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 |
|---|---|---|---|---|---|---|
50,301 | How come parents of $X$ always satisfy the backdoor criterion relative to $(X,Y)$? | The latter note is not obvious to me. Consider a DAG that is a simple
chain $$ Z \rightarrow X \rightarrow Y $$ Here, $\text{PA}(X)=Z$. At
the same time, there is no backdoor path between $X$ and $Y$, so $Z$
does not block any. Question: How come $Z$ satisfies the backdoor
criterion then?
$Z$ satisfy the backdoor crit... | How come parents of $X$ always satisfy the backdoor criterion relative to $(X,Y)$? | The latter note is not obvious to me. Consider a DAG that is a simple
chain $$ Z \rightarrow X \rightarrow Y $$ Here, $\text{PA}(X)=Z$. At
the same time, there is no backdoor path between $X$ and $Y$, | How come parents of $X$ always satisfy the backdoor criterion relative to $(X,Y)$?
The latter note is not obvious to me. Consider a DAG that is a simple
chain $$ Z \rightarrow X \rightarrow Y $$ Here, $\text{PA}(X)=Z$. At
the same time, there is no backdoor path between $X$ and $Y$, so $Z$
does not block any. Question:... | How come parents of $X$ always satisfy the backdoor criterion relative to $(X,Y)$?
The latter note is not obvious to me. Consider a DAG that is a simple
chain $$ Z \rightarrow X \rightarrow Y $$ Here, $\text{PA}(X)=Z$. At
the same time, there is no backdoor path between $X$ and $Y$, |
50,302 | How come parents of $X$ always satisfy the backdoor criterion relative to $(X,Y)$? | The reason that conditioning on the parents of $X$, irrespective of what the DAG looks like, always satisfies the backdoor criterion relative to $(X,Y)$ is that there is a parent of $X$ on each backdoor path and parents of $X$ cannot be colliders, by definition of parents of $X$ (which implies an arrow from the parent ... | How come parents of $X$ always satisfy the backdoor criterion relative to $(X,Y)$? | The reason that conditioning on the parents of $X$, irrespective of what the DAG looks like, always satisfies the backdoor criterion relative to $(X,Y)$ is that there is a parent of $X$ on each backdo | How come parents of $X$ always satisfy the backdoor criterion relative to $(X,Y)$?
The reason that conditioning on the parents of $X$, irrespective of what the DAG looks like, always satisfies the backdoor criterion relative to $(X,Y)$ is that there is a parent of $X$ on each backdoor path and parents of $X$ cannot be ... | How come parents of $X$ always satisfy the backdoor criterion relative to $(X,Y)$?
The reason that conditioning on the parents of $X$, irrespective of what the DAG looks like, always satisfies the backdoor criterion relative to $(X,Y)$ is that there is a parent of $X$ on each backdo |
50,303 | How total loss is manipulated in mini batch gradient descent as the loss function is calculated and minimized for mini batches? | You don't accumulate those losses unless you are reporting training loss, which is usually not part of the training where mini-batching matters. The mini-batch is assumed to approximate the full-batch loss function and we update the weight and bias under that assumption, in the hope that full batch also approximates th... | How total loss is manipulated in mini batch gradient descent as the loss function is calculated and | You don't accumulate those losses unless you are reporting training loss, which is usually not part of the training where mini-batching matters. The mini-batch is assumed to approximate the full-batch | How total loss is manipulated in mini batch gradient descent as the loss function is calculated and minimized for mini batches?
You don't accumulate those losses unless you are reporting training loss, which is usually not part of the training where mini-batching matters. The mini-batch is assumed to approximate the fu... | How total loss is manipulated in mini batch gradient descent as the loss function is calculated and
You don't accumulate those losses unless you are reporting training loss, which is usually not part of the training where mini-batching matters. The mini-batch is assumed to approximate the full-batch |
50,304 | Derivation of maximum likelihood for a Gaussian mixture model | To avoid any confusion, the summation index and the index of the $\mu$ that you differentiate with should be different. From the beginning, assume the likelihood is written with index $j$ and you want to differentiate it with $\mu_k$:
$$\frac{\partial \sum_{j=1}^K \pi_j N(x_n|\mu_j,\Sigma_j) }{\partial \mu_k}=\frac{ \p... | Derivation of maximum likelihood for a Gaussian mixture model | To avoid any confusion, the summation index and the index of the $\mu$ that you differentiate with should be different. From the beginning, assume the likelihood is written with index $j$ and you want | Derivation of maximum likelihood for a Gaussian mixture model
To avoid any confusion, the summation index and the index of the $\mu$ that you differentiate with should be different. From the beginning, assume the likelihood is written with index $j$ and you want to differentiate it with $\mu_k$:
$$\frac{\partial \sum_{... | Derivation of maximum likelihood for a Gaussian mixture model
To avoid any confusion, the summation index and the index of the $\mu$ that you differentiate with should be different. From the beginning, assume the likelihood is written with index $j$ and you want |
50,305 | Where are the Wald p-values and where are the LRT ones in the resulf of mixed models? [closed] | 1 . So, when I get an output of a mixed model, in any statistical package, I get the list of coefficients with its p-values. Are they Wald's?
Yes, generally they are. They may be $Z$-statistics/tests (i.e., assuming that the sample is big enough so the standard errors have no uncertainty) or $t$-statistics (allowing f... | Where are the Wald p-values and where are the LRT ones in the resulf of mixed models? [closed] | 1 . So, when I get an output of a mixed model, in any statistical package, I get the list of coefficients with its p-values. Are they Wald's?
Yes, generally they are. They may be $Z$-statistics/tests | Where are the Wald p-values and where are the LRT ones in the resulf of mixed models? [closed]
1 . So, when I get an output of a mixed model, in any statistical package, I get the list of coefficients with its p-values. Are they Wald's?
Yes, generally they are. They may be $Z$-statistics/tests (i.e., assuming that the... | Where are the Wald p-values and where are the LRT ones in the resulf of mixed models? [closed]
1 . So, when I get an output of a mixed model, in any statistical package, I get the list of coefficients with its p-values. Are they Wald's?
Yes, generally they are. They may be $Z$-statistics/tests |
50,306 | Range of values of $R^2$ for a two-feature linear model based on the $R^2$s of one-feature linear models? [duplicate] | A simple approach to this problem is considering it from a geometrical view of point.
Firstly, we immediately know answer is within range [0.1, 1], then let's check if it's tight.
Note regression is projection of $y$ on to column space of $x$.
If vector $x_1$ and $x_2$ are almost perfect linear dependent, it's easy to ... | Range of values of $R^2$ for a two-feature linear model based on the $R^2$s of one-feature linear mo | A simple approach to this problem is considering it from a geometrical view of point.
Firstly, we immediately know answer is within range [0.1, 1], then let's check if it's tight.
Note regression is p | Range of values of $R^2$ for a two-feature linear model based on the $R^2$s of one-feature linear models? [duplicate]
A simple approach to this problem is considering it from a geometrical view of point.
Firstly, we immediately know answer is within range [0.1, 1], then let's check if it's tight.
Note regression is pro... | Range of values of $R^2$ for a two-feature linear model based on the $R^2$s of one-feature linear mo
A simple approach to this problem is considering it from a geometrical view of point.
Firstly, we immediately know answer is within range [0.1, 1], then let's check if it's tight.
Note regression is p |
50,307 | Smoothed Moments as Function of Predictor | Continuing from the example data generated in the OP, we can construct a simple GAMLSS model for the mean of the data using a penalised B-spline. This model assumed a Normal distribution. We are only interested in the spline for the mean.
m1 <- gamlss(ys~pb(xs))
plot(NULL, xlim=c(0,xlim), ylim = c(0, 4), xlab="x", ylab... | Smoothed Moments as Function of Predictor | Continuing from the example data generated in the OP, we can construct a simple GAMLSS model for the mean of the data using a penalised B-spline. This model assumed a Normal distribution. We are only | Smoothed Moments as Function of Predictor
Continuing from the example data generated in the OP, we can construct a simple GAMLSS model for the mean of the data using a penalised B-spline. This model assumed a Normal distribution. We are only interested in the spline for the mean.
m1 <- gamlss(ys~pb(xs))
plot(NULL, xlim... | Smoothed Moments as Function of Predictor
Continuing from the example data generated in the OP, we can construct a simple GAMLSS model for the mean of the data using a penalised B-spline. This model assumed a Normal distribution. We are only |
50,308 | Kernel density estimate vs Dirichlet process mixture | After some research and thinking, here would be my own tentative answer to the question I posted; just in case someone else is interested in this question.
Given n data points, KDE uses a mixture of n kernels to approximate the "true" density while DPM, in finite samples, typically ends up with a smaller mixture even t... | Kernel density estimate vs Dirichlet process mixture | After some research and thinking, here would be my own tentative answer to the question I posted; just in case someone else is interested in this question.
Given n data points, KDE uses a mixture of n | Kernel density estimate vs Dirichlet process mixture
After some research and thinking, here would be my own tentative answer to the question I posted; just in case someone else is interested in this question.
Given n data points, KDE uses a mixture of n kernels to approximate the "true" density while DPM, in finite sam... | Kernel density estimate vs Dirichlet process mixture
After some research and thinking, here would be my own tentative answer to the question I posted; just in case someone else is interested in this question.
Given n data points, KDE uses a mixture of n |
50,309 | How to compare model coefficients from models with different distribution family and link functions | You can't directly compare the estimated coefficients since the units of the response variable are not the same in both models.
See, a logistic regression will estimate a binomial probability of observing the event you modelled. So a number between 0 and one is ultimately estimated. Note also that the estimate is not ... | How to compare model coefficients from models with different distribution family and link functions | You can't directly compare the estimated coefficients since the units of the response variable are not the same in both models.
See, a logistic regression will estimate a binomial probability of obse | How to compare model coefficients from models with different distribution family and link functions
You can't directly compare the estimated coefficients since the units of the response variable are not the same in both models.
See, a logistic regression will estimate a binomial probability of observing the event you ... | How to compare model coefficients from models with different distribution family and link functions
You can't directly compare the estimated coefficients since the units of the response variable are not the same in both models.
See, a logistic regression will estimate a binomial probability of obse |
50,310 | How to account for the no:of parameters in the Multihead self-Attention layer of BERT | After doing the multi-head attention, you have 12 heads context vectors of dimension 768 and you need to project them back to the model dimension, this gives you another 12 × 768 × 768 + 768 parameters. In addition, there is layer normalization with 2 × 768 parameters. | How to account for the no:of parameters in the Multihead self-Attention layer of BERT | After doing the multi-head attention, you have 12 heads context vectors of dimension 768 and you need to project them back to the model dimension, this gives you another 12 × 768 × 768 + 768 parameter | How to account for the no:of parameters in the Multihead self-Attention layer of BERT
After doing the multi-head attention, you have 12 heads context vectors of dimension 768 and you need to project them back to the model dimension, this gives you another 12 × 768 × 768 + 768 parameters. In addition, there is layer nor... | How to account for the no:of parameters in the Multihead self-Attention layer of BERT
After doing the multi-head attention, you have 12 heads context vectors of dimension 768 and you need to project them back to the model dimension, this gives you another 12 × 768 × 768 + 768 parameter |
50,311 | How to account for the no:of parameters in the Multihead self-Attention layer of BERT | I have found the answer after digging into a pytorch implementation and a few other blogs. Here's the explanation for the number of paramteres in the Transformer cell (only the mult-headed self-attention part):
We can see the inside of transformer cell in above picture. The input vector is transformed in multiple head... | How to account for the no:of parameters in the Multihead self-Attention layer of BERT | I have found the answer after digging into a pytorch implementation and a few other blogs. Here's the explanation for the number of paramteres in the Transformer cell (only the mult-headed self-attent | How to account for the no:of parameters in the Multihead self-Attention layer of BERT
I have found the answer after digging into a pytorch implementation and a few other blogs. Here's the explanation for the number of paramteres in the Transformer cell (only the mult-headed self-attention part):
We can see the inside ... | How to account for the no:of parameters in the Multihead self-Attention layer of BERT
I have found the answer after digging into a pytorch implementation and a few other blogs. Here's the explanation for the number of paramteres in the Transformer cell (only the mult-headed self-attent |
50,312 | Bootstrapping with more than one random effect | I think in this case it is recommended to do a parametric bootstrap: the mixed effect model gives you an estimate of the variance of the effects of words and subjects, so you can generate new random deviates from their distribution (thus without actually resampling the estimated values). It is not difficult to write th... | Bootstrapping with more than one random effect | I think in this case it is recommended to do a parametric bootstrap: the mixed effect model gives you an estimate of the variance of the effects of words and subjects, so you can generate new random d | Bootstrapping with more than one random effect
I think in this case it is recommended to do a parametric bootstrap: the mixed effect model gives you an estimate of the variance of the effects of words and subjects, so you can generate new random deviates from their distribution (thus without actually resampling the est... | Bootstrapping with more than one random effect
I think in this case it is recommended to do a parametric bootstrap: the mixed effect model gives you an estimate of the variance of the effects of words and subjects, so you can generate new random d |
50,313 | Shouldn't we sample from the output of variational auto-encoder? | There are two terms in the ELBO:
$$E_{z \sim q}[\log P(x|z)] - \text{KL}(q(z)||p(z))$$
We estimate the first term by sampling a single $z$ and computing $\log P(x|z)$.
Since the VAE models $x|z \sim \mathcal{N}(\mu, \sigma^2)$, where $\mu = f(z;\theta)$ for some decoder neural network $f$, and the log of the gaussian d... | Shouldn't we sample from the output of variational auto-encoder? | There are two terms in the ELBO:
$$E_{z \sim q}[\log P(x|z)] - \text{KL}(q(z)||p(z))$$
We estimate the first term by sampling a single $z$ and computing $\log P(x|z)$.
Since the VAE models $x|z \sim \ | Shouldn't we sample from the output of variational auto-encoder?
There are two terms in the ELBO:
$$E_{z \sim q}[\log P(x|z)] - \text{KL}(q(z)||p(z))$$
We estimate the first term by sampling a single $z$ and computing $\log P(x|z)$.
Since the VAE models $x|z \sim \mathcal{N}(\mu, \sigma^2)$, where $\mu = f(z;\theta)$ f... | Shouldn't we sample from the output of variational auto-encoder?
There are two terms in the ELBO:
$$E_{z \sim q}[\log P(x|z)] - \text{KL}(q(z)||p(z))$$
We estimate the first term by sampling a single $z$ and computing $\log P(x|z)$.
Since the VAE models $x|z \sim \ |
50,314 | Probabilities in the Raven paradox | I don't think tracking changes to $\Pr(B|R)$ captures completely how the probability of the raven hypothesis changes.
All ravens are black means for all things, if a thing has the predicate raven (R), then it has the predicate black (B).
So what is $\Pr(\forall x \,\ Rx \rightarrow Bx)$?
$\forall x \,\ Rx \rightarro... | Probabilities in the Raven paradox | I don't think tracking changes to $\Pr(B|R)$ captures completely how the probability of the raven hypothesis changes.
All ravens are black means for all things, if a thing has the predicate raven (R) | Probabilities in the Raven paradox
I don't think tracking changes to $\Pr(B|R)$ captures completely how the probability of the raven hypothesis changes.
All ravens are black means for all things, if a thing has the predicate raven (R), then it has the predicate black (B).
So what is $\Pr(\forall x \,\ Rx \rightarrow ... | Probabilities in the Raven paradox
I don't think tracking changes to $\Pr(B|R)$ captures completely how the probability of the raven hypothesis changes.
All ravens are black means for all things, if a thing has the predicate raven (R) |
50,315 | Probabilities in the Raven paradox | You haven't really analyzed the setup of the raven paradox; or rather, you've analyzed an extremely constrained variant of it. You say:
We now observe a number of green frogs...
Since we did not make any other sightings...
You started from a uniform prior and observed a universe consisting only of green frogs. Of cou... | Probabilities in the Raven paradox | You haven't really analyzed the setup of the raven paradox; or rather, you've analyzed an extremely constrained variant of it. You say:
We now observe a number of green frogs...
Since we did not make | Probabilities in the Raven paradox
You haven't really analyzed the setup of the raven paradox; or rather, you've analyzed an extremely constrained variant of it. You say:
We now observe a number of green frogs...
Since we did not make any other sightings...
You started from a uniform prior and observed a universe con... | Probabilities in the Raven paradox
You haven't really analyzed the setup of the raven paradox; or rather, you've analyzed an extremely constrained variant of it. You say:
We now observe a number of green frogs...
Since we did not make |
50,316 | Probabilities in the Raven paradox | So while the probability of raven-ness implying blackness did not increase
I started to write up an answer in which I noted that this was imprecise language, corrected it to "the probability of black-ness given raven-ness", but as I continued my answer, I noticed quite a bit of cognitive dissonance, and eventually gav... | Probabilities in the Raven paradox | So while the probability of raven-ness implying blackness did not increase
I started to write up an answer in which I noted that this was imprecise language, corrected it to "the probability of black | Probabilities in the Raven paradox
So while the probability of raven-ness implying blackness did not increase
I started to write up an answer in which I noted that this was imprecise language, corrected it to "the probability of black-ness given raven-ness", but as I continued my answer, I noticed quite a bit of cogni... | Probabilities in the Raven paradox
So while the probability of raven-ness implying blackness did not increase
I started to write up an answer in which I noted that this was imprecise language, corrected it to "the probability of black |
50,317 | How to prevent overfitting? [duplicate] | The main advice for dealing with it, usually is regularization. Is
there other practical advice to avoid overfitting?
I thought what you are actually asking is what is the relation between regularization and overfitting.
The answer is that the strategies designed to reduce overfitting or test error are known collect... | How to prevent overfitting? [duplicate] | The main advice for dealing with it, usually is regularization. Is
there other practical advice to avoid overfitting?
I thought what you are actually asking is what is the relation between regulari | How to prevent overfitting? [duplicate]
The main advice for dealing with it, usually is regularization. Is
there other practical advice to avoid overfitting?
I thought what you are actually asking is what is the relation between regularization and overfitting.
The answer is that the strategies designed to reduce ove... | How to prevent overfitting? [duplicate]
The main advice for dealing with it, usually is regularization. Is
there other practical advice to avoid overfitting?
I thought what you are actually asking is what is the relation between regulari |
50,318 | What is MultiOutputRegressor and how does it work? | I read that can work as a trick to make single output regressors like SVR to support multioutput. You can read a little bit more over here
https://scikit-learn.org/stable/modules/multiclass.html | What is MultiOutputRegressor and how does it work? | I read that can work as a trick to make single output regressors like SVR to support multioutput. You can read a little bit more over here
https://scikit-learn.org/stable/modules/multiclass.html | What is MultiOutputRegressor and how does it work?
I read that can work as a trick to make single output regressors like SVR to support multioutput. You can read a little bit more over here
https://scikit-learn.org/stable/modules/multiclass.html | What is MultiOutputRegressor and how does it work?
I read that can work as a trick to make single output regressors like SVR to support multioutput. You can read a little bit more over here
https://scikit-learn.org/stable/modules/multiclass.html |
50,319 | What is MultiOutputRegressor and how does it work? | Yes, from the documentation page you linked to:
This strategy consists of fitting one regressor per target.
and from the User Guide:
Multioutput regression support can be added to any regressor with MultiOutputRegressor. This strategy consists of fitting one regressor per target.
Since each target is represented by ... | What is MultiOutputRegressor and how does it work? | Yes, from the documentation page you linked to:
This strategy consists of fitting one regressor per target.
and from the User Guide:
Multioutput regression support can be added to any regressor wit | What is MultiOutputRegressor and how does it work?
Yes, from the documentation page you linked to:
This strategy consists of fitting one regressor per target.
and from the User Guide:
Multioutput regression support can be added to any regressor with MultiOutputRegressor. This strategy consists of fitting one regress... | What is MultiOutputRegressor and how does it work?
Yes, from the documentation page you linked to:
This strategy consists of fitting one regressor per target.
and from the User Guide:
Multioutput regression support can be added to any regressor wit |
50,320 | How are the various guarantees provided to SVMs by Statistical Learning Theory affected by the Kernel Function | Some thoughts on your interesting question:
Good features are problem dependent. So seems difficult (if possible) to incorporate feature engineering into any rigorous mathematical framework.
To me, pushing the problem of finding good features to finding good kernels is a way to separate the problem in two parts.
First,... | How are the various guarantees provided to SVMs by Statistical Learning Theory affected by the Kerne | Some thoughts on your interesting question:
Good features are problem dependent. So seems difficult (if possible) to incorporate feature engineering into any rigorous mathematical framework.
To me, pu | How are the various guarantees provided to SVMs by Statistical Learning Theory affected by the Kernel Function
Some thoughts on your interesting question:
Good features are problem dependent. So seems difficult (if possible) to incorporate feature engineering into any rigorous mathematical framework.
To me, pushing the... | How are the various guarantees provided to SVMs by Statistical Learning Theory affected by the Kerne
Some thoughts on your interesting question:
Good features are problem dependent. So seems difficult (if possible) to incorporate feature engineering into any rigorous mathematical framework.
To me, pu |
50,321 | How are the various guarantees provided to SVMs by Statistical Learning Theory affected by the Kernel Function | A lot of the theoretical underpinnings of the SVM are based on the linear maximum margin classifier. However, the advantage of a kernel is that the SVM can be viewed as a linear maximum margin classifier that is constructed in a feature space that is implicitly defined by the kernel. As imposing a fixed kernel is equ... | How are the various guarantees provided to SVMs by Statistical Learning Theory affected by the Kerne | A lot of the theoretical underpinnings of the SVM are based on the linear maximum margin classifier. However, the advantage of a kernel is that the SVM can be viewed as a linear maximum margin classi | How are the various guarantees provided to SVMs by Statistical Learning Theory affected by the Kernel Function
A lot of the theoretical underpinnings of the SVM are based on the linear maximum margin classifier. However, the advantage of a kernel is that the SVM can be viewed as a linear maximum margin classifier that... | How are the various guarantees provided to SVMs by Statistical Learning Theory affected by the Kerne
A lot of the theoretical underpinnings of the SVM are based on the linear maximum margin classifier. However, the advantage of a kernel is that the SVM can be viewed as a linear maximum margin classi |
50,322 | Interpretation of confidence interval in Bayesian terms | A non-mathematical answer:
There are a lot of procedures that lead to the same answer but have completely different underlying mechanisms or operations.
One simple example would be to compare the median with the mean. Both rely on different operations and both have quite different interpretations, but in a lot of cas... | Interpretation of confidence interval in Bayesian terms | A non-mathematical answer:
There are a lot of procedures that lead to the same answer but have completely different underlying mechanisms or operations.
One simple example would be to compare the me | Interpretation of confidence interval in Bayesian terms
A non-mathematical answer:
There are a lot of procedures that lead to the same answer but have completely different underlying mechanisms or operations.
One simple example would be to compare the median with the mean. Both rely on different operations and both h... | Interpretation of confidence interval in Bayesian terms
A non-mathematical answer:
There are a lot of procedures that lead to the same answer but have completely different underlying mechanisms or operations.
One simple example would be to compare the me |
50,323 | What is the distribution of the difference of two iid noncentral Student t variates | Looks like I am a little late. Anyway, as per Owen (D.B. Owen, “A Survey of Properties and Applications of the Noncentral t distribution”, Technometrics 10 (1968) 445-478), if x is noncentral t distributed and $\nu > 2$, then
$$var[x] = \frac{\nu}{\nu-2}+\delta^2[\frac{\nu}{\nu-2}-\frac{\nu}{2}\frac{\Gamma^2((\nu-1)/2... | What is the distribution of the difference of two iid noncentral Student t variates | Looks like I am a little late. Anyway, as per Owen (D.B. Owen, “A Survey of Properties and Applications of the Noncentral t distribution”, Technometrics 10 (1968) 445-478), if x is noncentral t distr | What is the distribution of the difference of two iid noncentral Student t variates
Looks like I am a little late. Anyway, as per Owen (D.B. Owen, “A Survey of Properties and Applications of the Noncentral t distribution”, Technometrics 10 (1968) 445-478), if x is noncentral t distributed and $\nu > 2$, then
$$var[x] ... | What is the distribution of the difference of two iid noncentral Student t variates
Looks like I am a little late. Anyway, as per Owen (D.B. Owen, “A Survey of Properties and Applications of the Noncentral t distribution”, Technometrics 10 (1968) 445-478), if x is noncentral t distr |
50,324 | What is the distribution of the difference of two iid noncentral Student t variates | Since you use R and don't need an exact solution, you may find the distr package for R useful, at least for exploring.
For fixed degrees of freedom and non-centrality parameter you can start exploring with code like:
library(distr)
d1 <- Td(df=10, ncp=5)
d2 <- Td(df=10, ncp=5)
plot(d1)
dd <- d1 - d2
plot(dd)
I am n... | What is the distribution of the difference of two iid noncentral Student t variates | Since you use R and don't need an exact solution, you may find the distr package for R useful, at least for exploring.
For fixed degrees of freedom and non-centrality parameter you can start exploring | What is the distribution of the difference of two iid noncentral Student t variates
Since you use R and don't need an exact solution, you may find the distr package for R useful, at least for exploring.
For fixed degrees of freedom and non-centrality parameter you can start exploring with code like:
library(distr)
d1 ... | What is the distribution of the difference of two iid noncentral Student t variates
Since you use R and don't need an exact solution, you may find the distr package for R useful, at least for exploring.
For fixed degrees of freedom and non-centrality parameter you can start exploring |
50,325 | How do I check in practice if a posterior is proper? | The fundamental issue with improper posteriors $\mu$ is that Markov chains associated with them are either transient (reaching almost surely and definitely some infinite region of the state space) or null recurrent (revisiting past places but in an infinite time). In the later case, there is a form of ergodic theorem, ... | How do I check in practice if a posterior is proper? | The fundamental issue with improper posteriors $\mu$ is that Markov chains associated with them are either transient (reaching almost surely and definitely some infinite region of the state space) or | How do I check in practice if a posterior is proper?
The fundamental issue with improper posteriors $\mu$ is that Markov chains associated with them are either transient (reaching almost surely and definitely some infinite region of the state space) or null recurrent (revisiting past places but in an infinite time). In... | How do I check in practice if a posterior is proper?
The fundamental issue with improper posteriors $\mu$ is that Markov chains associated with them are either transient (reaching almost surely and definitely some infinite region of the state space) or |
50,326 | How to estimate confidence intervals for LC50 | The most functional way is to use the tweaking the dose.p function that can be found in Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Springer.
The code below uses the Wald statistic for 95% CI
ec = 0.5
library(VGAM)
eta <- logit(ec)
beta <- coef(mod)[1:2]
ecx <- (eta - beta[1])/beta[2]
... | How to estimate confidence intervals for LC50 | The most functional way is to use the tweaking the dose.p function that can be found in Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Springer.
The code below uses the Wal | How to estimate confidence intervals for LC50
The most functional way is to use the tweaking the dose.p function that can be found in Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Springer.
The code below uses the Wald statistic for 95% CI
ec = 0.5
library(VGAM)
eta <- logit(ec)
beta <- co... | How to estimate confidence intervals for LC50
The most functional way is to use the tweaking the dose.p function that can be found in Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Springer.
The code below uses the Wal |
50,327 | How to estimate confidence intervals for LC50 | Let's go back to first principles here to see what you are trying to estimate. The GLM with the binomial family and the logit link function is just the logistic regression model, so we can use the regression equation for that model. Letting $p \equiv \mathbb{P}(Y=1)$ be the probability of a positive response outcome ... | How to estimate confidence intervals for LC50 | Let's go back to first principles here to see what you are trying to estimate. The GLM with the binomial family and the logit link function is just the logistic regression model, so we can use the re | How to estimate confidence intervals for LC50
Let's go back to first principles here to see what you are trying to estimate. The GLM with the binomial family and the logit link function is just the logistic regression model, so we can use the regression equation for that model. Letting $p \equiv \mathbb{P}(Y=1)$ be t... | How to estimate confidence intervals for LC50
Let's go back to first principles here to see what you are trying to estimate. The GLM with the binomial family and the logit link function is just the logistic regression model, so we can use the re |
50,328 | Interpreting interaction term on highly correlated variables | I agree that in the case of perfect collinearity the interaction is just the square and it is possible to main effects that are not significant but a significant interaction.
If you had perfect collinearity then one approach is to add some small random error to one of the variables, or you could combine them, if this m... | Interpreting interaction term on highly correlated variables | I agree that in the case of perfect collinearity the interaction is just the square and it is possible to main effects that are not significant but a significant interaction.
If you had perfect collin | Interpreting interaction term on highly correlated variables
I agree that in the case of perfect collinearity the interaction is just the square and it is possible to main effects that are not significant but a significant interaction.
If you had perfect collinearity then one approach is to add some small random error ... | Interpreting interaction term on highly correlated variables
I agree that in the case of perfect collinearity the interaction is just the square and it is possible to main effects that are not significant but a significant interaction.
If you had perfect collin |
50,329 | How does the celebrated result about the diffusion limit of the Random Walk Metroplis-Hastings algorithm help us to find the optimal scaling | (though, it's still not clear to me if we need additional assumptions on $f$ to ensure that $U_t$ weakly converges to $f$ and I would be happy about any comment related to that).
This concerns the convergence of the continuous-time Langevin diffusion to its invariant measure $f$. The paper assumes that $f \in C^2$, as... | How does the celebrated result about the diffusion limit of the Random Walk Metroplis-Hastings algor | (though, it's still not clear to me if we need additional assumptions on $f$ to ensure that $U_t$ weakly converges to $f$ and I would be happy about any comment related to that).
This concerns the co | How does the celebrated result about the diffusion limit of the Random Walk Metroplis-Hastings algorithm help us to find the optimal scaling
(though, it's still not clear to me if we need additional assumptions on $f$ to ensure that $U_t$ weakly converges to $f$ and I would be happy about any comment related to that).
... | How does the celebrated result about the diffusion limit of the Random Walk Metroplis-Hastings algor
(though, it's still not clear to me if we need additional assumptions on $f$ to ensure that $U_t$ weakly converges to $f$ and I would be happy about any comment related to that).
This concerns the co |
50,330 | Use regression as coefficient in another regression | This just looks like a way to write interaction terms and polynomials (and is also not specifically related to time series regression). Multiplying out the brackets gives
$$RV_{t+1} = \alpha + \beta_0RV_t + \beta_1 RET\cdot RV_t + \beta_2 RV_t^2 + \beta_3 RW + \beta_4 RM
$$
Try something like
n <- 10
x1 <- rnorm(n)
x2 ... | Use regression as coefficient in another regression | This just looks like a way to write interaction terms and polynomials (and is also not specifically related to time series regression). Multiplying out the brackets gives
$$RV_{t+1} = \alpha + \beta_0 | Use regression as coefficient in another regression
This just looks like a way to write interaction terms and polynomials (and is also not specifically related to time series regression). Multiplying out the brackets gives
$$RV_{t+1} = \alpha + \beta_0RV_t + \beta_1 RET\cdot RV_t + \beta_2 RV_t^2 + \beta_3 RW + \beta_4... | Use regression as coefficient in another regression
This just looks like a way to write interaction terms and polynomials (and is also not specifically related to time series regression). Multiplying out the brackets gives
$$RV_{t+1} = \alpha + \beta_0 |
50,331 | Keras LSTM Long Term Dependencies | It is option 1. LSTM will learn from the 10 samples.
If you like to include more history, obviously, you can increase the time step, or you can use LSTM with stateful=True. I have found stateful LSTM's tricky but here you can find more information about them. | Keras LSTM Long Term Dependencies | It is option 1. LSTM will learn from the 10 samples.
If you like to include more history, obviously, you can increase the time step, or you can use LSTM with stateful=True. I have found stateful LSTM | Keras LSTM Long Term Dependencies
It is option 1. LSTM will learn from the 10 samples.
If you like to include more history, obviously, you can increase the time step, or you can use LSTM with stateful=True. I have found stateful LSTM's tricky but here you can find more information about them. | Keras LSTM Long Term Dependencies
It is option 1. LSTM will learn from the 10 samples.
If you like to include more history, obviously, you can increase the time step, or you can use LSTM with stateful=True. I have found stateful LSTM |
50,332 | Why we do not accept the result of our simulation study as evidence of a limitation of one method | Simulation studies that show that it is great when the data generating model and the analysis model are the same are very common. What people really want to see is more general:
Model performing well when the data generating merchanism has all the complexity of real life. There is a lot of judgement here, but some oth... | Why we do not accept the result of our simulation study as evidence of a limitation of one method | Simulation studies that show that it is great when the data generating model and the analysis model are the same are very common. What people really want to see is more general:
Model performing well | Why we do not accept the result of our simulation study as evidence of a limitation of one method
Simulation studies that show that it is great when the data generating model and the analysis model are the same are very common. What people really want to see is more general:
Model performing well when the data generat... | Why we do not accept the result of our simulation study as evidence of a limitation of one method
Simulation studies that show that it is great when the data generating model and the analysis model are the same are very common. What people really want to see is more general:
Model performing well |
50,333 | Maximum entropy distribution on the hypercube | The solution will be a normal distribution truncated to the interval $[0,1]$. The details are messy, and in practice some numerical work will be needed. The proof follows the proof in the unrestricted case, the differences occurs first when we have to find the Lagrange multipliers. But note that the $\mu,\sigma^2$ pa... | Maximum entropy distribution on the hypercube | The solution will be a normal distribution truncated to the interval $[0,1]$. The details are messy, and in practice some numerical work will be needed. The proof follows the proof in the unrestricte | Maximum entropy distribution on the hypercube
The solution will be a normal distribution truncated to the interval $[0,1]$. The details are messy, and in practice some numerical work will be needed. The proof follows the proof in the unrestricted case, the differences occurs first when we have to find the Lagrange mul... | Maximum entropy distribution on the hypercube
The solution will be a normal distribution truncated to the interval $[0,1]$. The details are messy, and in practice some numerical work will be needed. The proof follows the proof in the unrestricte |
50,334 | Modeling Time Series Sensor Data with Machine Learning Techniques? | Edit and TL;DR version: this could be treated as a mediation/moderator analysis problem, but that would still require an independant measurement to calibrate the device.
This sounds like a mediation/moderation analysis problem, not machine learning.
Let M1 be a model of the voltage under clean air conditions as a func... | Modeling Time Series Sensor Data with Machine Learning Techniques? | Edit and TL;DR version: this could be treated as a mediation/moderator analysis problem, but that would still require an independant measurement to calibrate the device.
This sounds like a mediation/m | Modeling Time Series Sensor Data with Machine Learning Techniques?
Edit and TL;DR version: this could be treated as a mediation/moderator analysis problem, but that would still require an independant measurement to calibrate the device.
This sounds like a mediation/moderation analysis problem, not machine learning.
Le... | Modeling Time Series Sensor Data with Machine Learning Techniques?
Edit and TL;DR version: this could be treated as a mediation/moderator analysis problem, but that would still require an independant measurement to calibrate the device.
This sounds like a mediation/m |
50,335 | Build confidence intervals for random effects in intercept only models | When you are interested in predictions conditional on the random effects, to my view it is easier to work with the hiearachical formulation of the mixed model that has a intrinsically Bayesian flavor. In particular, in your specific case, your are interested in the mean of the Poisson model conditional on the random ef... | Build confidence intervals for random effects in intercept only models | When you are interested in predictions conditional on the random effects, to my view it is easier to work with the hiearachical formulation of the mixed model that has a intrinsically Bayesian flavor. | Build confidence intervals for random effects in intercept only models
When you are interested in predictions conditional on the random effects, to my view it is easier to work with the hiearachical formulation of the mixed model that has a intrinsically Bayesian flavor. In particular, in your specific case, your are i... | Build confidence intervals for random effects in intercept only models
When you are interested in predictions conditional on the random effects, to my view it is easier to work with the hiearachical formulation of the mixed model that has a intrinsically Bayesian flavor. |
50,336 | Bayesian networks for one-class classification | Quite simple, yet actionable approach:
Collect your data, preprocess them to get categorical features $X$.
Create, tune, optimize the Bayesian network for $X$ with bnlearn. As a result we have practically a probability distribution $p(X)$.
Take all your observations and calculate their likelihoods $L_i=p(x_i)$.
Based ... | Bayesian networks for one-class classification | Quite simple, yet actionable approach:
Collect your data, preprocess them to get categorical features $X$.
Create, tune, optimize the Bayesian network for $X$ with bnlearn. As a result we have practi | Bayesian networks for one-class classification
Quite simple, yet actionable approach:
Collect your data, preprocess them to get categorical features $X$.
Create, tune, optimize the Bayesian network for $X$ with bnlearn. As a result we have practically a probability distribution $p(X)$.
Take all your observations and c... | Bayesian networks for one-class classification
Quite simple, yet actionable approach:
Collect your data, preprocess them to get categorical features $X$.
Create, tune, optimize the Bayesian network for $X$ with bnlearn. As a result we have practi |
50,337 | How to get around the glmer warning : “Downdated VtV is not positive definite” | Want to improve this post? Provide detailed answers to this question, including citations and an explanation of why your answer is correct. Answers without enough detail may be edited or deleted.
Here is the code that allowed me to answer the questio... | How to get around the glmer warning : “Downdated VtV is not positive definite” | Want to improve this post? Provide detailed answers to this question, including citations and an explanation of why your answer is correct. Answers without enough detail may be edited or deleted.
| How to get around the glmer warning : “Downdated VtV is not positive definite”
Want to improve this post? Provide detailed answers to this question, including citations and an explanation of why your answer is correct. Answers without enough detail may be edited or deleted.
... | How to get around the glmer warning : “Downdated VtV is not positive definite”
Want to improve this post? Provide detailed answers to this question, including citations and an explanation of why your answer is correct. Answers without enough detail may be edited or deleted.
|
50,338 | Did I mess up the Poisson-Gamma relationship? | \begin{equation}
\begin{aligned}
P(X_1 > 3 \mid X_1 + X_2 > 3)
& = \frac{P(X_1 + X_2 > 3 \mid X_1 > 3)P(X_1 > 3)}{P(X_1 + X_2 > 3)} \\
& = \frac{P(X_1 > 3)}{P(X_1 + X_2 > 3)} \text{ since $ X_2 > 0 $ with prob. 1} \\
& = \frac{e^{-1.5}}{P(X_1 + X_2 > 3)} \text{ using Exp($\frac{1}{2}$) cdf} \\
\end{aligned}
\end{equati... | Did I mess up the Poisson-Gamma relationship? | \begin{equation}
\begin{aligned}
P(X_1 > 3 \mid X_1 + X_2 > 3)
& = \frac{P(X_1 + X_2 > 3 \mid X_1 > 3)P(X_1 > 3)}{P(X_1 + X_2 > 3)} \\
& = \frac{P(X_1 > 3)}{P(X_1 + X_2 > 3)} \text{ since $ X_2 > 0 $ | Did I mess up the Poisson-Gamma relationship?
\begin{equation}
\begin{aligned}
P(X_1 > 3 \mid X_1 + X_2 > 3)
& = \frac{P(X_1 + X_2 > 3 \mid X_1 > 3)P(X_1 > 3)}{P(X_1 + X_2 > 3)} \\
& = \frac{P(X_1 > 3)}{P(X_1 + X_2 > 3)} \text{ since $ X_2 > 0 $ with prob. 1} \\
& = \frac{e^{-1.5}}{P(X_1 + X_2 > 3)} \text{ using Exp($\... | Did I mess up the Poisson-Gamma relationship?
\begin{equation}
\begin{aligned}
P(X_1 > 3 \mid X_1 + X_2 > 3)
& = \frac{P(X_1 + X_2 > 3 \mid X_1 > 3)P(X_1 > 3)}{P(X_1 + X_2 > 3)} \\
& = \frac{P(X_1 > 3)}{P(X_1 + X_2 > 3)} \text{ since $ X_2 > 0 $ |
50,339 | Did I mess up the Poisson-Gamma relationship? | Z denotes the point in time when the second Poisson event occurred. Z>3 means that the second Poisson event occurred after time 3, and therefore it is equivalent to Q<2 (Q being the number of Poisson events up to time 3) and not to Q>=2 as you calculated. If you divide 0.223 by 1-0.442=0.558, you will get the correct a... | Did I mess up the Poisson-Gamma relationship? | Z denotes the point in time when the second Poisson event occurred. Z>3 means that the second Poisson event occurred after time 3, and therefore it is equivalent to Q<2 (Q being the number of Poisson | Did I mess up the Poisson-Gamma relationship?
Z denotes the point in time when the second Poisson event occurred. Z>3 means that the second Poisson event occurred after time 3, and therefore it is equivalent to Q<2 (Q being the number of Poisson events up to time 3) and not to Q>=2 as you calculated. If you divide 0.22... | Did I mess up the Poisson-Gamma relationship?
Z denotes the point in time when the second Poisson event occurred. Z>3 means that the second Poisson event occurred after time 3, and therefore it is equivalent to Q<2 (Q being the number of Poisson |
50,340 | Maximum Entropy: another name for Maximum Likelihood or a legit Bayes procedure? | I believe Ariel Caticha has given some interesting insights on the interpretation of Maximum Entropy and its relation to Bayesian Inference.
As himself says, a good pedagogical review is his (unfinished) book, but one can check the papers coming out in arXiV as well.
I'll refer to some of the main ideas here in the ho... | Maximum Entropy: another name for Maximum Likelihood or a legit Bayes procedure? | I believe Ariel Caticha has given some interesting insights on the interpretation of Maximum Entropy and its relation to Bayesian Inference.
As himself says, a good pedagogical review is his (unfinis | Maximum Entropy: another name for Maximum Likelihood or a legit Bayes procedure?
I believe Ariel Caticha has given some interesting insights on the interpretation of Maximum Entropy and its relation to Bayesian Inference.
As himself says, a good pedagogical review is his (unfinished) book, but one can check the papers... | Maximum Entropy: another name for Maximum Likelihood or a legit Bayes procedure?
I believe Ariel Caticha has given some interesting insights on the interpretation of Maximum Entropy and its relation to Bayesian Inference.
As himself says, a good pedagogical review is his (unfinis |
50,341 | Parameter optimization with Neural Networks | But beside the normal tricks - is there something fundamentally wrong with my problem.
Yes, I think there is something fundamentally wrong with your problem statement.
From your description of the training data and the loss function I infer that you train the network to predict $k$. However, at the same time you som... | Parameter optimization with Neural Networks | But beside the normal tricks - is there something fundamentally wrong with my problem.
Yes, I think there is something fundamentally wrong with your problem statement.
From your description of the | Parameter optimization with Neural Networks
But beside the normal tricks - is there something fundamentally wrong with my problem.
Yes, I think there is something fundamentally wrong with your problem statement.
From your description of the training data and the loss function I infer that you train the network to pr... | Parameter optimization with Neural Networks
But beside the normal tricks - is there something fundamentally wrong with my problem.
Yes, I think there is something fundamentally wrong with your problem statement.
From your description of the |
50,342 | Parameter optimization with Neural Networks | If you think that $\lambda$ depends on $x$, then you need to model that explicitly in your network. You will need to choose the form of the dependency of $\lambda$ on $x$, eg polynomial, linear, Gaussian Process, or whatever seems like a good idea to you.
You probably want to set aside some hold-out data, because you'r... | Parameter optimization with Neural Networks | If you think that $\lambda$ depends on $x$, then you need to model that explicitly in your network. You will need to choose the form of the dependency of $\lambda$ on $x$, eg polynomial, linear, Gauss | Parameter optimization with Neural Networks
If you think that $\lambda$ depends on $x$, then you need to model that explicitly in your network. You will need to choose the form of the dependency of $\lambda$ on $x$, eg polynomial, linear, Gaussian Process, or whatever seems like a good idea to you.
You probably want to... | Parameter optimization with Neural Networks
If you think that $\lambda$ depends on $x$, then you need to model that explicitly in your network. You will need to choose the form of the dependency of $\lambda$ on $x$, eg polynomial, linear, Gauss |
50,343 | $\sqrt{n}$-equivalence of M-estimator based on plug-in estimator | Background:
For the case $\eta_0$ known, we assume the existence of a function $S(\theta,\eta)$ such that
1) $\tilde{\theta} = \theta_0 + Op(n^{-1/2})$
2) $S(\theta,\eta)$ is differentiable in $\theta$ at $(\theta_0,\eta_0)$ with a derivative matrix $\Gamma$ of full rank
3) $ S(\tilde{\theta},\eta_0) - S(\theta_0,\eta... | $\sqrt{n}$-equivalence of M-estimator based on plug-in estimator | Background:
For the case $\eta_0$ known, we assume the existence of a function $S(\theta,\eta)$ such that
1) $\tilde{\theta} = \theta_0 + Op(n^{-1/2})$
2) $S(\theta,\eta)$ is differentiable in $\thet | $\sqrt{n}$-equivalence of M-estimator based on plug-in estimator
Background:
For the case $\eta_0$ known, we assume the existence of a function $S(\theta,\eta)$ such that
1) $\tilde{\theta} = \theta_0 + Op(n^{-1/2})$
2) $S(\theta,\eta)$ is differentiable in $\theta$ at $(\theta_0,\eta_0)$ with a derivative matrix $\Ga... | $\sqrt{n}$-equivalence of M-estimator based on plug-in estimator
Background:
For the case $\eta_0$ known, we assume the existence of a function $S(\theta,\eta)$ such that
1) $\tilde{\theta} = \theta_0 + Op(n^{-1/2})$
2) $S(\theta,\eta)$ is differentiable in $\thet |
50,344 | $\sqrt{n}$-equivalence of M-estimator based on plug-in estimator | The other answer doesn't assume that $S_n(\hat{\theta}, \eta_0)$ is differentiable. If we assume $S_n(\hat{\theta}, \eta_0)$ differentiable, our work is simplified somewhat.
Background: Assume
1) $\tilde{\theta} = \theta_0 + op(1); S_n(\tilde{\theta},\eta_0) = op(n^{-1/2}); S_n(\theta_0,\eta_0) = Op(n^{-1/2})$
2) $... | $\sqrt{n}$-equivalence of M-estimator based on plug-in estimator | The other answer doesn't assume that $S_n(\hat{\theta}, \eta_0)$ is differentiable. If we assume $S_n(\hat{\theta}, \eta_0)$ differentiable, our work is simplified somewhat.
Background: Assume
1) $\ | $\sqrt{n}$-equivalence of M-estimator based on plug-in estimator
The other answer doesn't assume that $S_n(\hat{\theta}, \eta_0)$ is differentiable. If we assume $S_n(\hat{\theta}, \eta_0)$ differentiable, our work is simplified somewhat.
Background: Assume
1) $\tilde{\theta} = \theta_0 + op(1); S_n(\tilde{\theta},... | $\sqrt{n}$-equivalence of M-estimator based on plug-in estimator
The other answer doesn't assume that $S_n(\hat{\theta}, \eta_0)$ is differentiable. If we assume $S_n(\hat{\theta}, \eta_0)$ differentiable, our work is simplified somewhat.
Background: Assume
1) $\ |
50,345 | When does Simpson's Paradox "end"? | Yes, you are right, we can create situations where the conditional association of one variable with another will change for each additional covariate you control for. For a simple simulation, I suggest you look Dagitty's Simpson's Machine based on Pearl's paper.
However, the question you should ask yourself is the fol... | When does Simpson's Paradox "end"? | Yes, you are right, we can create situations where the conditional association of one variable with another will change for each additional covariate you control for. For a simple simulation, I sugges | When does Simpson's Paradox "end"?
Yes, you are right, we can create situations where the conditional association of one variable with another will change for each additional covariate you control for. For a simple simulation, I suggest you look Dagitty's Simpson's Machine based on Pearl's paper.
However, the question... | When does Simpson's Paradox "end"?
Yes, you are right, we can create situations where the conditional association of one variable with another will change for each additional covariate you control for. For a simple simulation, I sugges |
50,346 | When does Simpson's Paradox "end"? | Yes, I think there can always be some unexplored factor that --- had we evaluated that factor --- would have changed our interpretation of the results. That's just a reality of imperfect knowledge. And particularly problematic in observational studies like the one described where the observations are not balanced. (... | When does Simpson's Paradox "end"? | Yes, I think there can always be some unexplored factor that --- had we evaluated that factor --- would have changed our interpretation of the results. That's just a reality of imperfect knowledge. | When does Simpson's Paradox "end"?
Yes, I think there can always be some unexplored factor that --- had we evaluated that factor --- would have changed our interpretation of the results. That's just a reality of imperfect knowledge. And particularly problematic in observational studies like the one described where th... | When does Simpson's Paradox "end"?
Yes, I think there can always be some unexplored factor that --- had we evaluated that factor --- would have changed our interpretation of the results. That's just a reality of imperfect knowledge. |
50,347 | Unbounded likelihoods for unpenalized mixed effects | Taking the simple model from amoeba
$$y_{ij} \sim N(\mu_i,\sigma_f^2) \qquad \text{with} \qquad \mu_i \sim N(0,\sigma_r^2)$$
The probability density to observe a sample of $\mathbf{ y_{ij} }$ is:
$$f_{\mathbf{ Y_{ij} }}(\mathbf{ y_{ij} }) =det((2\pi)^k\Sigma)^{-\frac{1}{2}} e^{\mathbf{ y_{ij}^T\Sigma y_{ij}}}$$
With $... | Unbounded likelihoods for unpenalized mixed effects | Taking the simple model from amoeba
$$y_{ij} \sim N(\mu_i,\sigma_f^2) \qquad \text{with} \qquad \mu_i \sim N(0,\sigma_r^2)$$
The probability density to observe a sample of $\mathbf{ y_{ij} }$ is:
$$f_ | Unbounded likelihoods for unpenalized mixed effects
Taking the simple model from amoeba
$$y_{ij} \sim N(\mu_i,\sigma_f^2) \qquad \text{with} \qquad \mu_i \sim N(0,\sigma_r^2)$$
The probability density to observe a sample of $\mathbf{ y_{ij} }$ is:
$$f_{\mathbf{ Y_{ij} }}(\mathbf{ y_{ij} }) =det((2\pi)^k\Sigma)^{-\frac{... | Unbounded likelihoods for unpenalized mixed effects
Taking the simple model from amoeba
$$y_{ij} \sim N(\mu_i,\sigma_f^2) \qquad \text{with} \qquad \mu_i \sim N(0,\sigma_r^2)$$
The probability density to observe a sample of $\mathbf{ y_{ij} }$ is:
$$f_ |
50,348 | Position of knots in piecewise linear regression as 'random effects' | You can do this in the R package mcp. Although your actual full model may be outside the scope of mcp, this is a way to do "random effects" change points.
The mcp package contains a demo dataset called ex_varying:
> library(mcp)
> head(ex_varying)
id x id_numeric y
1 John 1 5 30.792018
2 John 5... | Position of knots in piecewise linear regression as 'random effects' | You can do this in the R package mcp. Although your actual full model may be outside the scope of mcp, this is a way to do "random effects" change points.
The mcp package contains a demo dataset call | Position of knots in piecewise linear regression as 'random effects'
You can do this in the R package mcp. Although your actual full model may be outside the scope of mcp, this is a way to do "random effects" change points.
The mcp package contains a demo dataset called ex_varying:
> library(mcp)
> head(ex_varying)
... | Position of knots in piecewise linear regression as 'random effects'
You can do this in the R package mcp. Although your actual full model may be outside the scope of mcp, this is a way to do "random effects" change points.
The mcp package contains a demo dataset call |
50,349 | Why do orthogonal designs have the advantage of greater efficiency and interpretability? | In a multi-way ANOVA (e.g., a two-way ANOVA), unbalanced designs have the disadvantage that the main effects are not independent (orthogonal) to the interactions of which they are apart. As such, you get different estimates for the test of the main effects depending on whether you fit a Type I, II, or III sums-of-squar... | Why do orthogonal designs have the advantage of greater efficiency and interpretability? | In a multi-way ANOVA (e.g., a two-way ANOVA), unbalanced designs have the disadvantage that the main effects are not independent (orthogonal) to the interactions of which they are apart. As such, you | Why do orthogonal designs have the advantage of greater efficiency and interpretability?
In a multi-way ANOVA (e.g., a two-way ANOVA), unbalanced designs have the disadvantage that the main effects are not independent (orthogonal) to the interactions of which they are apart. As such, you get different estimates for the... | Why do orthogonal designs have the advantage of greater efficiency and interpretability?
In a multi-way ANOVA (e.g., a two-way ANOVA), unbalanced designs have the disadvantage that the main effects are not independent (orthogonal) to the interactions of which they are apart. As such, you |
50,350 | Drawing conclusions of several inferences with the same data in one study | First, in my understanding and in principle, testing a set of different predefined hypothesis on a given data set is a valid procedure.
However, it seems that your problematic is related to a set of none-predefined hypothesis and in my understanding, the very nature of your question is about what do you mean by "draw... | Drawing conclusions of several inferences with the same data in one study | First, in my understanding and in principle, testing a set of different predefined hypothesis on a given data set is a valid procedure.
However, it seems that your problematic is related to a set of | Drawing conclusions of several inferences with the same data in one study
First, in my understanding and in principle, testing a set of different predefined hypothesis on a given data set is a valid procedure.
However, it seems that your problematic is related to a set of none-predefined hypothesis and in my understa... | Drawing conclusions of several inferences with the same data in one study
First, in my understanding and in principle, testing a set of different predefined hypothesis on a given data set is a valid procedure.
However, it seems that your problematic is related to a set of |
50,351 | Drawing conclusions of several inferences with the same data in one study | The answer is yet tentative; I'll add to it -- or remove it -- later.
In principle you can extract as many different conclusions from your data as you want. This includes hypotheses and also inferences. You will notice however, that these conclusions might overlap or even contradict each other. You could argue that is ... | Drawing conclusions of several inferences with the same data in one study | The answer is yet tentative; I'll add to it -- or remove it -- later.
In principle you can extract as many different conclusions from your data as you want. This includes hypotheses and also inference | Drawing conclusions of several inferences with the same data in one study
The answer is yet tentative; I'll add to it -- or remove it -- later.
In principle you can extract as many different conclusions from your data as you want. This includes hypotheses and also inferences. You will notice however, that these conclus... | Drawing conclusions of several inferences with the same data in one study
The answer is yet tentative; I'll add to it -- or remove it -- later.
In principle you can extract as many different conclusions from your data as you want. This includes hypotheses and also inference |
50,352 | Pooling homogenous studies vs. using meta-analysis/bayesian | I will address frequentist meta-analysis, for which the answer is: The two approaches will give asymptotically equivalent point estimates if (1) you are using an effect size measure satisfying a property I will give below; and (2) the samples are homogenous not only in true effect size, but also in within-study varianc... | Pooling homogenous studies vs. using meta-analysis/bayesian | I will address frequentist meta-analysis, for which the answer is: The two approaches will give asymptotically equivalent point estimates if (1) you are using an effect size measure satisfying a prope | Pooling homogenous studies vs. using meta-analysis/bayesian
I will address frequentist meta-analysis, for which the answer is: The two approaches will give asymptotically equivalent point estimates if (1) you are using an effect size measure satisfying a property I will give below; and (2) the samples are homogenous no... | Pooling homogenous studies vs. using meta-analysis/bayesian
I will address frequentist meta-analysis, for which the answer is: The two approaches will give asymptotically equivalent point estimates if (1) you are using an effect size measure satisfying a prope |
50,353 | A question about the inversion method | This is an interesting question, somewhat related with copulas. In the first proposal, when defining
$$\begin{pmatrix} x_1 \\ x_2 \\ \vdots \\ x_d\end{pmatrix} = \begin{pmatrix} f_{1}(z_1) \\ f_{2}(z_2) \\ \vdots \\ f_{d}(z_d)\end{pmatrix}$$
the transforms are over the marginals. Therefore, $X_1$ has the correct margin... | A question about the inversion method | This is an interesting question, somewhat related with copulas. In the first proposal, when defining
$$\begin{pmatrix} x_1 \\ x_2 \\ \vdots \\ x_d\end{pmatrix} = \begin{pmatrix} f_{1}(z_1) \\ f_{2}(z_ | A question about the inversion method
This is an interesting question, somewhat related with copulas. In the first proposal, when defining
$$\begin{pmatrix} x_1 \\ x_2 \\ \vdots \\ x_d\end{pmatrix} = \begin{pmatrix} f_{1}(z_1) \\ f_{2}(z_2) \\ \vdots \\ f_{d}(z_d)\end{pmatrix}$$
the transforms are over the marginals. T... | A question about the inversion method
This is an interesting question, somewhat related with copulas. In the first proposal, when defining
$$\begin{pmatrix} x_1 \\ x_2 \\ \vdots \\ x_d\end{pmatrix} = \begin{pmatrix} f_{1}(z_1) \\ f_{2}(z_ |
50,354 | LSTM NN produces "shifted" forecast (low quality result) | So, after trying many input and parameter tweaks, I came to a conclusion that LSTM cannot long dependencies until it gets long enough vector of past time series values. In my experiments a so-so good quality of forecast could be obtained after feeding the net with 64 lags, which span over the seasonalities in the model... | LSTM NN produces "shifted" forecast (low quality result) | So, after trying many input and parameter tweaks, I came to a conclusion that LSTM cannot long dependencies until it gets long enough vector of past time series values. In my experiments a so-so good | LSTM NN produces "shifted" forecast (low quality result)
So, after trying many input and parameter tweaks, I came to a conclusion that LSTM cannot long dependencies until it gets long enough vector of past time series values. In my experiments a so-so good quality of forecast could be obtained after feeding the net wit... | LSTM NN produces "shifted" forecast (low quality result)
So, after trying many input and parameter tweaks, I came to a conclusion that LSTM cannot long dependencies until it gets long enough vector of past time series values. In my experiments a so-so good |
50,355 | Is stratified sampling and oversampling contradictory in imbalanced datasets? | To a large extent, the desire to apply artificial balancing comes from using improper scoring rules, chiefly accuracy.
In particular, it seems that people realized that a model with strong imbalance could achieve an impressive-looking $98\%$ accuracy by predicting yet underperform a model that always predicts the major... | Is stratified sampling and oversampling contradictory in imbalanced datasets? | To a large extent, the desire to apply artificial balancing comes from using improper scoring rules, chiefly accuracy.
In particular, it seems that people realized that a model with strong imbalance c | Is stratified sampling and oversampling contradictory in imbalanced datasets?
To a large extent, the desire to apply artificial balancing comes from using improper scoring rules, chiefly accuracy.
In particular, it seems that people realized that a model with strong imbalance could achieve an impressive-looking $98\%$ ... | Is stratified sampling and oversampling contradictory in imbalanced datasets?
To a large extent, the desire to apply artificial balancing comes from using improper scoring rules, chiefly accuracy.
In particular, it seems that people realized that a model with strong imbalance c |
50,356 | Run MAP estimates before MCMC in most cases? | MAP is mode of the posterior distribution, as noticed in the comments, it does not have to be a reasonable estimate to consider. Likely, you can see MAP in the tutorials, because they want to show different possible functionalities of their software, rather then the most methodologically sound solution. In some cases i... | Run MAP estimates before MCMC in most cases? | MAP is mode of the posterior distribution, as noticed in the comments, it does not have to be a reasonable estimate to consider. Likely, you can see MAP in the tutorials, because they want to show dif | Run MAP estimates before MCMC in most cases?
MAP is mode of the posterior distribution, as noticed in the comments, it does not have to be a reasonable estimate to consider. Likely, you can see MAP in the tutorials, because they want to show different possible functionalities of their software, rather then the most met... | Run MAP estimates before MCMC in most cases?
MAP is mode of the posterior distribution, as noticed in the comments, it does not have to be a reasonable estimate to consider. Likely, you can see MAP in the tutorials, because they want to show dif |
50,357 | How to compute $g_i$ and $h_i$, i.e. the first and second derivative of the loss function in XGBoost? | I think that part of the misunderstanding stems from using the symbol $h$ in two different places for two different meanings.
The code portion of the question seems to have little to do with the mathematics of XGBoost, since the code snippets are not part of the XGBoost software.
Denote the binary cross-entropy loss f... | How to compute $g_i$ and $h_i$, i.e. the first and second derivative of the loss function in XGBoost | I think that part of the misunderstanding stems from using the symbol $h$ in two different places for two different meanings.
The code portion of the question seems to have little to do with the math | How to compute $g_i$ and $h_i$, i.e. the first and second derivative of the loss function in XGBoost?
I think that part of the misunderstanding stems from using the symbol $h$ in two different places for two different meanings.
The code portion of the question seems to have little to do with the mathematics of XGBoost... | How to compute $g_i$ and $h_i$, i.e. the first and second derivative of the loss function in XGBoost
I think that part of the misunderstanding stems from using the symbol $h$ in two different places for two different meanings.
The code portion of the question seems to have little to do with the math |
50,358 | How to compute $g_i$ and $h_i$, i.e. the first and second derivative of the loss function in XGBoost? | The discrepancy is due to the interpretation of $y_i^{t-1}$. In your derivation, you're assuming it is the probability $h_i$, whereas the code author has defined it as the log odds $logit(h_i) = log(\frac{h_i}{1-h_i})$. Re-express the loss as a function of log odds instead of probability (define $O_i = logit(h_i)$):
$$... | How to compute $g_i$ and $h_i$, i.e. the first and second derivative of the loss function in XGBoost | The discrepancy is due to the interpretation of $y_i^{t-1}$. In your derivation, you're assuming it is the probability $h_i$, whereas the code author has defined it as the log odds $logit(h_i) = log(\ | How to compute $g_i$ and $h_i$, i.e. the first and second derivative of the loss function in XGBoost?
The discrepancy is due to the interpretation of $y_i^{t-1}$. In your derivation, you're assuming it is the probability $h_i$, whereas the code author has defined it as the log odds $logit(h_i) = log(\frac{h_i}{1-h_i})$... | How to compute $g_i$ and $h_i$, i.e. the first and second derivative of the loss function in XGBoost
The discrepancy is due to the interpretation of $y_i^{t-1}$. In your derivation, you're assuming it is the probability $h_i$, whereas the code author has defined it as the log odds $logit(h_i) = log(\ |
50,359 | How to compute $g_i$ and $h_i$, i.e. the first and second derivative of the loss function in XGBoost? | As mentioned by @StayLearning, in slide 4, the author defines the logistic loss $L = \sum_{i=1}^n l(y_i,\hat y_i)$ where
$$ l(y_i,\hat y_i) = y_i\log(1+\exp(-\hat y_i)) + (1-y_i)\log(1+\exp(\hat y_i)) $$
then grad =
\begin{align}
\frac{\partial l}{\partial \hat y_i} &=
- y_i\times\frac{1}{1+\exp(\hat y_i)} + (1-y_i)\t... | How to compute $g_i$ and $h_i$, i.e. the first and second derivative of the loss function in XGBoost | As mentioned by @StayLearning, in slide 4, the author defines the logistic loss $L = \sum_{i=1}^n l(y_i,\hat y_i)$ where
$$ l(y_i,\hat y_i) = y_i\log(1+\exp(-\hat y_i)) + (1-y_i)\log(1+\exp(\hat y_i)) | How to compute $g_i$ and $h_i$, i.e. the first and second derivative of the loss function in XGBoost?
As mentioned by @StayLearning, in slide 4, the author defines the logistic loss $L = \sum_{i=1}^n l(y_i,\hat y_i)$ where
$$ l(y_i,\hat y_i) = y_i\log(1+\exp(-\hat y_i)) + (1-y_i)\log(1+\exp(\hat y_i)) $$
then grad =
\b... | How to compute $g_i$ and $h_i$, i.e. the first and second derivative of the loss function in XGBoost
As mentioned by @StayLearning, in slide 4, the author defines the logistic loss $L = \sum_{i=1}^n l(y_i,\hat y_i)$ where
$$ l(y_i,\hat y_i) = y_i\log(1+\exp(-\hat y_i)) + (1-y_i)\log(1+\exp(\hat y_i)) |
50,360 | sampling from an unnormalised distribution | The question is too general, as @whuber points out, to be answered. For instance, you could think of $\{x_1,x_2,...\}$ to be an enumeration of the rational numbers (this can be done, of course), and $\{\omega_1,\omega_2,...\}$ to be an infinite sequence of weights with $\sum\omega_j=1$ and $\omega_j>0$ for all $j$ (per... | sampling from an unnormalised distribution | The question is too general, as @whuber points out, to be answered. For instance, you could think of $\{x_1,x_2,...\}$ to be an enumeration of the rational numbers (this can be done, of course), and $ | sampling from an unnormalised distribution
The question is too general, as @whuber points out, to be answered. For instance, you could think of $\{x_1,x_2,...\}$ to be an enumeration of the rational numbers (this can be done, of course), and $\{\omega_1,\omega_2,...\}$ to be an infinite sequence of weights with $\sum\o... | sampling from an unnormalised distribution
The question is too general, as @whuber points out, to be answered. For instance, you could think of $\{x_1,x_2,...\}$ to be an enumeration of the rational numbers (this can be done, of course), and $ |
50,361 | Can I use tanh activation function in the output layer for binary classification? | The line dotted = Dot(axes=1,normalize=True)([x1, x2]) computes the cosine of the angle $\theta$ between x1 and x2. If it's always true that $\cos(\theta)>0$, that implies $0 < \tanh(\cos(\theta)) < 1$. Under these conditions, this resolves the riddle of how you're getting proper probabilities using $\tanh$. But rememb... | Can I use tanh activation function in the output layer for binary classification? | The line dotted = Dot(axes=1,normalize=True)([x1, x2]) computes the cosine of the angle $\theta$ between x1 and x2. If it's always true that $\cos(\theta)>0$, that implies $0 < \tanh(\cos(\theta)) < 1 | Can I use tanh activation function in the output layer for binary classification?
The line dotted = Dot(axes=1,normalize=True)([x1, x2]) computes the cosine of the angle $\theta$ between x1 and x2. If it's always true that $\cos(\theta)>0$, that implies $0 < \tanh(\cos(\theta)) < 1$. Under these conditions, this resolv... | Can I use tanh activation function in the output layer for binary classification?
The line dotted = Dot(axes=1,normalize=True)([x1, x2]) computes the cosine of the angle $\theta$ between x1 and x2. If it's always true that $\cos(\theta)>0$, that implies $0 < \tanh(\cos(\theta)) < 1 |
50,362 | Why KL-divergence is not used as a measure to compare clusterings? | KL divergence assumes that you know which cluster is which label. But what if the number of clusters and classes is not the same? A good clustering may need to split a class into two parts, if the data has such a structure. Plus, KL is asymmetric.
NMI is closely related, but as it compares every cluster to every label,... | Why KL-divergence is not used as a measure to compare clusterings? | KL divergence assumes that you know which cluster is which label. But what if the number of clusters and classes is not the same? A good clustering may need to split a class into two parts, if the dat | Why KL-divergence is not used as a measure to compare clusterings?
KL divergence assumes that you know which cluster is which label. But what if the number of clusters and classes is not the same? A good clustering may need to split a class into two parts, if the data has such a structure. Plus, KL is asymmetric.
NMI i... | Why KL-divergence is not used as a measure to compare clusterings?
KL divergence assumes that you know which cluster is which label. But what if the number of clusters and classes is not the same? A good clustering may need to split a class into two parts, if the dat |
50,363 | Why KL-divergence is not used as a measure to compare clusterings? | The OP has phrased their question in terms of 'popularity.' This may not be the right way to think about the use of KL divergence wrt clustering. In point of fact, KL metrics are used in information-theoretic and complexity based cluster algorithms but evaluating the 'popularity' of such routines would be difficult.
Pe... | Why KL-divergence is not used as a measure to compare clusterings? | The OP has phrased their question in terms of 'popularity.' This may not be the right way to think about the use of KL divergence wrt clustering. In point of fact, KL metrics are used in information-t | Why KL-divergence is not used as a measure to compare clusterings?
The OP has phrased their question in terms of 'popularity.' This may not be the right way to think about the use of KL divergence wrt clustering. In point of fact, KL metrics are used in information-theoretic and complexity based cluster algorithms but ... | Why KL-divergence is not used as a measure to compare clusterings?
The OP has phrased their question in terms of 'popularity.' This may not be the right way to think about the use of KL divergence wrt clustering. In point of fact, KL metrics are used in information-t |
50,364 | Conditional distribution of $Z = (X-Y) / 3$, given $Y = y$ | Perhaps a solution based on understanding what geometric distributions mean would be of more interest than a purely algebraic one.
Preliminaries: notation; Geometric distributions
Recall that a Geometric distribution with parameter $\theta$ describes the chances of observing a sequence of $x\in\{0,1,2,\ldots\}$ failure... | Conditional distribution of $Z = (X-Y) / 3$, given $Y = y$ | Perhaps a solution based on understanding what geometric distributions mean would be of more interest than a purely algebraic one.
Preliminaries: notation; Geometric distributions
Recall that a Geomet | Conditional distribution of $Z = (X-Y) / 3$, given $Y = y$
Perhaps a solution based on understanding what geometric distributions mean would be of more interest than a purely algebraic one.
Preliminaries: notation; Geometric distributions
Recall that a Geometric distribution with parameter $\theta$ describes the chance... | Conditional distribution of $Z = (X-Y) / 3$, given $Y = y$
Perhaps a solution based on understanding what geometric distributions mean would be of more interest than a purely algebraic one.
Preliminaries: notation; Geometric distributions
Recall that a Geomet |
50,365 | When is a likelihood a likelihood? | In a way, you are correct: all our models are wrong, hence even "exact" likelihoods are but convenient pseudolikelihoods to the likelihood function for the true underlying data process (assuming it could even be parameterized).
However, to understand likelihood, you need to move away from Dr. Box's adage of 'all model... | When is a likelihood a likelihood? | In a way, you are correct: all our models are wrong, hence even "exact" likelihoods are but convenient pseudolikelihoods to the likelihood function for the true underlying data process (assuming it co | When is a likelihood a likelihood?
In a way, you are correct: all our models are wrong, hence even "exact" likelihoods are but convenient pseudolikelihoods to the likelihood function for the true underlying data process (assuming it could even be parameterized).
However, to understand likelihood, you need to move away... | When is a likelihood a likelihood?
In a way, you are correct: all our models are wrong, hence even "exact" likelihoods are but convenient pseudolikelihoods to the likelihood function for the true underlying data process (assuming it co |
50,366 | Regression: zeros in heavy-tailed independent variable from quantization | There are no distributional assumptions made for variables you condition on such as predictors. Having zero frequency of a categorical variable cell for a city should not be a problem. If you believe there is a slope discontinuity at zero for all cities, you could model that variable (let's say it's coded as a fracti... | Regression: zeros in heavy-tailed independent variable from quantization | There are no distributional assumptions made for variables you condition on such as predictors. Having zero frequency of a categorical variable cell for a city should not be a problem. If you believ | Regression: zeros in heavy-tailed independent variable from quantization
There are no distributional assumptions made for variables you condition on such as predictors. Having zero frequency of a categorical variable cell for a city should not be a problem. If you believe there is a slope discontinuity at zero for al... | Regression: zeros in heavy-tailed independent variable from quantization
There are no distributional assumptions made for variables you condition on such as predictors. Having zero frequency of a categorical variable cell for a city should not be a problem. If you believ |
50,367 | Regression: zeros in heavy-tailed independent variable from quantization | You are on the right track. You could do a log constant transformation, where you add a constant to each observation and then log transform it. Determining the constant should be defensible, but one suggestion is given by Rob Hybdman on his blog (https://robjhyndman.com/hyndsight/transformations/) as half of the smalle... | Regression: zeros in heavy-tailed independent variable from quantization | You are on the right track. You could do a log constant transformation, where you add a constant to each observation and then log transform it. Determining the constant should be defensible, but one s | Regression: zeros in heavy-tailed independent variable from quantization
You are on the right track. You could do a log constant transformation, where you add a constant to each observation and then log transform it. Determining the constant should be defensible, but one suggestion is given by Rob Hybdman on his blog (... | Regression: zeros in heavy-tailed independent variable from quantization
You are on the right track. You could do a log constant transformation, where you add a constant to each observation and then log transform it. Determining the constant should be defensible, but one s |
50,368 | Conditional Probability vs Conditional Probability Distribution | A conditional probability "distribution" is essentially just a bunch of conditional probabilities, sufficient to fully characterise the conditional behaviour of one random variable given another event or random variable. A probability "distribution" can be characterised in various different ways (e.g., by a probabilit... | Conditional Probability vs Conditional Probability Distribution | A conditional probability "distribution" is essentially just a bunch of conditional probabilities, sufficient to fully characterise the conditional behaviour of one random variable given another event | Conditional Probability vs Conditional Probability Distribution
A conditional probability "distribution" is essentially just a bunch of conditional probabilities, sufficient to fully characterise the conditional behaviour of one random variable given another event or random variable. A probability "distribution" can b... | Conditional Probability vs Conditional Probability Distribution
A conditional probability "distribution" is essentially just a bunch of conditional probabilities, sufficient to fully characterise the conditional behaviour of one random variable given another event |
50,369 | Conditional Probability vs Conditional Probability Distribution | It seems to me we can use what we already know, provided we have heard of distribution functions and conditional probabilities. Thus, the following remarks offer nothing new, but I hope that in making them the basic simplicity and familiarity of the situation will become apparent.
When you have any real-valued random... | Conditional Probability vs Conditional Probability Distribution | It seems to me we can use what we already know, provided we have heard of distribution functions and conditional probabilities. Thus, the following remarks offer nothing new, but I hope that in makin | Conditional Probability vs Conditional Probability Distribution
It seems to me we can use what we already know, provided we have heard of distribution functions and conditional probabilities. Thus, the following remarks offer nothing new, but I hope that in making them the basic simplicity and familiarity of the situa... | Conditional Probability vs Conditional Probability Distribution
It seems to me we can use what we already know, provided we have heard of distribution functions and conditional probabilities. Thus, the following remarks offer nothing new, but I hope that in makin |
50,370 | Conditional Probability vs Conditional Probability Distribution | Well I think the term "conditional probability" or "conditional probability distribution" can both extend to two or more variables (correct me if I am wrong). For example, let us suppose we have $X,Y,Z$ are i.i.d random variables uniformly distributed on (0,1) for simplicity. Then we are required to find the conditiona... | Conditional Probability vs Conditional Probability Distribution | Well I think the term "conditional probability" or "conditional probability distribution" can both extend to two or more variables (correct me if I am wrong). For example, let us suppose we have $X,Y, | Conditional Probability vs Conditional Probability Distribution
Well I think the term "conditional probability" or "conditional probability distribution" can both extend to two or more variables (correct me if I am wrong). For example, let us suppose we have $X,Y,Z$ are i.i.d random variables uniformly distributed on (... | Conditional Probability vs Conditional Probability Distribution
Well I think the term "conditional probability" or "conditional probability distribution" can both extend to two or more variables (correct me if I am wrong). For example, let us suppose we have $X,Y, |
50,371 | Fit a Weibull distribution to...right-censored data? | Fitting is implemented in R's classic survival package (this function), or flexsurv, which has more flexibility, but a different parametrization for Weibull (flexsurvreg function here). Both also provide a few other distributions to try out.
Although I am not entirely sure about the method, it looks like both packages ... | Fit a Weibull distribution to...right-censored data? | Fitting is implemented in R's classic survival package (this function), or flexsurv, which has more flexibility, but a different parametrization for Weibull (flexsurvreg function here). Both also prov | Fit a Weibull distribution to...right-censored data?
Fitting is implemented in R's classic survival package (this function), or flexsurv, which has more flexibility, but a different parametrization for Weibull (flexsurvreg function here). Both also provide a few other distributions to try out.
Although I am not entirel... | Fit a Weibull distribution to...right-censored data?
Fitting is implemented in R's classic survival package (this function), or flexsurv, which has more flexibility, but a different parametrization for Weibull (flexsurvreg function here). Both also prov |
50,372 | How to interpret concordance index in Cox models? | From the documentation on predict.coxph, the choices for type are
" the linear predictor ("lp"), the risk score exp(lp) ("risk"), the
expected number of events given the covariates and follow-up time
("expected"), and the terms of the linear predictor ("terms"). The
survival probability for a subject is equal to... | How to interpret concordance index in Cox models? | From the documentation on predict.coxph, the choices for type are
" the linear predictor ("lp"), the risk score exp(lp) ("risk"), the
expected number of events given the covariates and follow-up ti | How to interpret concordance index in Cox models?
From the documentation on predict.coxph, the choices for type are
" the linear predictor ("lp"), the risk score exp(lp) ("risk"), the
expected number of events given the covariates and follow-up time
("expected"), and the terms of the linear predictor ("terms"). Th... | How to interpret concordance index in Cox models?
From the documentation on predict.coxph, the choices for type are
" the linear predictor ("lp"), the risk score exp(lp) ("risk"), the
expected number of events given the covariates and follow-up ti |
50,373 | Under which assumptions does weak stationarity imply strong stationarity | Hint: consider what happens when you make more assumptions about the specific distribution of the errors. Then you can write down exact conditional densities. After multiplying a few together, you will have the joint density of all the time observations, and strong stationarity deals with this joint distribution.
For ... | Under which assumptions does weak stationarity imply strong stationarity | Hint: consider what happens when you make more assumptions about the specific distribution of the errors. Then you can write down exact conditional densities. After multiplying a few together, you wil | Under which assumptions does weak stationarity imply strong stationarity
Hint: consider what happens when you make more assumptions about the specific distribution of the errors. Then you can write down exact conditional densities. After multiplying a few together, you will have the joint density of all the time observ... | Under which assumptions does weak stationarity imply strong stationarity
Hint: consider what happens when you make more assumptions about the specific distribution of the errors. Then you can write down exact conditional densities. After multiplying a few together, you wil |
50,374 | What's the relation between Matrix Factorization (MF) and Latent Dirichlet Allocation (LDA)? | Want to improve this post? Provide detailed answers to this question, including citations and an explanation of why your answer is correct. Answers without enough detail may be edited or deleted.
This paper suggests an answer:
Faleiros, Thiago de P... | What's the relation between Matrix Factorization (MF) and Latent Dirichlet Allocation (LDA)? | Want to improve this post? Provide detailed answers to this question, including citations and an explanation of why your answer is correct. Answers without enough detail may be edited or deleted.
| What's the relation between Matrix Factorization (MF) and Latent Dirichlet Allocation (LDA)?
Want to improve this post? Provide detailed answers to this question, including citations and an explanation of why your answer is correct. Answers without enough detail may be edited or deleted.
... | What's the relation between Matrix Factorization (MF) and Latent Dirichlet Allocation (LDA)?
Want to improve this post? Provide detailed answers to this question, including citations and an explanation of why your answer is correct. Answers without enough detail may be edited or deleted.
|
50,375 | Goodness of fit for logistic regression in r | I suggest to use the Hosmer-Lemeshow goodness of fit test for logistic regression which is implemented in the ResourceSelection library with the hoslem.test function. See: thestatsgeek.com/2014/02/16/ - Marco Sandri
But as @kjetilbhalvorsen points out below, Frank Harrell disagrees:
The Hosmer-Lemeshow test is to som... | Goodness of fit for logistic regression in r | I suggest to use the Hosmer-Lemeshow goodness of fit test for logistic regression which is implemented in the ResourceSelection library with the hoslem.test function. See: thestatsgeek.com/2014/02/16/ | Goodness of fit for logistic regression in r
I suggest to use the Hosmer-Lemeshow goodness of fit test for logistic regression which is implemented in the ResourceSelection library with the hoslem.test function. See: thestatsgeek.com/2014/02/16/ - Marco Sandri
But as @kjetilbhalvorsen points out below, Frank Harrell di... | Goodness of fit for logistic regression in r
I suggest to use the Hosmer-Lemeshow goodness of fit test for logistic regression which is implemented in the ResourceSelection library with the hoslem.test function. See: thestatsgeek.com/2014/02/16/ |
50,376 | Differences between p-value, level of significane and size of a test | level and size
Wikipedia has the following:
A test is said to have significance level $\alpha$ if its size is less than or equal to $\alpha$.
I agree with this. It also says:
the size of a test is [...] the probability of making a Type I error.
this is not quite always true. (It corrects it lower down in the arti... | Differences between p-value, level of significane and size of a test | level and size
Wikipedia has the following:
A test is said to have significance level $\alpha$ if its size is less than or equal to $\alpha$.
I agree with this. It also says:
the size of a test is | Differences between p-value, level of significane and size of a test
level and size
Wikipedia has the following:
A test is said to have significance level $\alpha$ if its size is less than or equal to $\alpha$.
I agree with this. It also says:
the size of a test is [...] the probability of making a Type I error.
... | Differences between p-value, level of significane and size of a test
level and size
Wikipedia has the following:
A test is said to have significance level $\alpha$ if its size is less than or equal to $\alpha$.
I agree with this. It also says:
the size of a test is |
50,377 | Gaussian Mixture for detecting outliers | There is a smart way to do this that is implemented by JMP software. In the GMM fitting, there is an option for "outlier cluster" that can be checked. The description of this is below:
The outlier cluster option assumes a uniform distribution and is less
sensitive to outliers than the standard Normal Mixtures meth... | Gaussian Mixture for detecting outliers | There is a smart way to do this that is implemented by JMP software. In the GMM fitting, there is an option for "outlier cluster" that can be checked. The description of this is below:
The outlier | Gaussian Mixture for detecting outliers
There is a smart way to do this that is implemented by JMP software. In the GMM fitting, there is an option for "outlier cluster" that can be checked. The description of this is below:
The outlier cluster option assumes a uniform distribution and is less
sensitive to outlier... | Gaussian Mixture for detecting outliers
There is a smart way to do this that is implemented by JMP software. In the GMM fitting, there is an option for "outlier cluster" that can be checked. The description of this is below:
The outlier |
50,378 | Gaussian Mixture for detecting outliers | Just an idea, not using Gaussian processes:
If your dataset is not too big, you could use hierarchical clustering with a linkage method that creates unbalanced trees. The thinner branches of the tree would then represent the outliers.
I happen to know that the single linkage method of R's hclust() function method t... | Gaussian Mixture for detecting outliers | Just an idea, not using Gaussian processes:
If your dataset is not too big, you could use hierarchical clustering with a linkage method that creates unbalanced trees. The thinner branches of the tree | Gaussian Mixture for detecting outliers
Just an idea, not using Gaussian processes:
If your dataset is not too big, you could use hierarchical clustering with a linkage method that creates unbalanced trees. The thinner branches of the tree would then represent the outliers.
I happen to know that the single linkage me... | Gaussian Mixture for detecting outliers
Just an idea, not using Gaussian processes:
If your dataset is not too big, you could use hierarchical clustering with a linkage method that creates unbalanced trees. The thinner branches of the tree |
50,379 | How to interpret OOBerror while doing data imputation with missForest | Unless I'm mistaken, the units of the Mean Squared Errors of your imputations are expressed in your variables units-squared, not in percentage. Therefore, I believe it is yours to interpret whether a Root Mean Square Error of 0.02, 0.007 or 0.017 is acceptable or not with regards to the units of your variables (as I'm ... | How to interpret OOBerror while doing data imputation with missForest | Unless I'm mistaken, the units of the Mean Squared Errors of your imputations are expressed in your variables units-squared, not in percentage. Therefore, I believe it is yours to interpret whether a | How to interpret OOBerror while doing data imputation with missForest
Unless I'm mistaken, the units of the Mean Squared Errors of your imputations are expressed in your variables units-squared, not in percentage. Therefore, I believe it is yours to interpret whether a Root Mean Square Error of 0.02, 0.007 or 0.017 is ... | How to interpret OOBerror while doing data imputation with missForest
Unless I'm mistaken, the units of the Mean Squared Errors of your imputations are expressed in your variables units-squared, not in percentage. Therefore, I believe it is yours to interpret whether a |
50,380 | When is logistic regression Bayes-optimal? | The key question lies in modelling versus knowing the true law.
Assume your data obbeys an unknown perfect law $P(y=1|x)=f(x)$. Then the Bayes optimal classifier is "classify y=1 when $f(x)>0.5$". This is true for any law and not related to anything algebraic. In practice you don't know $f$ and you can't, so that the B... | When is logistic regression Bayes-optimal? | The key question lies in modelling versus knowing the true law.
Assume your data obbeys an unknown perfect law $P(y=1|x)=f(x)$. Then the Bayes optimal classifier is "classify y=1 when $f(x)>0.5$". Thi | When is logistic regression Bayes-optimal?
The key question lies in modelling versus knowing the true law.
Assume your data obbeys an unknown perfect law $P(y=1|x)=f(x)$. Then the Bayes optimal classifier is "classify y=1 when $f(x)>0.5$". This is true for any law and not related to anything algebraic. In practice you ... | When is logistic regression Bayes-optimal?
The key question lies in modelling versus knowing the true law.
Assume your data obbeys an unknown perfect law $P(y=1|x)=f(x)$. Then the Bayes optimal classifier is "classify y=1 when $f(x)>0.5$". Thi |
50,381 | When is logistic regression Bayes-optimal? | I think one could construct an example when the logistic regression is asymptotically Bayes-optimal (i.e., it minimises the expected 0/1 loss).
One way to do this would be to consider a domain with two balanced (i.e., with equal marginal probabilities) normally distributed classes with the same covariance matrix. In th... | When is logistic regression Bayes-optimal? | I think one could construct an example when the logistic regression is asymptotically Bayes-optimal (i.e., it minimises the expected 0/1 loss).
One way to do this would be to consider a domain with tw | When is logistic regression Bayes-optimal?
I think one could construct an example when the logistic regression is asymptotically Bayes-optimal (i.e., it minimises the expected 0/1 loss).
One way to do this would be to consider a domain with two balanced (i.e., with equal marginal probabilities) normally distributed cla... | When is logistic regression Bayes-optimal?
I think one could construct an example when the logistic regression is asymptotically Bayes-optimal (i.e., it minimises the expected 0/1 loss).
One way to do this would be to consider a domain with tw |
50,382 | Convert predicted probabilities after downsampling to actual probabilities in classification | The two formulas are equivalent (the first is rather more elegant, IMO).
Let $\alpha$ denote the "original fraction" from the second link, the fraction of the positive class in the population, and let $\alpha'$ denote the (re/over/under)sampled fraction. Keeping $p_s$ as the model's output "probability" score and $p$ ... | Convert predicted probabilities after downsampling to actual probabilities in classification | The two formulas are equivalent (the first is rather more elegant, IMO).
Let $\alpha$ denote the "original fraction" from the second link, the fraction of the positive class in the population, and let | Convert predicted probabilities after downsampling to actual probabilities in classification
The two formulas are equivalent (the first is rather more elegant, IMO).
Let $\alpha$ denote the "original fraction" from the second link, the fraction of the positive class in the population, and let $\alpha'$ denote the (re/o... | Convert predicted probabilities after downsampling to actual probabilities in classification
The two formulas are equivalent (the first is rather more elegant, IMO).
Let $\alpha$ denote the "original fraction" from the second link, the fraction of the positive class in the population, and let |
50,383 | how to handle missing data in clustering problem | If you exclude features with missing values, you might bias your conclusions or lose information.
Consider a dataset with 10 patients and their cholesterol values. You are interested in predicting cholesterol values based on these features. You might have one feature, age at beginning of study, and one feature # ch... | how to handle missing data in clustering problem | If you exclude features with missing values, you might bias your conclusions or lose information.
Consider a dataset with 10 patients and their cholesterol values. You are interested in predicting | how to handle missing data in clustering problem
If you exclude features with missing values, you might bias your conclusions or lose information.
Consider a dataset with 10 patients and their cholesterol values. You are interested in predicting cholesterol values based on these features. You might have one feature... | how to handle missing data in clustering problem
If you exclude features with missing values, you might bias your conclusions or lose information.
Consider a dataset with 10 patients and their cholesterol values. You are interested in predicting |
50,384 | Machine learning models that combine sequences and static features? | Just a suggestion, if your classifying a sequence with an RNN you could add a final fully-connected layer that combines the output of the RNN with your static features (by concatenation) before going to the softmax and outputting the predicted class probabilities. Since this final layer is fully-connect with its own se... | Machine learning models that combine sequences and static features? | Just a suggestion, if your classifying a sequence with an RNN you could add a final fully-connected layer that combines the output of the RNN with your static features (by concatenation) before going | Machine learning models that combine sequences and static features?
Just a suggestion, if your classifying a sequence with an RNN you could add a final fully-connected layer that combines the output of the RNN with your static features (by concatenation) before going to the softmax and outputting the predicted class pr... | Machine learning models that combine sequences and static features?
Just a suggestion, if your classifying a sequence with an RNN you could add a final fully-connected layer that combines the output of the RNN with your static features (by concatenation) before going |
50,385 | correlation between independent variables in linear multiple regression | I apologize in advance for the really long answer, I just don't want to assume any level of familiarity with linear regression. Also, the answer touches on 2-3 different topics, so I wanted to cover all bases.
The answer to your question has to do with what are $B1$ and $B2$. Linear regression is trying to find the un... | correlation between independent variables in linear multiple regression | I apologize in advance for the really long answer, I just don't want to assume any level of familiarity with linear regression. Also, the answer touches on 2-3 different topics, so I wanted to cover a | correlation between independent variables in linear multiple regression
I apologize in advance for the really long answer, I just don't want to assume any level of familiarity with linear regression. Also, the answer touches on 2-3 different topics, so I wanted to cover all bases.
The answer to your question has to do... | correlation between independent variables in linear multiple regression
I apologize in advance for the really long answer, I just don't want to assume any level of familiarity with linear regression. Also, the answer touches on 2-3 different topics, so I wanted to cover a |
50,386 | correlation between independent variables in linear multiple regression | If you are asking which one is the main driver then it will be TV because spending on TV will result in statistically increased sales and online ad due to being close to zero represents that it has no effect on sales but I can't say that for sure because you haven't mentioned the p-value of online ad budget as it will ... | correlation between independent variables in linear multiple regression | If you are asking which one is the main driver then it will be TV because spending on TV will result in statistically increased sales and online ad due to being close to zero represents that it has no | correlation between independent variables in linear multiple regression
If you are asking which one is the main driver then it will be TV because spending on TV will result in statistically increased sales and online ad due to being close to zero represents that it has no effect on sales but I can't say that for sure b... | correlation between independent variables in linear multiple regression
If you are asking which one is the main driver then it will be TV because spending on TV will result in statistically increased sales and online ad due to being close to zero represents that it has no |
50,387 | correlation between independent variables in linear multiple regression | I think a simple example may help. Assume $sale = TV$ (yes, exactly) and
$online = sale + \epsilon$, where $\epsilon \sim \mathcal{N}(0, 0.001)$ is some noise with small amplitude. If your regress $sale$ against $TV$ and $online$, the minimizer will always give all weight to $TV$ (because this gives an exact fit). If y... | correlation between independent variables in linear multiple regression | I think a simple example may help. Assume $sale = TV$ (yes, exactly) and
$online = sale + \epsilon$, where $\epsilon \sim \mathcal{N}(0, 0.001)$ is some noise with small amplitude. If your regress $sa | correlation between independent variables in linear multiple regression
I think a simple example may help. Assume $sale = TV$ (yes, exactly) and
$online = sale + \epsilon$, where $\epsilon \sim \mathcal{N}(0, 0.001)$ is some noise with small amplitude. If your regress $sale$ against $TV$ and $online$, the minimizer wil... | correlation between independent variables in linear multiple regression
I think a simple example may help. Assume $sale = TV$ (yes, exactly) and
$online = sale + \epsilon$, where $\epsilon \sim \mathcal{N}(0, 0.001)$ is some noise with small amplitude. If your regress $sa |
50,388 | Reported Coefficients for Glmnet using Caret | Caret will fit the final model using glmnet again, so it reports the coefficients in the same way as glmnet, which is in the scale of the original data:
library(mlbench)
library(caret)
library(glmnet)
data(BostonHousing)
mymodel = train(medv ~ .,data=BostonHousing,
method="glmnet",tuneLength=5,family="gaussian",
trCon... | Reported Coefficients for Glmnet using Caret | Caret will fit the final model using glmnet again, so it reports the coefficients in the same way as glmnet, which is in the scale of the original data:
library(mlbench)
library(caret)
library(glmnet) | Reported Coefficients for Glmnet using Caret
Caret will fit the final model using glmnet again, so it reports the coefficients in the same way as glmnet, which is in the scale of the original data:
library(mlbench)
library(caret)
library(glmnet)
data(BostonHousing)
mymodel = train(medv ~ .,data=BostonHousing,
method="... | Reported Coefficients for Glmnet using Caret
Caret will fit the final model using glmnet again, so it reports the coefficients in the same way as glmnet, which is in the scale of the original data:
library(mlbench)
library(caret)
library(glmnet) |
50,389 | Decompose a time series data into deterministic trend and stochastic trend | Before I receive your data I would like to take the "bully pulpit" and expound on the task at hand and how I would go about solving this riddle. Your suggested approach I believe is to form an ARIMA model using procedures which implicitly specify no time trend variables thus incorrectly concluding about required differ... | Decompose a time series data into deterministic trend and stochastic trend | Before I receive your data I would like to take the "bully pulpit" and expound on the task at hand and how I would go about solving this riddle. Your suggested approach I believe is to form an ARIMA m | Decompose a time series data into deterministic trend and stochastic trend
Before I receive your data I would like to take the "bully pulpit" and expound on the task at hand and how I would go about solving this riddle. Your suggested approach I believe is to form an ARIMA model using procedures which implicitly specif... | Decompose a time series data into deterministic trend and stochastic trend
Before I receive your data I would like to take the "bully pulpit" and expound on the task at hand and how I would go about solving this riddle. Your suggested approach I believe is to form an ARIMA m |
50,390 | predicting tree structure | I know its too late to answer, but still find below:
I think you are looking for Natural language to SQL statement kind of problem statement, there are few solutions developed in last few months listed below:
SEQ2SEQ method for SEQ2SQL
SQLNET https://arxiv.org/pdf/1711.04436.pdf
few more: https://github.com/sriniiy... | predicting tree structure | I know its too late to answer, but still find below:
I think you are looking for Natural language to SQL statement kind of problem statement, there are few solutions developed in last few months liste | predicting tree structure
I know its too late to answer, but still find below:
I think you are looking for Natural language to SQL statement kind of problem statement, there are few solutions developed in last few months listed below:
SEQ2SEQ method for SEQ2SQL
SQLNET https://arxiv.org/pdf/1711.04436.pdf
few more: ... | predicting tree structure
I know its too late to answer, but still find below:
I think you are looking for Natural language to SQL statement kind of problem statement, there are few solutions developed in last few months liste |
50,391 | Bias-variance: is it really a "trade-off"? | I share your skepticism that there is a tradeoff. A typical way to think about the bias-variance decomposition of MSE, such as in regularized regression, is that we accept a bit of bias in our estimator in exchange for a large reduction in variance. However, we do this to achieve lower MSE, not to maintain the MSE. Thu... | Bias-variance: is it really a "trade-off"? | I share your skepticism that there is a tradeoff. A typical way to think about the bias-variance decomposition of MSE, such as in regularized regression, is that we accept a bit of bias in our estimat | Bias-variance: is it really a "trade-off"?
I share your skepticism that there is a tradeoff. A typical way to think about the bias-variance decomposition of MSE, such as in regularized regression, is that we accept a bit of bias in our estimator in exchange for a large reduction in variance. However, we do this to achi... | Bias-variance: is it really a "trade-off"?
I share your skepticism that there is a tradeoff. A typical way to think about the bias-variance decomposition of MSE, such as in regularized regression, is that we accept a bit of bias in our estimat |
50,392 | Unsure if this derivation for covariance function is valid? | You are correct.
The computation boils down to figuring out the experession of:
$$f(s,t) = \mathbb{E}\left[\left(\int_0^t e^{au}dW_u\right) \left(\int_0^s e^{av}dW_v\right) \right]$$
We can suppose $s \leq t$ without any loss of generality.
Developing, then using the fact that the brownian motion has independent increm... | Unsure if this derivation for covariance function is valid? | You are correct.
The computation boils down to figuring out the experession of:
$$f(s,t) = \mathbb{E}\left[\left(\int_0^t e^{au}dW_u\right) \left(\int_0^s e^{av}dW_v\right) \right]$$
We can suppose $s | Unsure if this derivation for covariance function is valid?
You are correct.
The computation boils down to figuring out the experession of:
$$f(s,t) = \mathbb{E}\left[\left(\int_0^t e^{au}dW_u\right) \left(\int_0^s e^{av}dW_v\right) \right]$$
We can suppose $s \leq t$ without any loss of generality.
Developing, then us... | Unsure if this derivation for covariance function is valid?
You are correct.
The computation boils down to figuring out the experession of:
$$f(s,t) = \mathbb{E}\left[\left(\int_0^t e^{au}dW_u\right) \left(\int_0^s e^{av}dW_v\right) \right]$$
We can suppose $s |
50,393 | How can eigenfaces (PCA eigenvectors on face image data) be displayed as images? | PCA does dimensional reduction by expressing $D$ dimensional vectors on an $M$ dimensional subspace, with $M<D.$ The vector itself can be written as a linear combination of $M$ eigenvectors, where the eigenvector is itself a unit vector that lives in the $D$ dimensional space.
Consider, for example, a two dimensional s... | How can eigenfaces (PCA eigenvectors on face image data) be displayed as images? | PCA does dimensional reduction by expressing $D$ dimensional vectors on an $M$ dimensional subspace, with $M<D.$ The vector itself can be written as a linear combination of $M$ eigenvectors, where the | How can eigenfaces (PCA eigenvectors on face image data) be displayed as images?
PCA does dimensional reduction by expressing $D$ dimensional vectors on an $M$ dimensional subspace, with $M<D.$ The vector itself can be written as a linear combination of $M$ eigenvectors, where the eigenvector is itself a unit vector th... | How can eigenfaces (PCA eigenvectors on face image data) be displayed as images?
PCA does dimensional reduction by expressing $D$ dimensional vectors on an $M$ dimensional subspace, with $M<D.$ The vector itself can be written as a linear combination of $M$ eigenvectors, where the |
50,394 | Tails of products of random variables | A counter-example:
Let X be the distribution with 99% of its probability mass at 100, and the rest of its probability mass at 0. Let t be 99.5.
In cases where the realized value of X is 0, multiplication by Y will never result in a product above 99.5. (This is essentially true even if 1% of the probability mass conce... | Tails of products of random variables | A counter-example:
Let X be the distribution with 99% of its probability mass at 100, and the rest of its probability mass at 0. Let t be 99.5.
In cases where the realized value of X is 0, multiplica | Tails of products of random variables
A counter-example:
Let X be the distribution with 99% of its probability mass at 100, and the rest of its probability mass at 0. Let t be 99.5.
In cases where the realized value of X is 0, multiplication by Y will never result in a product above 99.5. (This is essentially true ev... | Tails of products of random variables
A counter-example:
Let X be the distribution with 99% of its probability mass at 100, and the rest of its probability mass at 0. Let t be 99.5.
In cases where the realized value of X is 0, multiplica |
50,395 | Tails of products of random variables | This property doesn't hold true for all non-negative distributions of $X$.
Consider the case $X \sim \text{Bernouli}(p)$, for some $0<p<1 \implies E(X)=p$
and $Y \sim \chi^2(1)$
For $t\ \text{such that, }\ p<t<1$, $P(X>t) = P(X=1) =p$
$P(X.Y>t) = P(Y>t/X=1)*P(X=1) = P(Y>t)*p<p$
$\implies P(X>t) > P(X.Y>t)\\$
#
Update... | Tails of products of random variables | This property doesn't hold true for all non-negative distributions of $X$.
Consider the case $X \sim \text{Bernouli}(p)$, for some $0<p<1 \implies E(X)=p$
and $Y \sim \chi^2(1)$
For $t\ \text{such t | Tails of products of random variables
This property doesn't hold true for all non-negative distributions of $X$.
Consider the case $X \sim \text{Bernouli}(p)$, for some $0<p<1 \implies E(X)=p$
and $Y \sim \chi^2(1)$
For $t\ \text{such that, }\ p<t<1$, $P(X>t) = P(X=1) =p$
$P(X.Y>t) = P(Y>t/X=1)*P(X=1) = P(Y>t)*p<p$
$... | Tails of products of random variables
This property doesn't hold true for all non-negative distributions of $X$.
Consider the case $X \sim \text{Bernouli}(p)$, for some $0<p<1 \implies E(X)=p$
and $Y \sim \chi^2(1)$
For $t\ \text{such t |
50,396 | Tails of products of random variables | I see the intuition behind your question, but I'm not sure this holds for the general case.
First, you can re-write your original inequality as:
$$
\Pr(X < t) > \Pr(X\cdot Y < t)
$$
This is equal to:
$$ F_X(t) > F_{X\cdot Y}(t) $$
Which is:
$$ \int_{0}^{t} f_X(i)di > \int_{0}^{t} f_X(i)g_Y(i)di $$
where $f_X(i)$ is the... | Tails of products of random variables | I see the intuition behind your question, but I'm not sure this holds for the general case.
First, you can re-write your original inequality as:
$$
\Pr(X < t) > \Pr(X\cdot Y < t)
$$
This is equal to:
| Tails of products of random variables
I see the intuition behind your question, but I'm not sure this holds for the general case.
First, you can re-write your original inequality as:
$$
\Pr(X < t) > \Pr(X\cdot Y < t)
$$
This is equal to:
$$ F_X(t) > F_{X\cdot Y}(t) $$
Which is:
$$ \int_{0}^{t} f_X(i)di > \int_{0}^{t} f... | Tails of products of random variables
I see the intuition behind your question, but I'm not sure this holds for the general case.
First, you can re-write your original inequality as:
$$
\Pr(X < t) > \Pr(X\cdot Y < t)
$$
This is equal to:
|
50,397 | Confused about order in probability | If we think of seating the people in 4 seats and insist that the first seat be occupied by a Mexican, the second by an Asian, the third by an African American and the fourth by a Caucasian, then the chance of this is: 5/12 x 2/11 x 3/10 x 2/9. In the problem you have set we don't care which person sits in which seat so... | Confused about order in probability | If we think of seating the people in 4 seats and insist that the first seat be occupied by a Mexican, the second by an Asian, the third by an African American and the fourth by a Caucasian, then the c | Confused about order in probability
If we think of seating the people in 4 seats and insist that the first seat be occupied by a Mexican, the second by an Asian, the third by an African American and the fourth by a Caucasian, then the chance of this is: 5/12 x 2/11 x 3/10 x 2/9. In the problem you have set we don't car... | Confused about order in probability
If we think of seating the people in 4 seats and insist that the first seat be occupied by a Mexican, the second by an Asian, the third by an African American and the fourth by a Caucasian, then the c |
50,398 | Confused about order in probability | There are $\binom{12}{5}$ possible committees.
Committees of $5$ that include at least one member from each group necessarily have just one group having two members on the committee, all other groups have just one. So, the number of such committees is
$$\binom{5}{2}\cdot 2\cdot 3\cdot 2 + 5\cdot \binom{2}{2}\cdot 3\cdo... | Confused about order in probability | There are $\binom{12}{5}$ possible committees.
Committees of $5$ that include at least one member from each group necessarily have just one group having two members on the committee, all other groups | Confused about order in probability
There are $\binom{12}{5}$ possible committees.
Committees of $5$ that include at least one member from each group necessarily have just one group having two members on the committee, all other groups have just one. So, the number of such committees is
$$\binom{5}{2}\cdot 2\cdot 3\cdo... | Confused about order in probability
There are $\binom{12}{5}$ possible committees.
Committees of $5$ that include at least one member from each group necessarily have just one group having two members on the committee, all other groups |
50,399 | Confused about order in probability | The numerator is the number of ways to choose $4$ people from $12$ people such that exactly one person is chosen from each ethnic group. The numerator is thus ${5 \choose 1} {2 \choose 1}{3 \choose 2}{2 \choose 2}$. The denominator is clearly ${12 \choose 4}$.
Alternatively, you could assume that the subcommittee ... | Confused about order in probability | The numerator is the number of ways to choose $4$ people from $12$ people such that exactly one person is chosen from each ethnic group. The numerator is thus ${5 \choose 1} {2 \choose 1}{3 \choose 2 | Confused about order in probability
The numerator is the number of ways to choose $4$ people from $12$ people such that exactly one person is chosen from each ethnic group. The numerator is thus ${5 \choose 1} {2 \choose 1}{3 \choose 2}{2 \choose 2}$. The denominator is clearly ${12 \choose 4}$.
Alternatively, you ... | Confused about order in probability
The numerator is the number of ways to choose $4$ people from $12$ people such that exactly one person is chosen from each ethnic group. The numerator is thus ${5 \choose 1} {2 \choose 1}{3 \choose 2 |
50,400 | Can you perform a multiple imputation on data that is missing not at random (MNAR)? | Is there a way to identify if your data is MNAR, MAR, or MCAR?
There is Little's MCAR test, which can evaluate if your missings are MCAR. More informations can be found here on page 12. As far as I know there is no test available, which differentiates between MAR and MNAR. In practice I would say that many people just... | Can you perform a multiple imputation on data that is missing not at random (MNAR)? | Is there a way to identify if your data is MNAR, MAR, or MCAR?
There is Little's MCAR test, which can evaluate if your missings are MCAR. More informations can be found here on page 12. As far as I k | Can you perform a multiple imputation on data that is missing not at random (MNAR)?
Is there a way to identify if your data is MNAR, MAR, or MCAR?
There is Little's MCAR test, which can evaluate if your missings are MCAR. More informations can be found here on page 12. As far as I know there is no test available, whic... | Can you perform a multiple imputation on data that is missing not at random (MNAR)?
Is there a way to identify if your data is MNAR, MAR, or MCAR?
There is Little's MCAR test, which can evaluate if your missings are MCAR. More informations can be found here on page 12. As far as I k |
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