statistic = 'F') |
42,249 | How to get rid of background noise in time series data? | This is an example of change-point analysis, for which tools are described for example here and, in the context of loess (a standard approach for smoothing), here. The changepoint package in R provides some potentially useful tools. Note the both the mean and the variance in depth readings change dramatically during a ... | How to get rid of background noise in time series data? | This is an example of change-point analysis, for which tools are described for example here and, in the context of loess (a standard approach for smoothing), here. The changepoint package in R provide | How to get rid of background noise in time series data?
This is an example of change-point analysis, for which tools are described for example here and, in the context of loess (a standard approach for smoothing), here. The changepoint package in R provides some potentially useful tools. Note the both the mean and the ... | How to get rid of background noise in time series data?
This is an example of change-point analysis, for which tools are described for example here and, in the context of loess (a standard approach for smoothing), here. The changepoint package in R provide |
42,250 | How to get rid of background noise in time series data? | Your question will likely get better answers at https://dsp.stackexchange.com/. What you are describing in your update is very close to a median filter. The median filter is part of a larger class of filters called order-statistic filters. Another order-statistic filter you may be interested in is the LULU filter.
From... | How to get rid of background noise in time series data? | Your question will likely get better answers at https://dsp.stackexchange.com/. What you are describing in your update is very close to a median filter. The median filter is part of a larger class of | How to get rid of background noise in time series data?
Your question will likely get better answers at https://dsp.stackexchange.com/. What you are describing in your update is very close to a median filter. The median filter is part of a larger class of filters called order-statistic filters. Another order-statistic ... | How to get rid of background noise in time series data?
Your question will likely get better answers at https://dsp.stackexchange.com/. What you are describing in your update is very close to a median filter. The median filter is part of a larger class of |
42,251 | What to do when your training and testing data have different distributions | Collect data from the population you want to predict, and use that data to train your model. This is the best approach.
Alternatively, think long and deep about how you can possibly post-process your predictions (from a model trained on a sample from population A) to apply to population B. How you do this will depend o... | What to do when your training and testing data have different distributions | Collect data from the population you want to predict, and use that data to train your model. This is the best approach.
Alternatively, think long and deep about how you can possibly post-process your | What to do when your training and testing data have different distributions
Collect data from the population you want to predict, and use that data to train your model. This is the best approach.
Alternatively, think long and deep about how you can possibly post-process your predictions (from a model trained on a sampl... | What to do when your training and testing data have different distributions
Collect data from the population you want to predict, and use that data to train your model. This is the best approach.
Alternatively, think long and deep about how you can possibly post-process your |
42,252 | What to do when your training and testing data have different distributions | Like I said in my comment, I don't necessarily see how a change in the range of the response is an issue. In particular, in your case, I think it is a red herring.
First, it's important to ask, should the test set have the same range of responses as the train set? In many cases it is not the case and I don't know why t... | What to do when your training and testing data have different distributions | Like I said in my comment, I don't necessarily see how a change in the range of the response is an issue. In particular, in your case, I think it is a red herring.
First, it's important to ask, should | What to do when your training and testing data have different distributions
Like I said in my comment, I don't necessarily see how a change in the range of the response is an issue. In particular, in your case, I think it is a red herring.
First, it's important to ask, should the test set have the same range of respons... | What to do when your training and testing data have different distributions
Like I said in my comment, I don't necessarily see how a change in the range of the response is an issue. In particular, in your case, I think it is a red herring.
First, it's important to ask, should |
42,253 | Is there a name for the increase in variance upon remeasurement after subsetting with a cut-off value? | This is a kind of regression toward the mean applied, in this specific case, to the variance or standard deviation. Regression toward the mean is observed when selecting subjects based on a very high or very low value and observing that subsequent measurements will be closer to the average.
Regression toward the mean c... | Is there a name for the increase in variance upon remeasurement after subsetting with a cut-off valu | This is a kind of regression toward the mean applied, in this specific case, to the variance or standard deviation. Regression toward the mean is observed when selecting subjects based on a very high | Is there a name for the increase in variance upon remeasurement after subsetting with a cut-off value?
This is a kind of regression toward the mean applied, in this specific case, to the variance or standard deviation. Regression toward the mean is observed when selecting subjects based on a very high or very low value... | Is there a name for the increase in variance upon remeasurement after subsetting with a cut-off valu
This is a kind of regression toward the mean applied, in this specific case, to the variance or standard deviation. Regression toward the mean is observed when selecting subjects based on a very high |
42,254 | Serial correlation AR(1) model for residuals: how to generalize to irregular times | The Ornstein-Uhlenbeck (OU) process can be considered as it is a natural extension of the (V)AR(1).
I here skip the mathematical derivation. I first present the multivariate version, which I worked with. The OU process can be specified as follows:
$Y(0)\sim N(\mu, \Omega)$,
$Y(t+\Delta t)|Y(t) \sim N(\mu + e^{-\Gamma \... | Serial correlation AR(1) model for residuals: how to generalize to irregular times | The Ornstein-Uhlenbeck (OU) process can be considered as it is a natural extension of the (V)AR(1).
I here skip the mathematical derivation. I first present the multivariate version, which I worked wi | Serial correlation AR(1) model for residuals: how to generalize to irregular times
The Ornstein-Uhlenbeck (OU) process can be considered as it is a natural extension of the (V)AR(1).
I here skip the mathematical derivation. I first present the multivariate version, which I worked with. The OU process can be specified a... | Serial correlation AR(1) model for residuals: how to generalize to irregular times
The Ornstein-Uhlenbeck (OU) process can be considered as it is a natural extension of the (V)AR(1).
I here skip the mathematical derivation. I first present the multivariate version, which I worked wi |
42,255 | Serial correlation AR(1) model for residuals: how to generalize to irregular times | Assuming the data to be at irregular intervals with different number of measurements for each subject:
$y_{t_{11}},y_{t_{12}},\ldots,y_{t_{1K_1}}$
$y_{t_{21}},y_{t_{22}},\ldots,y_{t_{2K_2}}$
$\vdots$
$y_{t_{N1}},y_{t_{N2}},\ldots,y_{t_{NK_N}}$
For sake of simplicity, I am writing the equations for linear models instead... | Serial correlation AR(1) model for residuals: how to generalize to irregular times | Assuming the data to be at irregular intervals with different number of measurements for each subject:
$y_{t_{11}},y_{t_{12}},\ldots,y_{t_{1K_1}}$
$y_{t_{21}},y_{t_{22}},\ldots,y_{t_{2K_2}}$
$\vdots$
| Serial correlation AR(1) model for residuals: how to generalize to irregular times
Assuming the data to be at irregular intervals with different number of measurements for each subject:
$y_{t_{11}},y_{t_{12}},\ldots,y_{t_{1K_1}}$
$y_{t_{21}},y_{t_{22}},\ldots,y_{t_{2K_2}}$
$\vdots$
$y_{t_{N1}},y_{t_{N2}},\ldots,y_{t_{N... | Serial correlation AR(1) model for residuals: how to generalize to irregular times
Assuming the data to be at irregular intervals with different number of measurements for each subject:
$y_{t_{11}},y_{t_{12}},\ldots,y_{t_{1K_1}}$
$y_{t_{21}},y_{t_{22}},\ldots,y_{t_{2K_2}}$
$\vdots$
|
42,256 | Serial correlation AR(1) model for residuals: how to generalize to irregular times | When you generalize to a continuous time form, you only need the random effects relevant to your specific observations, because the covariance with earlier random effects will be conditioned on the time interval. This paper describes a continuous-time Rasch model https://psycnet.apa.org/record/2019-22131-001 , using th... | Serial correlation AR(1) model for residuals: how to generalize to irregular times | When you generalize to a continuous time form, you only need the random effects relevant to your specific observations, because the covariance with earlier random effects will be conditioned on the ti | Serial correlation AR(1) model for residuals: how to generalize to irregular times
When you generalize to a continuous time form, you only need the random effects relevant to your specific observations, because the covariance with earlier random effects will be conditioned on the time interval. This paper describes a c... | Serial correlation AR(1) model for residuals: how to generalize to irregular times
When you generalize to a continuous time form, you only need the random effects relevant to your specific observations, because the covariance with earlier random effects will be conditioned on the ti |
42,257 | Two sample test for exponential distribution with only two observations | Consider a likelihood ratio test. Since the likelihood maximizing $\hat\lambda_0$, $\hat\lambda_1$, $\hat\lambda_2$, are respectively $1/\bar{x}=2/(x_1+x_2)$, $1/x_1$, and $1/x_2$, the likelihood ratio $\Lambda$ is
$$
\begin{align}
\Lambda &= \frac{f_{\hat\lambda_0}(x_1,x_2)}{f_{\hat \lambda_1}(x_1)f_{\hat \lambda_2}(... | Two sample test for exponential distribution with only two observations | Consider a likelihood ratio test. Since the likelihood maximizing $\hat\lambda_0$, $\hat\lambda_1$, $\hat\lambda_2$, are respectively $1/\bar{x}=2/(x_1+x_2)$, $1/x_1$, and $1/x_2$, the likelihood rat | Two sample test for exponential distribution with only two observations
Consider a likelihood ratio test. Since the likelihood maximizing $\hat\lambda_0$, $\hat\lambda_1$, $\hat\lambda_2$, are respectively $1/\bar{x}=2/(x_1+x_2)$, $1/x_1$, and $1/x_2$, the likelihood ratio $\Lambda$ is
$$
\begin{align}
\Lambda &= \fra... | Two sample test for exponential distribution with only two observations
Consider a likelihood ratio test. Since the likelihood maximizing $\hat\lambda_0$, $\hat\lambda_1$, $\hat\lambda_2$, are respectively $1/\bar{x}=2/(x_1+x_2)$, $1/x_1$, and $1/x_2$, the likelihood rat |
42,258 | Two sample test for exponential distribution with only two observations | This question relates to the more general question Find the distribution of the statistic and the critical region of the generalized test at level $\alpha$ for two sample test, which asks the same question but with samples of potentially different sizes than one.
An answer to that question uses a statistic that follows... | Two sample test for exponential distribution with only two observations | This question relates to the more general question Find the distribution of the statistic and the critical region of the generalized test at level $\alpha$ for two sample test, which asks the same que | Two sample test for exponential distribution with only two observations
This question relates to the more general question Find the distribution of the statistic and the critical region of the generalized test at level $\alpha$ for two sample test, which asks the same question but with samples of potentially different ... | Two sample test for exponential distribution with only two observations
This question relates to the more general question Find the distribution of the statistic and the critical region of the generalized test at level $\alpha$ for two sample test, which asks the same que |
42,259 | MDP and Sate Value Finding? | For action $a$, we have $Q(A, d) = 0.1 V(B) + 0.9 V(A)$. For action $b$, we have $Q(A, b) = 0.8 V(B) + 0.2 V(A)$.
Then, we have $V(A) = -0.1 + \max(Q(A, a), Q(A, b))$. We also have $V(B) = 1$.
That is all you need to solve the problem. The easiest way might be by fixing the policy. I.e. assuming $Q(A, a) > Q(A, b)$ and... | MDP and Sate Value Finding? | For action $a$, we have $Q(A, d) = 0.1 V(B) + 0.9 V(A)$. For action $b$, we have $Q(A, b) = 0.8 V(B) + 0.2 V(A)$.
Then, we have $V(A) = -0.1 + \max(Q(A, a), Q(A, b))$. We also have $V(B) = 1$.
That is | MDP and Sate Value Finding?
For action $a$, we have $Q(A, d) = 0.1 V(B) + 0.9 V(A)$. For action $b$, we have $Q(A, b) = 0.8 V(B) + 0.2 V(A)$.
Then, we have $V(A) = -0.1 + \max(Q(A, a), Q(A, b))$. We also have $V(B) = 1$.
That is all you need to solve the problem. The easiest way might be by fixing the policy. I.e. assu... | MDP and Sate Value Finding?
For action $a$, we have $Q(A, d) = 0.1 V(B) + 0.9 V(A)$. For action $b$, we have $Q(A, b) = 0.8 V(B) + 0.2 V(A)$.
Then, we have $V(A) = -0.1 + \max(Q(A, a), Q(A, b))$. We also have $V(B) = 1$.
That is |
42,260 | How to prove positive (semi-)definitness in matrix notation without numbers | Note that $X$ is generally not square, unless you have as many regressors as observations. In that case - see the derivation at the end of my answer - OLS and GLS are equally efficient.
Notice also a mistake in the above expression in that the correct variance of GLS is
$$
\sigma^2(X'\Omega^{-1} X)^{-1}
$$
A standard r... | How to prove positive (semi-)definitness in matrix notation without numbers | Note that $X$ is generally not square, unless you have as many regressors as observations. In that case - see the derivation at the end of my answer - OLS and GLS are equally efficient.
Notice also a | How to prove positive (semi-)definitness in matrix notation without numbers
Note that $X$ is generally not square, unless you have as many regressors as observations. In that case - see the derivation at the end of my answer - OLS and GLS are equally efficient.
Notice also a mistake in the above expression in that the ... | How to prove positive (semi-)definitness in matrix notation without numbers
Note that $X$ is generally not square, unless you have as many regressors as observations. In that case - see the derivation at the end of my answer - OLS and GLS are equally efficient.
Notice also a |
42,261 | How to calculate 95% CI of vaccine with 90% efficacy? | One way to do it is to fit a Poisson model (a very close approximation to the binomial with such low rates), and compare the estimated risks:
library("emmeans")
dat <- data.frame(
group = c("placebo", "vaccine"),
infected = c(86, 8),
N = c(86, 8) + c(21683, 21761))
mod <- glm(infected ~ group + offset(log... | How to calculate 95% CI of vaccine with 90% efficacy? | One way to do it is to fit a Poisson model (a very close approximation to the binomial with such low rates), and compare the estimated risks:
library("emmeans")
dat <- data.frame(
group = c("plac | How to calculate 95% CI of vaccine with 90% efficacy?
One way to do it is to fit a Poisson model (a very close approximation to the binomial with such low rates), and compare the estimated risks:
library("emmeans")
dat <- data.frame(
group = c("placebo", "vaccine"),
infected = c(86, 8),
N = c(86, 8) + c(21... | How to calculate 95% CI of vaccine with 90% efficacy?
One way to do it is to fit a Poisson model (a very close approximation to the binomial with such low rates), and compare the estimated risks:
library("emmeans")
dat <- data.frame(
group = c("plac |
42,262 | How to calculate 95% CI of vaccine with 90% efficacy? | Use the online calculator. The relative risk (RR), its standard error and 95% confidence interval are calculated according to Altman, 1991. | How to calculate 95% CI of vaccine with 90% efficacy? | Use the online calculator. The relative risk (RR), its standard error and 95% confidence interval are calculated according to Altman, 1991. | How to calculate 95% CI of vaccine with 90% efficacy?
Use the online calculator. The relative risk (RR), its standard error and 95% confidence interval are calculated according to Altman, 1991. | How to calculate 95% CI of vaccine with 90% efficacy?
Use the online calculator. The relative risk (RR), its standard error and 95% confidence interval are calculated according to Altman, 1991. |
42,263 | How to calculate and interpret a marginal treatment effect (local instrumental variable)? (Intuition through simple example.) | I think this is a good way to explain the details. I got it from Counterfactuals and Causal Inference by Morgan and Winship, which is a wonderful book.
Let's say we are interested in the effect on wages from attending college ($D$). I am not a huge fan of distance, so imagine we had an instrumental variable $Z$ that is... | How to calculate and interpret a marginal treatment effect (local instrumental variable)? (Intuition | I think this is a good way to explain the details. I got it from Counterfactuals and Causal Inference by Morgan and Winship, which is a wonderful book.
Let's say we are interested in the effect on wag | How to calculate and interpret a marginal treatment effect (local instrumental variable)? (Intuition through simple example.)
I think this is a good way to explain the details. I got it from Counterfactuals and Causal Inference by Morgan and Winship, which is a wonderful book.
Let's say we are interested in the effect ... | How to calculate and interpret a marginal treatment effect (local instrumental variable)? (Intuition
I think this is a good way to explain the details. I got it from Counterfactuals and Causal Inference by Morgan and Winship, which is a wonderful book.
Let's say we are interested in the effect on wag |
42,264 | Evaluating (Uniform) Expectations over Non-simple Region | Let's solve the more general problem and then apply it to the specific setting as an illustration.
Suppose $g:\mathcal{X}\to\mathbb{R}$ is a measurable function. Let $\{\mathcal{A}_i\}\subset \mathscr{P}(\mathcal{X})$ be a finite or countable collection of subsets of $\mathcal X,$ each with finite positive measure $p_... | Evaluating (Uniform) Expectations over Non-simple Region | Let's solve the more general problem and then apply it to the specific setting as an illustration.
Suppose $g:\mathcal{X}\to\mathbb{R}$ is a measurable function. Let $\{\mathcal{A}_i\}\subset \mathsc | Evaluating (Uniform) Expectations over Non-simple Region
Let's solve the more general problem and then apply it to the specific setting as an illustration.
Suppose $g:\mathcal{X}\to\mathbb{R}$ is a measurable function. Let $\{\mathcal{A}_i\}\subset \mathscr{P}(\mathcal{X})$ be a finite or countable collection of subse... | Evaluating (Uniform) Expectations over Non-simple Region
Let's solve the more general problem and then apply it to the specific setting as an illustration.
Suppose $g:\mathcal{X}\to\mathbb{R}$ is a measurable function. Let $\{\mathcal{A}_i\}\subset \mathsc |
42,265 | Should reconstruction loss be computed as sum or average over input for variational autoencoders? | To go directly to the answer, the loss does have a precise derivation (but that doesn't mean you can't necessarily change it).
It's important to remember that Variational Auto-encoders are at their core a method for doing variational inference over some latent variables we assume to be generating the data. In this fram... | Should reconstruction loss be computed as sum or average over input for variational autoencoders? | To go directly to the answer, the loss does have a precise derivation (but that doesn't mean you can't necessarily change it).
It's important to remember that Variational Auto-encoders are at their co | Should reconstruction loss be computed as sum or average over input for variational autoencoders?
To go directly to the answer, the loss does have a precise derivation (but that doesn't mean you can't necessarily change it).
It's important to remember that Variational Auto-encoders are at their core a method for doing ... | Should reconstruction loss be computed as sum or average over input for variational autoencoders?
To go directly to the answer, the loss does have a precise derivation (but that doesn't mean you can't necessarily change it).
It's important to remember that Variational Auto-encoders are at their co |
42,266 | Should reconstruction loss be computed as sum or average over input for variational autoencoders? | As I understand how VAE works, the KL loss can be considered as the regulariser and reconstruction loss is one that drives the model weighs to produce the correct output.
To answer your specific question: "Can I use a lambda parameter to capture the tradeoff between kl divergence and reconstruction"; yes you can use a ... | Should reconstruction loss be computed as sum or average over input for variational autoencoders? | As I understand how VAE works, the KL loss can be considered as the regulariser and reconstruction loss is one that drives the model weighs to produce the correct output.
To answer your specific quest | Should reconstruction loss be computed as sum or average over input for variational autoencoders?
As I understand how VAE works, the KL loss can be considered as the regulariser and reconstruction loss is one that drives the model weighs to produce the correct output.
To answer your specific question: "Can I use a lamb... | Should reconstruction loss be computed as sum or average over input for variational autoencoders?
As I understand how VAE works, the KL loss can be considered as the regulariser and reconstruction loss is one that drives the model weighs to produce the correct output.
To answer your specific quest |
42,267 | In mgcv::gam(), what is the difference between s(x, by=cat) and s(x, cat, bs='fs')? | Q3
The by smooth variant has a separate smoothness parameter for each level of cat. In one sense you can think of these smooths as creating entirely separate smooth functions (they're aren't quite, they share the same basis for example), hence you have nlevels(cat) entries in the summary() output.
fs smooths share a si... | In mgcv::gam(), what is the difference between s(x, by=cat) and s(x, cat, bs='fs')? | Q3
The by smooth variant has a separate smoothness parameter for each level of cat. In one sense you can think of these smooths as creating entirely separate smooth functions (they're aren't quite, th | In mgcv::gam(), what is the difference between s(x, by=cat) and s(x, cat, bs='fs')?
Q3
The by smooth variant has a separate smoothness parameter for each level of cat. In one sense you can think of these smooths as creating entirely separate smooth functions (they're aren't quite, they share the same basis for example)... | In mgcv::gam(), what is the difference between s(x, by=cat) and s(x, cat, bs='fs')?
Q3
The by smooth variant has a separate smoothness parameter for each level of cat. In one sense you can think of these smooths as creating entirely separate smooth functions (they're aren't quite, th |
42,268 | Linear Changepoint Model with LASSO | Nice question.
I have more to say tomorrow, but for now the main point here is that your predictor matrix, changepoints is just a weighted matrix of piecewise linear basis functions, where the weights are set to fit the 25 equally-spaced points in your data.
It is common enough to use lasso to penalise regression spli... | Linear Changepoint Model with LASSO | Nice question.
I have more to say tomorrow, but for now the main point here is that your predictor matrix, changepoints is just a weighted matrix of piecewise linear basis functions, where the weights | Linear Changepoint Model with LASSO
Nice question.
I have more to say tomorrow, but for now the main point here is that your predictor matrix, changepoints is just a weighted matrix of piecewise linear basis functions, where the weights are set to fit the 25 equally-spaced points in your data.
It is common enough to u... | Linear Changepoint Model with LASSO
Nice question.
I have more to say tomorrow, but for now the main point here is that your predictor matrix, changepoints is just a weighted matrix of piecewise linear basis functions, where the weights |
42,269 | Nonparametric theory textbook(s)? | I would recommend A Distribution-Free Theory of Nonparametric Regression by Györfi, Kohler, Krzyżak and Walk. It looks like what you are looking for: proofs use sigma fields as needed, there is plenty of use of dominated convergence and Fatou's Lemma, and it hits topics like kernels and k-nearest neighbors.
The online ... | Nonparametric theory textbook(s)? | I would recommend A Distribution-Free Theory of Nonparametric Regression by Györfi, Kohler, Krzyżak and Walk. It looks like what you are looking for: proofs use sigma fields as needed, there is plenty | Nonparametric theory textbook(s)?
I would recommend A Distribution-Free Theory of Nonparametric Regression by Györfi, Kohler, Krzyżak and Walk. It looks like what you are looking for: proofs use sigma fields as needed, there is plenty of use of dominated convergence and Fatou's Lemma, and it hits topics like kernels an... | Nonparametric theory textbook(s)?
I would recommend A Distribution-Free Theory of Nonparametric Regression by Györfi, Kohler, Krzyżak and Walk. It looks like what you are looking for: proofs use sigma fields as needed, there is plenty |
42,270 | Nonparametric theory textbook(s)? | There's a chapter in this book on nonparametric statistics: "Modern Statistical Methods for Astronomy With R Applications", Feigelson and Babu https://www.cambridge.org/us/academic/subjects/physics/astronomy-general/modern-statistical-methods-astronomy-r-applications?format=HB&isbn=9780521767279 | Nonparametric theory textbook(s)? | There's a chapter in this book on nonparametric statistics: "Modern Statistical Methods for Astronomy With R Applications", Feigelson and Babu https://www.cambridge.org/us/academic/subjects/physics/as | Nonparametric theory textbook(s)?
There's a chapter in this book on nonparametric statistics: "Modern Statistical Methods for Astronomy With R Applications", Feigelson and Babu https://www.cambridge.org/us/academic/subjects/physics/astronomy-general/modern-statistical-methods-astronomy-r-applications?format=HB&isbn=978... | Nonparametric theory textbook(s)?
There's a chapter in this book on nonparametric statistics: "Modern Statistical Methods for Astronomy With R Applications", Feigelson and Babu https://www.cambridge.org/us/academic/subjects/physics/as |
42,271 | Meaning of Gaussian mixture weights? | The simple answer is that the weights estimated by GMM seek to estimate the true weights of the GMM. Sticking the the one-dimensional case, a GMM has $K$ components, where each component is a different normal distribution. A classic example is to consider heights of humans: if you look at the density, it looks like it ... | Meaning of Gaussian mixture weights? | The simple answer is that the weights estimated by GMM seek to estimate the true weights of the GMM. Sticking the the one-dimensional case, a GMM has $K$ components, where each component is a differen | Meaning of Gaussian mixture weights?
The simple answer is that the weights estimated by GMM seek to estimate the true weights of the GMM. Sticking the the one-dimensional case, a GMM has $K$ components, where each component is a different normal distribution. A classic example is to consider heights of humans: if you l... | Meaning of Gaussian mixture weights?
The simple answer is that the weights estimated by GMM seek to estimate the true weights of the GMM. Sticking the the one-dimensional case, a GMM has $K$ components, where each component is a differen |
42,272 | Is power law distribution for extreme event special like normal distribution? | With respect to the first question, whether there is a convergence theorem leading to power-law distributions, the Extremal Types Theorem should be mentioned (Fisher and Tippett, 1928, Gnedenko 1934), leading to the three max-stable Extreme Value Distributions (Type I to III, also known as Gumbel, Fréchet and Weibull d... | Is power law distribution for extreme event special like normal distribution? | With respect to the first question, whether there is a convergence theorem leading to power-law distributions, the Extremal Types Theorem should be mentioned (Fisher and Tippett, 1928, Gnedenko 1934), | Is power law distribution for extreme event special like normal distribution?
With respect to the first question, whether there is a convergence theorem leading to power-law distributions, the Extremal Types Theorem should be mentioned (Fisher and Tippett, 1928, Gnedenko 1934), leading to the three max-stable Extreme V... | Is power law distribution for extreme event special like normal distribution?
With respect to the first question, whether there is a convergence theorem leading to power-law distributions, the Extremal Types Theorem should be mentioned (Fisher and Tippett, 1928, Gnedenko 1934), |
42,273 | Is power law distribution for extreme event special like normal distribution? | $\bullet$ First, heavy-tailed/Pareto distributions (aka power laws) frequently occur outside of finance and economy. They are used to describe the size/height/magnitude/severity distribution of countless natural phenomena.
A few examples are ocean waves, volcanic eruptions, asteroid impacts (a well-known example is the... | Is power law distribution for extreme event special like normal distribution? | $\bullet$ First, heavy-tailed/Pareto distributions (aka power laws) frequently occur outside of finance and economy. They are used to describe the size/height/magnitude/severity distribution of countl | Is power law distribution for extreme event special like normal distribution?
$\bullet$ First, heavy-tailed/Pareto distributions (aka power laws) frequently occur outside of finance and economy. They are used to describe the size/height/magnitude/severity distribution of countless natural phenomena.
A few examples are ... | Is power law distribution for extreme event special like normal distribution?
$\bullet$ First, heavy-tailed/Pareto distributions (aka power laws) frequently occur outside of finance and economy. They are used to describe the size/height/magnitude/severity distribution of countl |
42,274 | Correlation between normal and log-normal variables | As is often the case, precisely formulating the question helped me work out the answer.
My approach makes use of the marginal expectation of the bivariate normal:
$$E_X(y) = E(X|Y=y) = \mu_x + \rho\frac{\sigma_x}{\sigma_y}(y-\mu_y)$$
Returning to my notation from the question above, this gives us:
$$\begin{split}E(X_1Y... | Correlation between normal and log-normal variables | As is often the case, precisely formulating the question helped me work out the answer.
My approach makes use of the marginal expectation of the bivariate normal:
$$E_X(y) = E(X|Y=y) = \mu_x + \rho\fr | Correlation between normal and log-normal variables
As is often the case, precisely formulating the question helped me work out the answer.
My approach makes use of the marginal expectation of the bivariate normal:
$$E_X(y) = E(X|Y=y) = \mu_x + \rho\frac{\sigma_x}{\sigma_y}(y-\mu_y)$$
Returning to my notation from the ... | Correlation between normal and log-normal variables
As is often the case, precisely formulating the question helped me work out the answer.
My approach makes use of the marginal expectation of the bivariate normal:
$$E_X(y) = E(X|Y=y) = \mu_x + \rho\fr |
42,275 | Can I use the Mann-Whitney U test sequentially (pairwise) when I have three groups or do I need to use the Kruskal-Wallis test? | I think these are very valid questions.
Sequential testing leads to the problem of multiple testing. For
this problem, plenty of corrections are easily available (Bonferroni being
the simplest and probably most popular). The real problem with
sequential applying the Mann-Whitney-U-Test is that it can lead to
inconsist... | Can I use the Mann-Whitney U test sequentially (pairwise) when I have three groups or do I need to u | I think these are very valid questions.
Sequential testing leads to the problem of multiple testing. For
this problem, plenty of corrections are easily available (Bonferroni being
the simplest and pr | Can I use the Mann-Whitney U test sequentially (pairwise) when I have three groups or do I need to use the Kruskal-Wallis test?
I think these are very valid questions.
Sequential testing leads to the problem of multiple testing. For
this problem, plenty of corrections are easily available (Bonferroni being
the simples... | Can I use the Mann-Whitney U test sequentially (pairwise) when I have three groups or do I need to u
I think these are very valid questions.
Sequential testing leads to the problem of multiple testing. For
this problem, plenty of corrections are easily available (Bonferroni being
the simplest and pr |
42,276 | Can I use the Mann-Whitney U test sequentially (pairwise) when I have three groups or do I need to use the Kruskal-Wallis test? | Point by point answers:
You should do Kruskall-Wallis test. The problem with multiple Mann-Whitney tests, or broadly speaking multiple pairwise comparisons has a name - Multiple Comparisons Problem. The wikipedia article linked is a good start but you'll find several explanations if you google "multiple comparisons pr... | Can I use the Mann-Whitney U test sequentially (pairwise) when I have three groups or do I need to u | Point by point answers:
You should do Kruskall-Wallis test. The problem with multiple Mann-Whitney tests, or broadly speaking multiple pairwise comparisons has a name - Multiple Comparisons Problem. | Can I use the Mann-Whitney U test sequentially (pairwise) when I have three groups or do I need to use the Kruskal-Wallis test?
Point by point answers:
You should do Kruskall-Wallis test. The problem with multiple Mann-Whitney tests, or broadly speaking multiple pairwise comparisons has a name - Multiple Comparisons P... | Can I use the Mann-Whitney U test sequentially (pairwise) when I have three groups or do I need to u
Point by point answers:
You should do Kruskall-Wallis test. The problem with multiple Mann-Whitney tests, or broadly speaking multiple pairwise comparisons has a name - Multiple Comparisons Problem. |
42,277 | Can I use the Mann-Whitney U test sequentially (pairwise) when I have three groups or do I need to use the Kruskal-Wallis test? | Before employing non-parametric sample test, as you are, in effect, doing a failure analysis, perhaps explore the underlying data from the perspective of Reliability Theory. In particular, compute an empirical hazard function (see this lecture).
Note, the exponential distribution is characterized by a constant instanta... | Can I use the Mann-Whitney U test sequentially (pairwise) when I have three groups or do I need to u | Before employing non-parametric sample test, as you are, in effect, doing a failure analysis, perhaps explore the underlying data from the perspective of Reliability Theory. In particular, compute an | Can I use the Mann-Whitney U test sequentially (pairwise) when I have three groups or do I need to use the Kruskal-Wallis test?
Before employing non-parametric sample test, as you are, in effect, doing a failure analysis, perhaps explore the underlying data from the perspective of Reliability Theory. In particular, com... | Can I use the Mann-Whitney U test sequentially (pairwise) when I have three groups or do I need to u
Before employing non-parametric sample test, as you are, in effect, doing a failure analysis, perhaps explore the underlying data from the perspective of Reliability Theory. In particular, compute an |
42,278 | Markov chain as sum of iid random variables | I think you are somehow mixing independence and conditional independence.
The idea is not that $X_{n+1}$ is independent from $X_0 ... X_{n-1}$, but that it is conditionally independent given $X_n$.
This simply means that, once you know the value of $X_n$, the previous values $X_0...X_{n-1}$ are irrelevant for the dis... | Markov chain as sum of iid random variables | I think you are somehow mixing independence and conditional independence.
The idea is not that $X_{n+1}$ is independent from $X_0 ... X_{n-1}$, but that it is conditionally independent given $X_n$.
| Markov chain as sum of iid random variables
I think you are somehow mixing independence and conditional independence.
The idea is not that $X_{n+1}$ is independent from $X_0 ... X_{n-1}$, but that it is conditionally independent given $X_n$.
This simply means that, once you know the value of $X_n$, the previous value... | Markov chain as sum of iid random variables
I think you are somehow mixing independence and conditional independence.
The idea is not that $X_{n+1}$ is independent from $X_0 ... X_{n-1}$, but that it is conditionally independent given $X_n$.
|
42,279 | Question about Casella and Berger's proof of MLE invariance | The occurrences of suprema (instead of maxima, which might not exist) are troublesome. Let us therefore isolate the basic underlying idea and rigorously establish it.
Definitions
Suppose $f:\Theta\to\mathbb{R}$ is any real-valued function on a set $\Theta.$ By definition, its supremum is the least upper bound of the ... | Question about Casella and Berger's proof of MLE invariance | The occurrences of suprema (instead of maxima, which might not exist) are troublesome. Let us therefore isolate the basic underlying idea and rigorously establish it.
Definitions
Suppose $f:\Theta\to | Question about Casella and Berger's proof of MLE invariance
The occurrences of suprema (instead of maxima, which might not exist) are troublesome. Let us therefore isolate the basic underlying idea and rigorously establish it.
Definitions
Suppose $f:\Theta\to\mathbb{R}$ is any real-valued function on a set $\Theta.$ ... | Question about Casella and Berger's proof of MLE invariance
The occurrences of suprema (instead of maxima, which might not exist) are troublesome. Let us therefore isolate the basic underlying idea and rigorously establish it.
Definitions
Suppose $f:\Theta\to |
42,280 | Akaike Information Criterion (AIC) derivation | Consider scalar parameters $\theta_0$ and the corresponding scalar estimate $\hat \theta$ for simplicity.
I will answer Q1 and Q3 which are essentially asking why is the mean of the score function $\Bbb{E}_{\theta}(s(\theta)) =0 $. This is a widely known result.. To put it simply, Notice that score function $s(\theta)... | Akaike Information Criterion (AIC) derivation | Consider scalar parameters $\theta_0$ and the corresponding scalar estimate $\hat \theta$ for simplicity.
I will answer Q1 and Q3 which are essentially asking why is the mean of the score function $\ | Akaike Information Criterion (AIC) derivation
Consider scalar parameters $\theta_0$ and the corresponding scalar estimate $\hat \theta$ for simplicity.
I will answer Q1 and Q3 which are essentially asking why is the mean of the score function $\Bbb{E}_{\theta}(s(\theta)) =0 $. This is a widely known result.. To put it... | Akaike Information Criterion (AIC) derivation
Consider scalar parameters $\theta_0$ and the corresponding scalar estimate $\hat \theta$ for simplicity.
I will answer Q1 and Q3 which are essentially asking why is the mean of the score function $\ |
42,281 | What is the quantile covariance? | Setup
We'll assume that the feature covariance $\mathrm{var}(X) \in \mathbb{R}^{p \times p}$ is full rank. As you have in the original post, define $$(\hat{\alpha}, \hat{\beta}) = \arg\min_{\alpha, \beta} \mathbb{E} \left[ \left(Y - \left\{ \alpha + \beta^T \Sigma_{XX}^{-1} (X - \mu_X) \right\} \right)^2 \right]$$ and ... | What is the quantile covariance? | Setup
We'll assume that the feature covariance $\mathrm{var}(X) \in \mathbb{R}^{p \times p}$ is full rank. As you have in the original post, define $$(\hat{\alpha}, \hat{\beta}) = \arg\min_{\alpha, \b | What is the quantile covariance?
Setup
We'll assume that the feature covariance $\mathrm{var}(X) \in \mathbb{R}^{p \times p}$ is full rank. As you have in the original post, define $$(\hat{\alpha}, \hat{\beta}) = \arg\min_{\alpha, \beta} \mathbb{E} \left[ \left(Y - \left\{ \alpha + \beta^T \Sigma_{XX}^{-1} (X - \mu_X) ... | What is the quantile covariance?
Setup
We'll assume that the feature covariance $\mathrm{var}(X) \in \mathbb{R}^{p \times p}$ is full rank. As you have in the original post, define $$(\hat{\alpha}, \hat{\beta}) = \arg\min_{\alpha, \b |
42,282 | Understanding the reproducing property of RKHS | You're overthinking this: the result with $M$ is just a restatement of the reproducing property. Using wikipedia's notation, we have that the reproducing property is defined as having an element $k_x \in \mathcal H$ for each $x\in\mathcal X$, the domain, such that
$$
\langle f, k_x\rangle = f(x)
$$
for each $f\in\mathc... | Understanding the reproducing property of RKHS | You're overthinking this: the result with $M$ is just a restatement of the reproducing property. Using wikipedia's notation, we have that the reproducing property is defined as having an element $k_x | Understanding the reproducing property of RKHS
You're overthinking this: the result with $M$ is just a restatement of the reproducing property. Using wikipedia's notation, we have that the reproducing property is defined as having an element $k_x \in \mathcal H$ for each $x\in\mathcal X$, the domain, such that
$$
\lang... | Understanding the reproducing property of RKHS
You're overthinking this: the result with $M$ is just a restatement of the reproducing property. Using wikipedia's notation, we have that the reproducing property is defined as having an element $k_x |
42,283 | Are loss functions necessarily additive in observations? | Loss functions are not always additive in observations: A loss function is function of an estimator (or predictor) and the thing it is estimating (predicting). The loss function is often, but not always, a distance function. Moreover, the estimator (predictor) sometimes, but not always, involves a sum of terms involv... | Are loss functions necessarily additive in observations? | Loss functions are not always additive in observations: A loss function is function of an estimator (or predictor) and the thing it is estimating (predicting). The loss function is often, but not alw | Are loss functions necessarily additive in observations?
Loss functions are not always additive in observations: A loss function is function of an estimator (or predictor) and the thing it is estimating (predicting). The loss function is often, but not always, a distance function. Moreover, the estimator (predictor) ... | Are loss functions necessarily additive in observations?
Loss functions are not always additive in observations: A loss function is function of an estimator (or predictor) and the thing it is estimating (predicting). The loss function is often, but not alw |
42,284 | Are loss functions necessarily additive in observations? | There are two most common causes for loss function being a sum/average.
First, you may simply define your loss as average of some metric. It's related to concept of risk minimization.
Second reason is that you use Maximum Likelihood or something related, like Maximum A Posteriori. Additivity comes from the fact that Ma... | Are loss functions necessarily additive in observations? | There are two most common causes for loss function being a sum/average.
First, you may simply define your loss as average of some metric. It's related to concept of risk minimization.
Second reason is | Are loss functions necessarily additive in observations?
There are two most common causes for loss function being a sum/average.
First, you may simply define your loss as average of some metric. It's related to concept of risk minimization.
Second reason is that you use Maximum Likelihood or something related, like Max... | Are loss functions necessarily additive in observations?
There are two most common causes for loss function being a sum/average.
First, you may simply define your loss as average of some metric. It's related to concept of risk minimization.
Second reason is |
42,285 | Chi Square vs F Tests for GLM Model Comparisons | Basically, yes. $F$ is used when the dispersion parameter is estimated rather than assumed to be fixed to some known value. $F$ is also often used for quasi-likelihood models where a somewhat ad hoc overdispersion parameter is estimated (see e.g. Venables and Ripley Modern Applied Statistics with S).
For a Tweedie dist... | Chi Square vs F Tests for GLM Model Comparisons | Basically, yes. $F$ is used when the dispersion parameter is estimated rather than assumed to be fixed to some known value. $F$ is also often used for quasi-likelihood models where a somewhat ad hoc o | Chi Square vs F Tests for GLM Model Comparisons
Basically, yes. $F$ is used when the dispersion parameter is estimated rather than assumed to be fixed to some known value. $F$ is also often used for quasi-likelihood models where a somewhat ad hoc overdispersion parameter is estimated (see e.g. Venables and Ripley Moder... | Chi Square vs F Tests for GLM Model Comparisons
Basically, yes. $F$ is used when the dispersion parameter is estimated rather than assumed to be fixed to some known value. $F$ is also often used for quasi-likelihood models where a somewhat ad hoc o |
42,286 | Can I judge skewness from a scatterplot with bivariate data in R? | Is it safe to say that the data is left or negatively skewed?
No, it is not safe: Firstly, the appearance of the plot is of positive (right) skew, not negative (left) skew. Regardless, you need to be careful here because there is over-plotting, which means that you can't actually see what is going on in that big red ... | Can I judge skewness from a scatterplot with bivariate data in R? | Is it safe to say that the data is left or negatively skewed?
No, it is not safe: Firstly, the appearance of the plot is of positive (right) skew, not negative (left) skew. Regardless, you need to b | Can I judge skewness from a scatterplot with bivariate data in R?
Is it safe to say that the data is left or negatively skewed?
No, it is not safe: Firstly, the appearance of the plot is of positive (right) skew, not negative (left) skew. Regardless, you need to be careful here because there is over-plotting, which m... | Can I judge skewness from a scatterplot with bivariate data in R?
Is it safe to say that the data is left or negatively skewed?
No, it is not safe: Firstly, the appearance of the plot is of positive (right) skew, not negative (left) skew. Regardless, you need to b |
42,287 | Can I judge skewness from a scatterplot with bivariate data in R? | This approad may be missleading and this is why.
The scatterplot can tell you something about the distribution of each variable. But the scatterplot also tells you something about the relationsship between two variables, which can lead to problems if one is making an interpretation about one of the variables alone, e.g... | Can I judge skewness from a scatterplot with bivariate data in R? | This approad may be missleading and this is why.
The scatterplot can tell you something about the distribution of each variable. But the scatterplot also tells you something about the relationsship be | Can I judge skewness from a scatterplot with bivariate data in R?
This approad may be missleading and this is why.
The scatterplot can tell you something about the distribution of each variable. But the scatterplot also tells you something about the relationsship between two variables, which can lead to problems if one... | Can I judge skewness from a scatterplot with bivariate data in R?
This approad may be missleading and this is why.
The scatterplot can tell you something about the distribution of each variable. But the scatterplot also tells you something about the relationsship be |
42,288 | Use and misuse of Winsorization | When winsorizing the data, the $\alpha\%$ winsorization is defined as replacing the $(100\%-\alpha)/2$ smallest values with value above them, and $(100\%-\alpha)/2$ largest values with the value below them (with $\alpha\in[0\%, 100\%]$),
for example, a 90% winsorization would see all data below the 5th
percentile s... | Use and misuse of Winsorization | When winsorizing the data, the $\alpha\%$ winsorization is defined as replacing the $(100\%-\alpha)/2$ smallest values with value above them, and $(100\%-\alpha)/2$ largest values with the value below | Use and misuse of Winsorization
When winsorizing the data, the $\alpha\%$ winsorization is defined as replacing the $(100\%-\alpha)/2$ smallest values with value above them, and $(100\%-\alpha)/2$ largest values with the value below them (with $\alpha\in[0\%, 100\%]$),
for example, a 90% winsorization would see all d... | Use and misuse of Winsorization
When winsorizing the data, the $\alpha\%$ winsorization is defined as replacing the $(100\%-\alpha)/2$ smallest values with value above them, and $(100\%-\alpha)/2$ largest values with the value below |
42,289 | How to interpret a two-way interaction in a 3-way interaction model | My question is, is there a significant ab interaction? If I trust model A, then I would say no, but if I trust model B, then I would say yes. Which model is more correct, or does it depend on details of the model? Why does adding a 3-way interaction make an originally non-significant two-way interaction (model A) signi... | How to interpret a two-way interaction in a 3-way interaction model | My question is, is there a significant ab interaction? If I trust model A, then I would say no, but if I trust model B, then I would say yes. Which model is more correct, or does it depend on details | How to interpret a two-way interaction in a 3-way interaction model
My question is, is there a significant ab interaction? If I trust model A, then I would say no, but if I trust model B, then I would say yes. Which model is more correct, or does it depend on details of the model? Why does adding a 3-way interaction ma... | How to interpret a two-way interaction in a 3-way interaction model
My question is, is there a significant ab interaction? If I trust model A, then I would say no, but if I trust model B, then I would say yes. Which model is more correct, or does it depend on details |
42,290 | Does sampling from a large dataset lead to correct inferences? | If you have the whole population, you are not really doing any inference of a variable, that only happens when you are taking a sample. Let's say you are using a model that predicts weight based on height, so it's
$$w = a\cdot h + \epsilon$$
Where $\epsilon$ is some error. Somehow you have collected data on the whole ... | Does sampling from a large dataset lead to correct inferences? | If you have the whole population, you are not really doing any inference of a variable, that only happens when you are taking a sample. Let's say you are using a model that predicts weight based on he | Does sampling from a large dataset lead to correct inferences?
If you have the whole population, you are not really doing any inference of a variable, that only happens when you are taking a sample. Let's say you are using a model that predicts weight based on height, so it's
$$w = a\cdot h + \epsilon$$
Where $\epsilo... | Does sampling from a large dataset lead to correct inferences?
If you have the whole population, you are not really doing any inference of a variable, that only happens when you are taking a sample. Let's say you are using a model that predicts weight based on he |
42,291 | Does sampling from a large dataset lead to correct inferences? | Yes, this works. All data is a sample population. If you have enough to achieve some level of performance on some metric, than you have achieved your goal. There will generally be a point of diminishing returns on the size of the data. Thus, more data will make little difference. As long as you have enough to make an a... | Does sampling from a large dataset lead to correct inferences? | Yes, this works. All data is a sample population. If you have enough to achieve some level of performance on some metric, than you have achieved your goal. There will generally be a point of diminishi | Does sampling from a large dataset lead to correct inferences?
Yes, this works. All data is a sample population. If you have enough to achieve some level of performance on some metric, than you have achieved your goal. There will generally be a point of diminishing returns on the size of the data. Thus, more data will ... | Does sampling from a large dataset lead to correct inferences?
Yes, this works. All data is a sample population. If you have enough to achieve some level of performance on some metric, than you have achieved your goal. There will generally be a point of diminishi |
42,292 | Does sampling from a large dataset lead to correct inferences? | I imagine it depends on what kind of inferences you're trying to make about the population. In general you could be making any kind of inference, including inferences about the estimators used to learn population parameters. This question immediately made me think of the bootstrap and jackknife resampling techniques, w... | Does sampling from a large dataset lead to correct inferences? | I imagine it depends on what kind of inferences you're trying to make about the population. In general you could be making any kind of inference, including inferences about the estimators used to lear | Does sampling from a large dataset lead to correct inferences?
I imagine it depends on what kind of inferences you're trying to make about the population. In general you could be making any kind of inference, including inferences about the estimators used to learn population parameters. This question immediately made m... | Does sampling from a large dataset lead to correct inferences?
I imagine it depends on what kind of inferences you're trying to make about the population. In general you could be making any kind of inference, including inferences about the estimators used to lear |
42,293 | Does sampling from a large dataset lead to correct inferences? | This is certainly the case in the infinite population setting, but IRL that's rarely the case at least as far as big data are concerned.
For instance, if I run an insurance company and manage claims, I can do statistical analyses of all claims or even just a large subset. There's a challenge here. If I do a simple ran... | Does sampling from a large dataset lead to correct inferences? | This is certainly the case in the infinite population setting, but IRL that's rarely the case at least as far as big data are concerned.
For instance, if I run an insurance company and manage claims, | Does sampling from a large dataset lead to correct inferences?
This is certainly the case in the infinite population setting, but IRL that's rarely the case at least as far as big data are concerned.
For instance, if I run an insurance company and manage claims, I can do statistical analyses of all claims or even just... | Does sampling from a large dataset lead to correct inferences?
This is certainly the case in the infinite population setting, but IRL that's rarely the case at least as far as big data are concerned.
For instance, if I run an insurance company and manage claims, |
42,294 | Why increasing the batch size has the same effect as decaying the learning rate? | I think it may be a confusion about the different meanings of stability -- stable as in numerically stable / weights don't go to infinity, versus stable as in the loss steadily monotonically decreases and you eventually converge to some good solution.
L2 regularization accomplishes the first, but doesn't necessarily he... | Why increasing the batch size has the same effect as decaying the learning rate? | I think it may be a confusion about the different meanings of stability -- stable as in numerically stable / weights don't go to infinity, versus stable as in the loss steadily monotonically decreases | Why increasing the batch size has the same effect as decaying the learning rate?
I think it may be a confusion about the different meanings of stability -- stable as in numerically stable / weights don't go to infinity, versus stable as in the loss steadily monotonically decreases and you eventually converge to some go... | Why increasing the batch size has the same effect as decaying the learning rate?
I think it may be a confusion about the different meanings of stability -- stable as in numerically stable / weights don't go to infinity, versus stable as in the loss steadily monotonically decreases |
42,295 | Random Forest Regression - R^2 score or MSE for Comparison | There is no real difference in discrimination between the mean squared error and the R-squared, when it is used on a test dataset as the R-Squared is just the MSE divided by the MSE of the prediction of the mean, which is a constant. So MSE and R-Squared are proportional to each other and the ranking will never be diff... | Random Forest Regression - R^2 score or MSE for Comparison | There is no real difference in discrimination between the mean squared error and the R-squared, when it is used on a test dataset as the R-Squared is just the MSE divided by the MSE of the prediction | Random Forest Regression - R^2 score or MSE for Comparison
There is no real difference in discrimination between the mean squared error and the R-squared, when it is used on a test dataset as the R-Squared is just the MSE divided by the MSE of the prediction of the mean, which is a constant. So MSE and R-Squared are pr... | Random Forest Regression - R^2 score or MSE for Comparison
There is no real difference in discrimination between the mean squared error and the R-squared, when it is used on a test dataset as the R-Squared is just the MSE divided by the MSE of the prediction |
42,296 | Random Forest Regression - R^2 score or MSE for Comparison | The r2_score is a statistical description of how your samples fit along a linear model. It only works well if there is a linear relationship between features and outcome (with few outliers).
Instead you should calculate the mean-absolute-error or mean-squared-error using labeled samples from the testset, that your mod... | Random Forest Regression - R^2 score or MSE for Comparison | The r2_score is a statistical description of how your samples fit along a linear model. It only works well if there is a linear relationship between features and outcome (with few outliers).
Instead | Random Forest Regression - R^2 score or MSE for Comparison
The r2_score is a statistical description of how your samples fit along a linear model. It only works well if there is a linear relationship between features and outcome (with few outliers).
Instead you should calculate the mean-absolute-error or mean-squared-... | Random Forest Regression - R^2 score or MSE for Comparison
The r2_score is a statistical description of how your samples fit along a linear model. It only works well if there is a linear relationship between features and outcome (with few outliers).
Instead |
42,297 | Correlation between an observation and its rank in a random sample | I will give a hint. The key concept is exchangeability, meaning that the random vector $(X_1, \dotsc, X_n)$ has the same distribution as $(X_{\pi 1}, \dotsc, X_{\pi n})$ for all permutations $\pi$ of $(1,2,\dotsc, n)$. Then you can check that the vector of ranks $(R_1, \dotsc, R_n)$ also will be exchangeable. Exchang... | Correlation between an observation and its rank in a random sample | I will give a hint. The key concept is exchangeability, meaning that the random vector $(X_1, \dotsc, X_n)$ has the same distribution as $(X_{\pi 1}, \dotsc, X_{\pi n})$ for all permutations $\pi$ of | Correlation between an observation and its rank in a random sample
I will give a hint. The key concept is exchangeability, meaning that the random vector $(X_1, \dotsc, X_n)$ has the same distribution as $(X_{\pi 1}, \dotsc, X_{\pi n})$ for all permutations $\pi$ of $(1,2,\dotsc, n)$. Then you can check that the vecto... | Correlation between an observation and its rank in a random sample
I will give a hint. The key concept is exchangeability, meaning that the random vector $(X_1, \dotsc, X_n)$ has the same distribution as $(X_{\pi 1}, \dotsc, X_{\pi n})$ for all permutations $\pi$ of |
42,298 | Correlation between an observation and its rank in a random sample | We can find $\operatorname E\left[R_1X_1\right]$ using the conditional distribution of $X_1$ given $R_1$. The distribution of $X_1$ conditioned on $R_1=j$ is simply the distribution of $X_{(j)}$, since $R_1=j \implies X_1=X_{(j)}$ by definition for every $j=1,\ldots,n$.
Hence,
\begin{align}
\operatorname E\left[R_1X_1\... | Correlation between an observation and its rank in a random sample | We can find $\operatorname E\left[R_1X_1\right]$ using the conditional distribution of $X_1$ given $R_1$. The distribution of $X_1$ conditioned on $R_1=j$ is simply the distribution of $X_{(j)}$, sinc | Correlation between an observation and its rank in a random sample
We can find $\operatorname E\left[R_1X_1\right]$ using the conditional distribution of $X_1$ given $R_1$. The distribution of $X_1$ conditioned on $R_1=j$ is simply the distribution of $X_{(j)}$, since $R_1=j \implies X_1=X_{(j)}$ by definition for ever... | Correlation between an observation and its rank in a random sample
We can find $\operatorname E\left[R_1X_1\right]$ using the conditional distribution of $X_1$ given $R_1$. The distribution of $X_1$ conditioned on $R_1=j$ is simply the distribution of $X_{(j)}$, sinc |
42,299 | How to Bayesian update on two events which occur with measure zero? | The paradox is one of measure theory and conditioning rather than one of Bayesian inference (and thus you should modify the title of the question). To quote Andrei Kolmogorov,
"The concept of a conditional probability with regard to an isolated
hypothesis whose probability equals 0 is inadmissible."
When one define... | How to Bayesian update on two events which occur with measure zero? | The paradox is one of measure theory and conditioning rather than one of Bayesian inference (and thus you should modify the title of the question). To quote Andrei Kolmogorov,
"The concept of a condi | How to Bayesian update on two events which occur with measure zero?
The paradox is one of measure theory and conditioning rather than one of Bayesian inference (and thus you should modify the title of the question). To quote Andrei Kolmogorov,
"The concept of a conditional probability with regard to an isolated
hypo... | How to Bayesian update on two events which occur with measure zero?
The paradox is one of measure theory and conditioning rather than one of Bayesian inference (and thus you should modify the title of the question). To quote Andrei Kolmogorov,
"The concept of a condi |
42,300 | When do we use an even size kernel in convolutional neural network and why? | To the best of my knowledge, there is no consistent answer to the first question. It's like asking "is it better to use (3,3) kernel size or (5,5) kernel size?". As far as I know, the reason behind choosing either an even or odd kernel comes from trial and error in practical implementations and can vary from one case t... | When do we use an even size kernel in convolutional neural network and why? | To the best of my knowledge, there is no consistent answer to the first question. It's like asking "is it better to use (3,3) kernel size or (5,5) kernel size?". As far as I know, the reason behind ch | When do we use an even size kernel in convolutional neural network and why?
To the best of my knowledge, there is no consistent answer to the first question. It's like asking "is it better to use (3,3) kernel size or (5,5) kernel size?". As far as I know, the reason behind choosing either an even or odd kernel comes fr... | When do we use an even size kernel in convolutional neural network and why?
To the best of my knowledge, there is no consistent answer to the first question. It's like asking "is it better to use (3,3) kernel size or (5,5) kernel size?". As far as I know, the reason behind ch |
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