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 |
|---|---|---|---|---|---|---|
41,301 | Big-O Scaling of R's cmdscale() | You should be able to test this on your system via Monte Carlo. For example:
try.cmdscale <- function(n) {
x <- matrix(rnorm(n*n) ** 2,nrow=n,ncol=n);
took.time <- system.time(cmdscale(x))
}
#repeat multiple times and take the median of the user.self + sys.self
#probably a better way to do timing?
multi.cmdsca... | Big-O Scaling of R's cmdscale() | You should be able to test this on your system via Monte Carlo. For example:
try.cmdscale <- function(n) {
x <- matrix(rnorm(n*n) ** 2,nrow=n,ncol=n);
took.time <- system.time(cmdscale(x))
}
| Big-O Scaling of R's cmdscale()
You should be able to test this on your system via Monte Carlo. For example:
try.cmdscale <- function(n) {
x <- matrix(rnorm(n*n) ** 2,nrow=n,ncol=n);
took.time <- system.time(cmdscale(x))
}
#repeat multiple times and take the median of the user.self + sys.self
#probably a bette... | Big-O Scaling of R's cmdscale()
You should be able to test this on your system via Monte Carlo. For example:
try.cmdscale <- function(n) {
x <- matrix(rnorm(n*n) ** 2,nrow=n,ncol=n);
took.time <- system.time(cmdscale(x))
}
|
41,302 | Big-O Scaling of R's cmdscale() | Ironically, the MDS actually wasn't my problem. The preprocessing I was doing was the issue. I'm used to coding in lower-level languages and forgot how slow looping is in R. I rewrote the preprocessing code using vector ops and the MDS actually only takes a few seconds. | Big-O Scaling of R's cmdscale() | Ironically, the MDS actually wasn't my problem. The preprocessing I was doing was the issue. I'm used to coding in lower-level languages and forgot how slow looping is in R. I rewrote the preproces | Big-O Scaling of R's cmdscale()
Ironically, the MDS actually wasn't my problem. The preprocessing I was doing was the issue. I'm used to coding in lower-level languages and forgot how slow looping is in R. I rewrote the preprocessing code using vector ops and the MDS actually only takes a few seconds. | Big-O Scaling of R's cmdscale()
Ironically, the MDS actually wasn't my problem. The preprocessing I was doing was the issue. I'm used to coding in lower-level languages and forgot how slow looping is in R. I rewrote the preproces |
41,303 | Maximum likelihood estimation of dlmModReg | I think your setup is not correct. Try this:
set.seed(1234)
r <- rnorm(100)
X <- r
u <- -1*X + 0.5*rnorm(100)
MyModel <- function(x) dlmModReg(X, FALSE, dV = x[1]^2)
fit <- dlmMLE(u, parm = c(0.3), build = MyModel)
mod <- MyModel(fit$par)
dlmFilter(u,mod)$a
You recover the estimate of the observation variance from th... | Maximum likelihood estimation of dlmModReg | I think your setup is not correct. Try this:
set.seed(1234)
r <- rnorm(100)
X <- r
u <- -1*X + 0.5*rnorm(100)
MyModel <- function(x) dlmModReg(X, FALSE, dV = x[1]^2)
fit <- dlmMLE(u, parm = c(0.3), b | Maximum likelihood estimation of dlmModReg
I think your setup is not correct. Try this:
set.seed(1234)
r <- rnorm(100)
X <- r
u <- -1*X + 0.5*rnorm(100)
MyModel <- function(x) dlmModReg(X, FALSE, dV = x[1]^2)
fit <- dlmMLE(u, parm = c(0.3), build = MyModel)
mod <- MyModel(fit$par)
dlmFilter(u,mod)$a
You recover the e... | Maximum likelihood estimation of dlmModReg
I think your setup is not correct. Try this:
set.seed(1234)
r <- rnorm(100)
X <- r
u <- -1*X + 0.5*rnorm(100)
MyModel <- function(x) dlmModReg(X, FALSE, dV = x[1]^2)
fit <- dlmMLE(u, parm = c(0.3), b |
41,304 | Maximum likelihood estimation of dlmModReg | Below is code which implements my solution and Paramonov's solution (a slight edit: I have changed dlmFilter(u,mod)$a in the orginally posted answer by
dlmFilter(u,mod)$m).
library(dlm)
set.seed(1234)
reps <- 100
MyEstimates <- YourEstimates <- matrix(0,reps,2)
for (i in (1:reps) ) {
X <- r <- rnorm(100)
u <- -1*... | Maximum likelihood estimation of dlmModReg | Below is code which implements my solution and Paramonov's solution (a slight edit: I have changed dlmFilter(u,mod)$a in the orginally posted answer by
dlmFilter(u,mod)$m).
library(dlm)
set.seed(1234 | Maximum likelihood estimation of dlmModReg
Below is code which implements my solution and Paramonov's solution (a slight edit: I have changed dlmFilter(u,mod)$a in the orginally posted answer by
dlmFilter(u,mod)$m).
library(dlm)
set.seed(1234)
reps <- 100
MyEstimates <- YourEstimates <- matrix(0,reps,2)
for (i in... | Maximum likelihood estimation of dlmModReg
Below is code which implements my solution and Paramonov's solution (a slight edit: I have changed dlmFilter(u,mod)$a in the orginally posted answer by
dlmFilter(u,mod)$m).
library(dlm)
set.seed(1234 |
41,305 | Maximum likelihood estimation of dlmModReg | After reading help for dlmFilter, I could come up with the following code:
r <- rnorm(100)
u <- -1*r + 0.5*rnorm(100)
fit <- dlmMLE(u, parm = c(1, sd(u)),
build = function(x)
dlmModReg(r, FALSE, dV = x[2]^2,
m0 = x[1], C0 = matrix(0)))
fit$par
[1] -1.1330088 0.4... | Maximum likelihood estimation of dlmModReg | After reading help for dlmFilter, I could come up with the following code:
r <- rnorm(100)
u <- -1*r + 0.5*rnorm(100)
fit <- dlmMLE(u, parm = c(1, sd(u)),
build = function(x)
| Maximum likelihood estimation of dlmModReg
After reading help for dlmFilter, I could come up with the following code:
r <- rnorm(100)
u <- -1*r + 0.5*rnorm(100)
fit <- dlmMLE(u, parm = c(1, sd(u)),
build = function(x)
dlmModReg(r, FALSE, dV = x[2]^2,
m0 = x[1], C0... | Maximum likelihood estimation of dlmModReg
After reading help for dlmFilter, I could come up with the following code:
r <- rnorm(100)
u <- -1*r + 0.5*rnorm(100)
fit <- dlmMLE(u, parm = c(1, sd(u)),
build = function(x)
|
41,306 | Naive Bayes classification for "That's what she said" problem | You are not using Naive Bayes, you are actually using something I'd call "Multiplicative Decision Stump"-Classifer ;). You can do that, but I'd recommend in this case to calculate the micro or macro-average across all words in the sentence (instead of multiplying them). E.g. macro-average:
$p(Positive|sentence)=\frac{... | Naive Bayes classification for "That's what she said" problem | You are not using Naive Bayes, you are actually using something I'd call "Multiplicative Decision Stump"-Classifer ;). You can do that, but I'd recommend in this case to calculate the micro or macro-a | Naive Bayes classification for "That's what she said" problem
You are not using Naive Bayes, you are actually using something I'd call "Multiplicative Decision Stump"-Classifer ;). You can do that, but I'd recommend in this case to calculate the micro or macro-average across all words in the sentence (instead of multip... | Naive Bayes classification for "That's what she said" problem
You are not using Naive Bayes, you are actually using something I'd call "Multiplicative Decision Stump"-Classifer ;). You can do that, but I'd recommend in this case to calculate the micro or macro-a |
41,307 | Naive Bayes classification for "That's what she said" problem | Here is a Web site that uses a classifier to determine the gender of an author of text:
http://bookblog.net/gender/genie.php
There are a number of articles on the subject at the Web site and the composer of the
site has written a number of articles on the subject as well. There are a number of
good methods that... | Naive Bayes classification for "That's what she said" problem | Here is a Web site that uses a classifier to determine the gender of an author of text:
http://bookblog.net/gender/genie.php
There are a number of articles on the subject at the Web site and t | Naive Bayes classification for "That's what she said" problem
Here is a Web site that uses a classifier to determine the gender of an author of text:
http://bookblog.net/gender/genie.php
There are a number of articles on the subject at the Web site and the composer of the
site has written a number of articles o... | Naive Bayes classification for "That's what she said" problem
Here is a Web site that uses a classifier to determine the gender of an author of text:
http://bookblog.net/gender/genie.php
There are a number of articles on the subject at the Web site and t |
41,308 | Naive Bayes classification for "That's what she said" problem | An interesting source of suggestions for this problem might be the That's What She Said Quora thread. Specifically, the first comment identifies that it might make sense to use Twitter streams as a source of statements to which there has been a response of "That's What She Said". Another thing you could do would be to ... | Naive Bayes classification for "That's what she said" problem | An interesting source of suggestions for this problem might be the That's What She Said Quora thread. Specifically, the first comment identifies that it might make sense to use Twitter streams as a so | Naive Bayes classification for "That's what she said" problem
An interesting source of suggestions for this problem might be the That's What She Said Quora thread. Specifically, the first comment identifies that it might make sense to use Twitter streams as a source of statements to which there has been a response of "... | Naive Bayes classification for "That's what she said" problem
An interesting source of suggestions for this problem might be the That's What She Said Quora thread. Specifically, the first comment identifies that it might make sense to use Twitter streams as a so |
41,309 | Hot topics in mathematical statistics [closed] | Persi Diaconis wrote an article on "Mathematical Statistics" in the Princeton Companion of Mathematics. He discusses several ongoing research areas in mathematical statistics, including the search for high-dimensional admissible estimators (Stein's paradox). | Hot topics in mathematical statistics [closed] | Persi Diaconis wrote an article on "Mathematical Statistics" in the Princeton Companion of Mathematics. He discusses several ongoing research areas in mathematical statistics, including the search fo | Hot topics in mathematical statistics [closed]
Persi Diaconis wrote an article on "Mathematical Statistics" in the Princeton Companion of Mathematics. He discusses several ongoing research areas in mathematical statistics, including the search for high-dimensional admissible estimators (Stein's paradox). | Hot topics in mathematical statistics [closed]
Persi Diaconis wrote an article on "Mathematical Statistics" in the Princeton Companion of Mathematics. He discusses several ongoing research areas in mathematical statistics, including the search fo |
41,310 | Hot topics in mathematical statistics [closed] | Hopefully, modelling the dynamics of tumor progression qualifies for this:
Anderson & Quaranta. Integrative mathematical oncology. Nature Reviews Cancer, 2008. | Hot topics in mathematical statistics [closed] | Hopefully, modelling the dynamics of tumor progression qualifies for this:
Anderson & Quaranta. Integrative mathematical oncology. Nature Reviews Cancer, 2008. | Hot topics in mathematical statistics [closed]
Hopefully, modelling the dynamics of tumor progression qualifies for this:
Anderson & Quaranta. Integrative mathematical oncology. Nature Reviews Cancer, 2008. | Hot topics in mathematical statistics [closed]
Hopefully, modelling the dynamics of tumor progression qualifies for this:
Anderson & Quaranta. Integrative mathematical oncology. Nature Reviews Cancer, 2008. |
41,311 | Multiple regression with no origin and mix of directly entered and stepwise entered variables using R | I think you can set up your base model, that is the one with your 12 IVs and then use add1() with the remaining predictors. So, say you have a model mod1 defined like mod1 <- lm(y ~ 0+x1+x2+x3) (0+ means no intercept), then
add1(mod1, ~ .+x4+x5+x6, test="F")
will add and test one predictor after the other on top of th... | Multiple regression with no origin and mix of directly entered and stepwise entered variables using | I think you can set up your base model, that is the one with your 12 IVs and then use add1() with the remaining predictors. So, say you have a model mod1 defined like mod1 <- lm(y ~ 0+x1+x2+x3) (0+ me | Multiple regression with no origin and mix of directly entered and stepwise entered variables using R
I think you can set up your base model, that is the one with your 12 IVs and then use add1() with the remaining predictors. So, say you have a model mod1 defined like mod1 <- lm(y ~ 0+x1+x2+x3) (0+ means no intercept),... | Multiple regression with no origin and mix of directly entered and stepwise entered variables using
I think you can set up your base model, that is the one with your 12 IVs and then use add1() with the remaining predictors. So, say you have a model mod1 defined like mod1 <- lm(y ~ 0+x1+x2+x3) (0+ me |
41,312 | Learning from unordered tuples? | For regression models, one way would be to generate derived variables that are invariant to permutation of the labelling of the $x_i$s.
E.g. in your three-variable example, considering only polynomials of total order up to 3, such combinations would be:
$w_1 = x_1 + x_2 + x_3$
$w_2 = x_1x_2 + x_1x_3 + x_2x_3$
$w_3 = x... | Learning from unordered tuples? | For regression models, one way would be to generate derived variables that are invariant to permutation of the labelling of the $x_i$s.
E.g. in your three-variable example, considering only polynomial | Learning from unordered tuples?
For regression models, one way would be to generate derived variables that are invariant to permutation of the labelling of the $x_i$s.
E.g. in your three-variable example, considering only polynomials of total order up to 3, such combinations would be:
$w_1 = x_1 + x_2 + x_3$
$w_2 = x_... | Learning from unordered tuples?
For regression models, one way would be to generate derived variables that are invariant to permutation of the labelling of the $x_i$s.
E.g. in your three-variable example, considering only polynomial |
41,313 | Learning from unordered tuples? | To add to onestop's response, it was confirmed on math.SE that the polynomials
$$w_1 = x_1 + \cdots + x_n$$
$$w_2 = x_1^2 + \cdots + x_n^2$$
$$\cdots$$
$$w_n = x_1^n + \cdots + x_n ^n$$
give you all the information needed to determine the original $X=(x_1, \cdots, x_n)$.
This is a neat result because it also applies to... | Learning from unordered tuples? | To add to onestop's response, it was confirmed on math.SE that the polynomials
$$w_1 = x_1 + \cdots + x_n$$
$$w_2 = x_1^2 + \cdots + x_n^2$$
$$\cdots$$
$$w_n = x_1^n + \cdots + x_n ^n$$
give you all t | Learning from unordered tuples?
To add to onestop's response, it was confirmed on math.SE that the polynomials
$$w_1 = x_1 + \cdots + x_n$$
$$w_2 = x_1^2 + \cdots + x_n^2$$
$$\cdots$$
$$w_n = x_1^n + \cdots + x_n ^n$$
give you all the information needed to determine the original $X=(x_1, \cdots, x_n)$.
This is a neat r... | Learning from unordered tuples?
To add to onestop's response, it was confirmed on math.SE that the polynomials
$$w_1 = x_1 + \cdots + x_n$$
$$w_2 = x_1^2 + \cdots + x_n^2$$
$$\cdots$$
$$w_n = x_1^n + \cdots + x_n ^n$$
give you all t |
41,314 | Learning from unordered tuples? | Deep Sets and PointNet provide two (fairly recent) examples of permutation-invariant deep learning architectures. Both these methods provided state-of-the-art results at their time of introduction and are continuous (in senses described in their papers) with respect to perturbations of the underlying sets.
The permutat... | Learning from unordered tuples? | Deep Sets and PointNet provide two (fairly recent) examples of permutation-invariant deep learning architectures. Both these methods provided state-of-the-art results at their time of introduction and | Learning from unordered tuples?
Deep Sets and PointNet provide two (fairly recent) examples of permutation-invariant deep learning architectures. Both these methods provided state-of-the-art results at their time of introduction and are continuous (in senses described in their papers) with respect to perturbations of t... | Learning from unordered tuples?
Deep Sets and PointNet provide two (fairly recent) examples of permutation-invariant deep learning architectures. Both these methods provided state-of-the-art results at their time of introduction and |
41,315 | What are the major machine learning theories that maybe used by Twitter for suggesting followers? | Three different approaches come to my mind
decisions based solely on the following / follower lists. If a lot of people you are following, follow a particular person, the chance is high you might be interested in this persons tweet.
using links and hashtags. Assuming you link very often to specific websites or use spe... | What are the major machine learning theories that maybe used by Twitter for suggesting followers? | Three different approaches come to my mind
decisions based solely on the following / follower lists. If a lot of people you are following, follow a particular person, the chance is high you might be | What are the major machine learning theories that maybe used by Twitter for suggesting followers?
Three different approaches come to my mind
decisions based solely on the following / follower lists. If a lot of people you are following, follow a particular person, the chance is high you might be interested in this per... | What are the major machine learning theories that maybe used by Twitter for suggesting followers?
Three different approaches come to my mind
decisions based solely on the following / follower lists. If a lot of people you are following, follow a particular person, the chance is high you might be |
41,316 | Choice of weight function in Moran's I | Moran's I statistic is used to explore a specific type of spatial clustering: whether high values are located in proximity to other high values and whether low values are located in proximity to other low values.
The trick then is 1st to get a sense of what you mean by proximity and 2nd formulating this mathematically.... | Choice of weight function in Moran's I | Moran's I statistic is used to explore a specific type of spatial clustering: whether high values are located in proximity to other high values and whether low values are located in proximity to other | Choice of weight function in Moran's I
Moran's I statistic is used to explore a specific type of spatial clustering: whether high values are located in proximity to other high values and whether low values are located in proximity to other low values.
The trick then is 1st to get a sense of what you mean by proximity a... | Choice of weight function in Moran's I
Moran's I statistic is used to explore a specific type of spatial clustering: whether high values are located in proximity to other high values and whether low values are located in proximity to other |
41,317 | Choice of weight function in Moran's I | Although not within the domain of geostatistics, for question #2, I would casually say the most frequent weighting function used in my field (Criminology) would be a a binary weighting scheme. Although I have rarely seen a good theoretical or empirical argument to use one weighting scheme over another (or how one defin... | Choice of weight function in Moran's I | Although not within the domain of geostatistics, for question #2, I would casually say the most frequent weighting function used in my field (Criminology) would be a a binary weighting scheme. Althoug | Choice of weight function in Moran's I
Although not within the domain of geostatistics, for question #2, I would casually say the most frequent weighting function used in my field (Criminology) would be a a binary weighting scheme. Although I have rarely seen a good theoretical or empirical argument to use one weightin... | Choice of weight function in Moran's I
Although not within the domain of geostatistics, for question #2, I would casually say the most frequent weighting function used in my field (Criminology) would be a a binary weighting scheme. Althoug |
41,318 | What is the closed form solution for the inverse CDF for Epanechnikov | You mean for a random variable with a single Epanechnikov kernel as PDF? Well, the PDF is $\frac{3}{4}(1-u^2)$, so the CDF is $\frac{1}{4}(2 + 3 u - u^3)$. Inverting this in Maple leads to three solutions, of which $$u = -1/2\,{\frac { \left( 1-2\,t+2\,i\sqrt {t}\sqrt {1-t} \right) ^{2/3}+1 +i\sqrt {3} \left( 1-2\,t+2... | What is the closed form solution for the inverse CDF for Epanechnikov | You mean for a random variable with a single Epanechnikov kernel as PDF? Well, the PDF is $\frac{3}{4}(1-u^2)$, so the CDF is $\frac{1}{4}(2 + 3 u - u^3)$. Inverting this in Maple leads to three solut | What is the closed form solution for the inverse CDF for Epanechnikov
You mean for a random variable with a single Epanechnikov kernel as PDF? Well, the PDF is $\frac{3}{4}(1-u^2)$, so the CDF is $\frac{1}{4}(2 + 3 u - u^3)$. Inverting this in Maple leads to three solutions, of which $$u = -1/2\,{\frac { \left( 1-2\,t... | What is the closed form solution for the inverse CDF for Epanechnikov
You mean for a random variable with a single Epanechnikov kernel as PDF? Well, the PDF is $\frac{3}{4}(1-u^2)$, so the CDF is $\frac{1}{4}(2 + 3 u - u^3)$. Inverting this in Maple leads to three solut |
41,319 | Balanced sampling for network training? | Yes, it is reasonable to select a balanced dataset, however if you do your model will probably over-predict the minority class in operation (or on the test set). This is easily overcome by using a threshold probability that is not 0.5. The best way to choose the new threshold is to optimise on a validation sample tha... | Balanced sampling for network training? | Yes, it is reasonable to select a balanced dataset, however if you do your model will probably over-predict the minority class in operation (or on the test set). This is easily overcome by using a th | Balanced sampling for network training?
Yes, it is reasonable to select a balanced dataset, however if you do your model will probably over-predict the minority class in operation (or on the test set). This is easily overcome by using a threshold probability that is not 0.5. The best way to choose the new threshold i... | Balanced sampling for network training?
Yes, it is reasonable to select a balanced dataset, however if you do your model will probably over-predict the minority class in operation (or on the test set). This is easily overcome by using a th |
41,320 | When is a deviation statistically significant? | This question gets to the heart of statistical thinking by recognizing that both (a) "every experiment is different," implying no single "cookbook" recipe will suffice to assess experimental results in all cases and (b) "significance should depend on the deviations in measurements," pointing towards the importance of p... | When is a deviation statistically significant? | This question gets to the heart of statistical thinking by recognizing that both (a) "every experiment is different," implying no single "cookbook" recipe will suffice to assess experimental results i | When is a deviation statistically significant?
This question gets to the heart of statistical thinking by recognizing that both (a) "every experiment is different," implying no single "cookbook" recipe will suffice to assess experimental results in all cases and (b) "significance should depend on the deviations in meas... | When is a deviation statistically significant?
This question gets to the heart of statistical thinking by recognizing that both (a) "every experiment is different," implying no single "cookbook" recipe will suffice to assess experimental results i |
41,321 | Gradient descent oscillating a lot. Have I chosen my step direction incorrectly? | When you say 'a absolute loss function', do you mean you're using least absolute deviations (LAD) instead of the more usual ordinary least squares (OLS)? As that wikipedia article says, although LAD is more robust to outliers than OLS it can be unstable and even have multiple solutions, so it doesn't seem that surprisi... | Gradient descent oscillating a lot. Have I chosen my step direction incorrectly? | When you say 'a absolute loss function', do you mean you're using least absolute deviations (LAD) instead of the more usual ordinary least squares (OLS)? As that wikipedia article says, although LAD i | Gradient descent oscillating a lot. Have I chosen my step direction incorrectly?
When you say 'a absolute loss function', do you mean you're using least absolute deviations (LAD) instead of the more usual ordinary least squares (OLS)? As that wikipedia article says, although LAD is more robust to outliers than OLS it c... | Gradient descent oscillating a lot. Have I chosen my step direction incorrectly?
When you say 'a absolute loss function', do you mean you're using least absolute deviations (LAD) instead of the more usual ordinary least squares (OLS)? As that wikipedia article says, although LAD i |
41,322 | Gradient descent oscillating a lot. Have I chosen my step direction incorrectly? | This is possibly a consequence of a known deficiency of steepest descent algorithms in general. Using a conjugate gradient algorithm may improve convergence. | Gradient descent oscillating a lot. Have I chosen my step direction incorrectly? | This is possibly a consequence of a known deficiency of steepest descent algorithms in general. Using a conjugate gradient algorithm may improve convergence. | Gradient descent oscillating a lot. Have I chosen my step direction incorrectly?
This is possibly a consequence of a known deficiency of steepest descent algorithms in general. Using a conjugate gradient algorithm may improve convergence. | Gradient descent oscillating a lot. Have I chosen my step direction incorrectly?
This is possibly a consequence of a known deficiency of steepest descent algorithms in general. Using a conjugate gradient algorithm may improve convergence. |
41,323 | Repositories and data analysis projects | Regarding your first question:
What strategies do people use to map studies, publications, and analyses onto repositories?
One year ago or so, I decided to have one repository for each publication, presentation or semester/class. My typical directory looks like this:
.git
.gitignore
README.org
ana
dat
doc
org
The un... | Repositories and data analysis projects | Regarding your first question:
What strategies do people use to map studies, publications, and analyses onto repositories?
One year ago or so, I decided to have one repository for each publication, | Repositories and data analysis projects
Regarding your first question:
What strategies do people use to map studies, publications, and analyses onto repositories?
One year ago or so, I decided to have one repository for each publication, presentation or semester/class. My typical directory looks like this:
.git
.git... | Repositories and data analysis projects
Regarding your first question:
What strategies do people use to map studies, publications, and analyses onto repositories?
One year ago or so, I decided to have one repository for each publication, |
41,324 | Repositories and data analysis projects | I keep a separate repository for each project, with a project being centered around a particular data set or question being addressed. The repo contains the data, code, and Sweave documents/plots that explain and express the results.
I maintain a separate repo for each discrete publication or presentation because
A si... | Repositories and data analysis projects | I keep a separate repository for each project, with a project being centered around a particular data set or question being addressed. The repo contains the data, code, and Sweave documents/plots that | Repositories and data analysis projects
I keep a separate repository for each project, with a project being centered around a particular data set or question being addressed. The repo contains the data, code, and Sweave documents/plots that explain and express the results.
I maintain a separate repo for each discrete p... | Repositories and data analysis projects
I keep a separate repository for each project, with a project being centered around a particular data set or question being addressed. The repo contains the data, code, and Sweave documents/plots that |
41,325 | Fractal alternative to correlation | I doubt you're going to find a single answer to this, given the space of fractal dimensions. Most papers (in physics, geology) looking at correlation simply stick to a Pearson correlation with fractal math reserved for identifying dimension/self-similarity, etc.
But you might be interested in the following papers w... | Fractal alternative to correlation | I doubt you're going to find a single answer to this, given the space of fractal dimensions. Most papers (in physics, geology) looking at correlation simply stick to a Pearson correlation with fracta | Fractal alternative to correlation
I doubt you're going to find a single answer to this, given the space of fractal dimensions. Most papers (in physics, geology) looking at correlation simply stick to a Pearson correlation with fractal math reserved for identifying dimension/self-similarity, etc.
But you might be in... | Fractal alternative to correlation
I doubt you're going to find a single answer to this, given the space of fractal dimensions. Most papers (in physics, geology) looking at correlation simply stick to a Pearson correlation with fracta |
41,326 | Fractal alternative to correlation | I agree with @ars that you are unlikely to get one answer for this (you may also have more success on http://mathoverflow.net, since our community tends to be more applied, while this technique would have very little real-world usage). The Abrahao/Barbosa paper is a good reference. Just to provide some additional sou... | Fractal alternative to correlation | I agree with @ars that you are unlikely to get one answer for this (you may also have more success on http://mathoverflow.net, since our community tends to be more applied, while this technique would | Fractal alternative to correlation
I agree with @ars that you are unlikely to get one answer for this (you may also have more success on http://mathoverflow.net, since our community tends to be more applied, while this technique would have very little real-world usage). The Abrahao/Barbosa paper is a good reference. ... | Fractal alternative to correlation
I agree with @ars that you are unlikely to get one answer for this (you may also have more success on http://mathoverflow.net, since our community tends to be more applied, while this technique would |
41,327 | Dealing with missing data due to variable not being measured over initial period of a study | I like the partial identification approach to missing data of Manski. The basic idea is to ask: given all possible values the missing data could have, what is the set of values that the estimated parameters could take? This set might be very large, in which case you could consider restricting the distribution of the mi... | Dealing with missing data due to variable not being measured over initial period of a study | I like the partial identification approach to missing data of Manski. The basic idea is to ask: given all possible values the missing data could have, what is the set of values that the estimated para | Dealing with missing data due to variable not being measured over initial period of a study
I like the partial identification approach to missing data of Manski. The basic idea is to ask: given all possible values the missing data could have, what is the set of values that the estimated parameters could take? This set ... | Dealing with missing data due to variable not being measured over initial period of a study
I like the partial identification approach to missing data of Manski. The basic idea is to ask: given all possible values the missing data could have, what is the set of values that the estimated para |
41,328 | Analytical solutions to limits of correlation stress testing | This is not a complete answer but it was too long to fit in as a comment and hopefully gives you some ideas.
What I am about to say is not really a proof but more of an intuitive sketch as to why the minimum eigenvalue may matter as far as the upper stress boundary is concerned.
Every correlation matrix can be decompos... | Analytical solutions to limits of correlation stress testing | This is not a complete answer but it was too long to fit in as a comment and hopefully gives you some ideas.
What I am about to say is not really a proof but more of an intuitive sketch as to why the | Analytical solutions to limits of correlation stress testing
This is not a complete answer but it was too long to fit in as a comment and hopefully gives you some ideas.
What I am about to say is not really a proof but more of an intuitive sketch as to why the minimum eigenvalue may matter as far as the upper stress bo... | Analytical solutions to limits of correlation stress testing
This is not a complete answer but it was too long to fit in as a comment and hopefully gives you some ideas.
What I am about to say is not really a proof but more of an intuitive sketch as to why the |
41,329 | Analytical solutions to limits of correlation stress testing | As kwak has pointed out, my question was answered on another forum:
http://www.or-exchange.com/questions/695/analytical-solutions-to-limits-of-correlation-stress-testing
I did several quick calculations and the suggested analytical solution is consistent with the numerical ones. I still need to check the proof. | Analytical solutions to limits of correlation stress testing | As kwak has pointed out, my question was answered on another forum:
http://www.or-exchange.com/questions/695/analytical-solutions-to-limits-of-correlation-stress-testing
I did several quick calculatio | Analytical solutions to limits of correlation stress testing
As kwak has pointed out, my question was answered on another forum:
http://www.or-exchange.com/questions/695/analytical-solutions-to-limits-of-correlation-stress-testing
I did several quick calculations and the suggested analytical solution is consistent with... | Analytical solutions to limits of correlation stress testing
As kwak has pointed out, my question was answered on another forum:
http://www.or-exchange.com/questions/695/analytical-solutions-to-limits-of-correlation-stress-testing
I did several quick calculatio |
41,330 | Analytical solutions to limits of correlation stress testing | The proof should be rather simple. Let $C$ be your correlation matrix (it has all ones on the diagonal). You multiply each element on the off diagonal by $(1+k)$. This is equivalent to computing the matrix $\hat{C} = (1+k) C - k \operatorname{diag}(C) = (1+k)C - k I,$ where $\operatorname{diag}$ is the diagonal part of... | Analytical solutions to limits of correlation stress testing | The proof should be rather simple. Let $C$ be your correlation matrix (it has all ones on the diagonal). You multiply each element on the off diagonal by $(1+k)$. This is equivalent to computing the m | Analytical solutions to limits of correlation stress testing
The proof should be rather simple. Let $C$ be your correlation matrix (it has all ones on the diagonal). You multiply each element on the off diagonal by $(1+k)$. This is equivalent to computing the matrix $\hat{C} = (1+k) C - k \operatorname{diag}(C) = (1+k)... | Analytical solutions to limits of correlation stress testing
The proof should be rather simple. Let $C$ be your correlation matrix (it has all ones on the diagonal). You multiply each element on the off diagonal by $(1+k)$. This is equivalent to computing the m |
41,331 | Analytical solutions to limits of correlation stress testing | I am not sure what the real question is, but suppose instead of changing every non-diagonal element, you changed just 2 (to keep the resulting matrix symmetric). That is let $\hat{C}$ be $C$ with $\hat{C_{i,j}} = C_{i,j} + \Delta C / 2= \hat{C_{j,i}},$ for some choice of $i,j$ with $i \ne j$. (alternatively, imagine $\... | Analytical solutions to limits of correlation stress testing | I am not sure what the real question is, but suppose instead of changing every non-diagonal element, you changed just 2 (to keep the resulting matrix symmetric). That is let $\hat{C}$ be $C$ with $\ha | Analytical solutions to limits of correlation stress testing
I am not sure what the real question is, but suppose instead of changing every non-diagonal element, you changed just 2 (to keep the resulting matrix symmetric). That is let $\hat{C}$ be $C$ with $\hat{C_{i,j}} = C_{i,j} + \Delta C / 2= \hat{C_{j,i}},$ for so... | Analytical solutions to limits of correlation stress testing
I am not sure what the real question is, but suppose instead of changing every non-diagonal element, you changed just 2 (to keep the resulting matrix symmetric). That is let $\hat{C}$ be $C$ with $\ha |
41,332 | Preferred method for identifying curvilinear effect in multi-variable regression framework | It sounds as though you are interested in formal inference and for that method 4 is best. Add X^2 to a model containing terms you wish to control for and conduct a test to assess the streght of evidence for the quadratic term given the terms in the model. Note however that "absence of evidence is not evidence of abse... | Preferred method for identifying curvilinear effect in multi-variable regression framework | It sounds as though you are interested in formal inference and for that method 4 is best. Add X^2 to a model containing terms you wish to control for and conduct a test to assess the streght of evide | Preferred method for identifying curvilinear effect in multi-variable regression framework
It sounds as though you are interested in formal inference and for that method 4 is best. Add X^2 to a model containing terms you wish to control for and conduct a test to assess the streght of evidence for the quadratic term gi... | Preferred method for identifying curvilinear effect in multi-variable regression framework
It sounds as though you are interested in formal inference and for that method 4 is best. Add X^2 to a model containing terms you wish to control for and conduct a test to assess the streght of evide |
41,333 | Preferred method for identifying curvilinear effect in multi-variable regression framework | Thanks again for the response, and any other responses in the future will be much appreciated. I think I personally prefer using exploratory tools to identify the relationships, especially since the original researcher did not give any real reason why a curvilinear relationship would exist theoretically. Although explo... | Preferred method for identifying curvilinear effect in multi-variable regression framework | Thanks again for the response, and any other responses in the future will be much appreciated. I think I personally prefer using exploratory tools to identify the relationships, especially since the o | Preferred method for identifying curvilinear effect in multi-variable regression framework
Thanks again for the response, and any other responses in the future will be much appreciated. I think I personally prefer using exploratory tools to identify the relationships, especially since the original researcher did not gi... | Preferred method for identifying curvilinear effect in multi-variable regression framework
Thanks again for the response, and any other responses in the future will be much appreciated. I think I personally prefer using exploratory tools to identify the relationships, especially since the o |
41,334 | Mixed regression models and custom link functions in R? | Douglas Bates addressed this on the sig-ME list a while back:
using glmer with user-defined link function
I'm not aware of significant changes since, but his recommendation (using a quasi family with specified link and variance) might be of use. Hopefully this addresses your first and third questions. I'm not aware... | Mixed regression models and custom link functions in R? | Douglas Bates addressed this on the sig-ME list a while back:
using glmer with user-defined link function
I'm not aware of significant changes since, but his recommendation (using a quasi family wit | Mixed regression models and custom link functions in R?
Douglas Bates addressed this on the sig-ME list a while back:
using glmer with user-defined link function
I'm not aware of significant changes since, but his recommendation (using a quasi family with specified link and variance) might be of use. Hopefully this ... | Mixed regression models and custom link functions in R?
Douglas Bates addressed this on the sig-ME list a while back:
using glmer with user-defined link function
I'm not aware of significant changes since, but his recommendation (using a quasi family wit |
41,335 | Mixed regression models and custom link functions in R? | repeated::gnlmix()
PROC NLMIXED -- If the link or its inverse can be represented with the functions available in SAS.
I need to dig more into the code.
Some repeated::gnlmix() examples:
library(repeated)
set.seed(99)
dat <- data.frame(id = c(1,1,1, 2,2,2, 3,3,3, 4,4,4),
y = c(1,0,1, 0,1,1, 0,0,0, 1,... | Mixed regression models and custom link functions in R? | repeated::gnlmix()
PROC NLMIXED -- If the link or its inverse can be represented with the functions available in SAS.
I need to dig more into the code.
Some repeated::gnlmix() examples:
library(repea | Mixed regression models and custom link functions in R?
repeated::gnlmix()
PROC NLMIXED -- If the link or its inverse can be represented with the functions available in SAS.
I need to dig more into the code.
Some repeated::gnlmix() examples:
library(repeated)
set.seed(99)
dat <- data.frame(id = c(1,1,1, 2,2,2, 3,3,3, ... | Mixed regression models and custom link functions in R?
repeated::gnlmix()
PROC NLMIXED -- If the link or its inverse can be represented with the functions available in SAS.
I need to dig more into the code.
Some repeated::gnlmix() examples:
library(repea |
41,336 | Mixed regression models and custom link functions in R? | As pointed out by @Ben Bolker, this isn't a problem for versions of lme4 >= 1.0-4 (circa 09-2013). Link functions can now be specified in R code - which seems to answer 1) and 3) from above with the answer being that the constraints for link functions were due to how lme4 pre 1.0 was programmed as opposed to conceptua... | Mixed regression models and custom link functions in R? | As pointed out by @Ben Bolker, this isn't a problem for versions of lme4 >= 1.0-4 (circa 09-2013). Link functions can now be specified in R code - which seems to answer 1) and 3) from above with the | Mixed regression models and custom link functions in R?
As pointed out by @Ben Bolker, this isn't a problem for versions of lme4 >= 1.0-4 (circa 09-2013). Link functions can now be specified in R code - which seems to answer 1) and 3) from above with the answer being that the constraints for link functions were due to... | Mixed regression models and custom link functions in R?
As pointed out by @Ben Bolker, this isn't a problem for versions of lme4 >= 1.0-4 (circa 09-2013). Link functions can now be specified in R code - which seems to answer 1) and 3) from above with the |
41,337 | Modeling of real-time streaming data? | This area roughly falls into two categories. The first concerns stream processing and querying issues and associated models and algorithms. The second is efficient algorithms and models for learning from data streams (or data stream mining).
It's my impression that the CEP industry is connected to the first area. Fo... | Modeling of real-time streaming data? | This area roughly falls into two categories. The first concerns stream processing and querying issues and associated models and algorithms. The second is efficient algorithms and models for learning | Modeling of real-time streaming data?
This area roughly falls into two categories. The first concerns stream processing and querying issues and associated models and algorithms. The second is efficient algorithms and models for learning from data streams (or data stream mining).
It's my impression that the CEP indust... | Modeling of real-time streaming data?
This area roughly falls into two categories. The first concerns stream processing and querying issues and associated models and algorithms. The second is efficient algorithms and models for learning |
41,338 | Modeling of real-time streaming data? | It is going to depend a lot on what exactly you are looking for, but start at Data Streams: Algorithms and Application by Muthukrishnan .
There are many others that can be found by googling "data stream algorithms", or following the references in the paper. | Modeling of real-time streaming data? | It is going to depend a lot on what exactly you are looking for, but start at Data Streams: Algorithms and Application by Muthukrishnan .
There are many others that can be found by googling "data stre | Modeling of real-time streaming data?
It is going to depend a lot on what exactly you are looking for, but start at Data Streams: Algorithms and Application by Muthukrishnan .
There are many others that can be found by googling "data stream algorithms", or following the references in the paper. | Modeling of real-time streaming data?
It is going to depend a lot on what exactly you are looking for, but start at Data Streams: Algorithms and Application by Muthukrishnan .
There are many others that can be found by googling "data stre |
41,339 | Modeling of real-time streaming data? | I am not sure how far this would be relevant to what you want to do but see the paper on adaptive question design called FASTPACE. The goal of the algorithm is to ask the next question from a survey respondent based on his/her previous questions and answers.
The data does not arrive as fast as stock prices but neverthe... | Modeling of real-time streaming data? | I am not sure how far this would be relevant to what you want to do but see the paper on adaptive question design called FASTPACE. The goal of the algorithm is to ask the next question from a survey r | Modeling of real-time streaming data?
I am not sure how far this would be relevant to what you want to do but see the paper on adaptive question design called FASTPACE. The goal of the algorithm is to ask the next question from a survey respondent based on his/her previous questions and answers.
The data does not arriv... | Modeling of real-time streaming data?
I am not sure how far this would be relevant to what you want to do but see the paper on adaptive question design called FASTPACE. The goal of the algorithm is to ask the next question from a survey r |
41,340 | Modeling of real-time streaming data? | Bayesian networks are perfect for online estimation, and offer a great diversity of models. | Modeling of real-time streaming data? | Bayesian networks are perfect for online estimation, and offer a great diversity of models. | Modeling of real-time streaming data?
Bayesian networks are perfect for online estimation, and offer a great diversity of models. | Modeling of real-time streaming data?
Bayesian networks are perfect for online estimation, and offer a great diversity of models. |
41,341 | Modeling of real-time streaming data? | I'm not sure what sort of data you need to process, but statistical algorithms are used quite frequently in robotics, media art, digital signal processing etc. It may be worthwhile to borrow from these domains. | Modeling of real-time streaming data? | I'm not sure what sort of data you need to process, but statistical algorithms are used quite frequently in robotics, media art, digital signal processing etc. It may be worthwhile to borrow from thes | Modeling of real-time streaming data?
I'm not sure what sort of data you need to process, but statistical algorithms are used quite frequently in robotics, media art, digital signal processing etc. It may be worthwhile to borrow from these domains. | Modeling of real-time streaming data?
I'm not sure what sort of data you need to process, but statistical algorithms are used quite frequently in robotics, media art, digital signal processing etc. It may be worthwhile to borrow from thes |
41,342 | Modeling of real-time streaming data? | you have postrank
http://data.postrank.com/content
How do you sort what content is current and meaningful? We do it for you. PostRank gathers original content, as well as information at the feed and story level. This includes title, author, language, tags, and related links.
We analyze that data to deliver timely, soc... | Modeling of real-time streaming data? | you have postrank
http://data.postrank.com/content
How do you sort what content is current and meaningful? We do it for you. PostRank gathers original content, as well as information at the feed and s | Modeling of real-time streaming data?
you have postrank
http://data.postrank.com/content
How do you sort what content is current and meaningful? We do it for you. PostRank gathers original content, as well as information at the feed and story level. This includes title, author, language, tags, and related links.
We an... | Modeling of real-time streaming data?
you have postrank
http://data.postrank.com/content
How do you sort what content is current and meaningful? We do it for you. PostRank gathers original content, as well as information at the feed and s |
41,343 | What's the purpose of window function in spectral analysis? | It depends on where you apply the window function. If you do it in the time domain, it's because you only want to analyze the periodic behavior of the function in a short duration. You do this when you don't believe that your data is from a stationary process.
If you do it in the frequency domain, then you do it to... | What's the purpose of window function in spectral analysis? | It depends on where you apply the window function. If you do it in the time domain, it's because you only want to analyze the periodic behavior of the function in a short duration. You do this when | What's the purpose of window function in spectral analysis?
It depends on where you apply the window function. If you do it in the time domain, it's because you only want to analyze the periodic behavior of the function in a short duration. You do this when you don't believe that your data is from a stationary proces... | What's the purpose of window function in spectral analysis?
It depends on where you apply the window function. If you do it in the time domain, it's because you only want to analyze the periodic behavior of the function in a short duration. You do this when |
41,344 | What's the purpose of window function in spectral analysis? | The main aim of windowing in spectral analysis is the ability of zooming into the finer details of the signal rather than looking the whole signal as such. Short Time Fourier Transforms(STFT) are of prime importance in case of speech signal processing where the information like pitch or the formant frequencies are extr... | What's the purpose of window function in spectral analysis? | The main aim of windowing in spectral analysis is the ability of zooming into the finer details of the signal rather than looking the whole signal as such. Short Time Fourier Transforms(STFT) are of p | What's the purpose of window function in spectral analysis?
The main aim of windowing in spectral analysis is the ability of zooming into the finer details of the signal rather than looking the whole signal as such. Short Time Fourier Transforms(STFT) are of prime importance in case of speech signal processing where th... | What's the purpose of window function in spectral analysis?
The main aim of windowing in spectral analysis is the ability of zooming into the finer details of the signal rather than looking the whole signal as such. Short Time Fourier Transforms(STFT) are of p |
41,345 | Kullback–Leibler divergence between two multivariate t distributions with different degrees of freedom? | Check the following post:
Kullback Leibler divergence between two multivariate t distributions
The authors reduce the dimension of the integral from $p$ (in your notation) to 1, which seems to be easier to handle. The post contains numerical examples in R.
Edit. As mentioned by @utobi in a comment, it is not a closed-... | Kullback–Leibler divergence between two multivariate t distributions with different degrees of freed | Check the following post:
Kullback Leibler divergence between two multivariate t distributions
The authors reduce the dimension of the integral from $p$ (in your notation) to 1, which seems to be easi | Kullback–Leibler divergence between two multivariate t distributions with different degrees of freedom?
Check the following post:
Kullback Leibler divergence between two multivariate t distributions
The authors reduce the dimension of the integral from $p$ (in your notation) to 1, which seems to be easier to handle. Th... | Kullback–Leibler divergence between two multivariate t distributions with different degrees of freed
Check the following post:
Kullback Leibler divergence between two multivariate t distributions
The authors reduce the dimension of the integral from $p$ (in your notation) to 1, which seems to be easi |
41,346 | EM algorithm for Bivariate Normal | Denoting the Normal parameters by $\theta$, the observed likelihood is
$$\pi_0^{n_0}\pi_1^{n_1}\pi_2^{n_2}\prod_{i:\,c_i=0}f_X(u_i,v_i;\theta)
\prod_{i:\,c_i=1}f_U(u_i;\theta)\prod_{i:\,c_i=2}f_V(v_i;\theta)$$
with each term being in closed (Normal) form. Hence this likelihood can be optimised in $(\theta,\pi)$ and doe... | EM algorithm for Bivariate Normal | Denoting the Normal parameters by $\theta$, the observed likelihood is
$$\pi_0^{n_0}\pi_1^{n_1}\pi_2^{n_2}\prod_{i:\,c_i=0}f_X(u_i,v_i;\theta)
\prod_{i:\,c_i=1}f_U(u_i;\theta)\prod_{i:\,c_i=2}f_V(v_i; | EM algorithm for Bivariate Normal
Denoting the Normal parameters by $\theta$, the observed likelihood is
$$\pi_0^{n_0}\pi_1^{n_1}\pi_2^{n_2}\prod_{i:\,c_i=0}f_X(u_i,v_i;\theta)
\prod_{i:\,c_i=1}f_U(u_i;\theta)\prod_{i:\,c_i=2}f_V(v_i;\theta)$$
with each term being in closed (Normal) form. Hence this likelihood can be o... | EM algorithm for Bivariate Normal
Denoting the Normal parameters by $\theta$, the observed likelihood is
$$\pi_0^{n_0}\pi_1^{n_1}\pi_2^{n_2}\prod_{i:\,c_i=0}f_X(u_i,v_i;\theta)
\prod_{i:\,c_i=1}f_U(u_i;\theta)\prod_{i:\,c_i=2}f_V(v_i; |
41,347 | Can robust standard errors be less than those from normal OLS? | OLS gives every point equal weight in estimating the error of the estimates. The variance/error is estimated as
$$\widehat{\text{Var}(\beta) }= \hat{\sigma} (X^TX)^{-1} $$
A weighted least squares estimator might use an estimate like
$$\widehat{\text{Var}(\beta) }= \hat{\sigma} (X^TWX)^{-1} $$
The weights might make so... | Can robust standard errors be less than those from normal OLS? | OLS gives every point equal weight in estimating the error of the estimates. The variance/error is estimated as
$$\widehat{\text{Var}(\beta) }= \hat{\sigma} (X^TX)^{-1} $$
A weighted least squares est | Can robust standard errors be less than those from normal OLS?
OLS gives every point equal weight in estimating the error of the estimates. The variance/error is estimated as
$$\widehat{\text{Var}(\beta) }= \hat{\sigma} (X^TX)^{-1} $$
A weighted least squares estimator might use an estimate like
$$\widehat{\text{Var}(\... | Can robust standard errors be less than those from normal OLS?
OLS gives every point equal weight in estimating the error of the estimates. The variance/error is estimated as
$$\widehat{\text{Var}(\beta) }= \hat{\sigma} (X^TX)^{-1} $$
A weighted least squares est |
41,348 | Can robust standard errors be less than those from normal OLS? | Yes they can be smaller than the standard variance estimates. The reason is that even in the case of linear models, robust standard errors are biased but consistent. Their variance estimates might be (severely) biased downwards due to this small-sample bias, see Imbens & Kolesar (2016, The Review of Economics and Stati... | Can robust standard errors be less than those from normal OLS? | Yes they can be smaller than the standard variance estimates. The reason is that even in the case of linear models, robust standard errors are biased but consistent. Their variance estimates might be | Can robust standard errors be less than those from normal OLS?
Yes they can be smaller than the standard variance estimates. The reason is that even in the case of linear models, robust standard errors are biased but consistent. Their variance estimates might be (severely) biased downwards due to this small-sample bias... | Can robust standard errors be less than those from normal OLS?
Yes they can be smaller than the standard variance estimates. The reason is that even in the case of linear models, robust standard errors are biased but consistent. Their variance estimates might be |
41,349 | Can robust standard errors be less than those from normal OLS? | If the response is, conditionally on the covariates, Gaussian, then we know that OLS are best linear unbiased estimators by Gauss-Markov theorem; no other estimator can have lower variance than OLS.
If the Gaussian assumption is not met we have no such guarantee anymore. Indeed, since the influence function (IF) of the... | Can robust standard errors be less than those from normal OLS? | If the response is, conditionally on the covariates, Gaussian, then we know that OLS are best linear unbiased estimators by Gauss-Markov theorem; no other estimator can have lower variance than OLS.
I | Can robust standard errors be less than those from normal OLS?
If the response is, conditionally on the covariates, Gaussian, then we know that OLS are best linear unbiased estimators by Gauss-Markov theorem; no other estimator can have lower variance than OLS.
If the Gaussian assumption is not met we have no such guar... | Can robust standard errors be less than those from normal OLS?
If the response is, conditionally on the covariates, Gaussian, then we know that OLS are best linear unbiased estimators by Gauss-Markov theorem; no other estimator can have lower variance than OLS.
I |
41,350 | Why Do Residuals Need To Be Homoscedastic (Equal Variance)? | The bounty asks for citations. Some relevant citations appear in comments to Literature on robustness of regression assumptions. I reproduce them here:
Whuber:
Draper & Smith (Applied Regression Analysis, 2nd Ed.) develop the regression equations at the beginning of section 2.6, then discuss what can be done in a subs... | Why Do Residuals Need To Be Homoscedastic (Equal Variance)? | The bounty asks for citations. Some relevant citations appear in comments to Literature on robustness of regression assumptions. I reproduce them here:
Whuber:
Draper & Smith (Applied Regression Anal | Why Do Residuals Need To Be Homoscedastic (Equal Variance)?
The bounty asks for citations. Some relevant citations appear in comments to Literature on robustness of regression assumptions. I reproduce them here:
Whuber:
Draper & Smith (Applied Regression Analysis, 2nd Ed.) develop the regression equations at the begin... | Why Do Residuals Need To Be Homoscedastic (Equal Variance)?
The bounty asks for citations. Some relevant citations appear in comments to Literature on robustness of regression assumptions. I reproduce them here:
Whuber:
Draper & Smith (Applied Regression Anal |
41,351 | Why Do Residuals Need To Be Homoscedastic (Equal Variance)? | The assumptions of residual normality and homoscedaticity are used in the theoretical derivation of the Mean Squared Error. This loss is actually a scaled negative logarithmic likelihood for the following regression model:
$$y = f(\theta, x) + \epsilon$$
where $\epsilon$ is a zero mean normal random variable, independe... | Why Do Residuals Need To Be Homoscedastic (Equal Variance)? | The assumptions of residual normality and homoscedaticity are used in the theoretical derivation of the Mean Squared Error. This loss is actually a scaled negative logarithmic likelihood for the follo | Why Do Residuals Need To Be Homoscedastic (Equal Variance)?
The assumptions of residual normality and homoscedaticity are used in the theoretical derivation of the Mean Squared Error. This loss is actually a scaled negative logarithmic likelihood for the following regression model:
$$y = f(\theta, x) + \epsilon$$
where... | Why Do Residuals Need To Be Homoscedastic (Equal Variance)?
The assumptions of residual normality and homoscedaticity are used in the theoretical derivation of the Mean Squared Error. This loss is actually a scaled negative logarithmic likelihood for the follo |
41,352 | Why Do Residuals Need To Be Homoscedastic (Equal Variance)? | I have written quite a bit on model assumptions here and here.
Just to add a general remark to the discussion: Statistical model assumptions are required for proving mathematical theorems regarding the quality of a method. In case model assumptions are violated, the theoretical "guarantees" of the theorems cannot be ta... | Why Do Residuals Need To Be Homoscedastic (Equal Variance)? | I have written quite a bit on model assumptions here and here.
Just to add a general remark to the discussion: Statistical model assumptions are required for proving mathematical theorems regarding th | Why Do Residuals Need To Be Homoscedastic (Equal Variance)?
I have written quite a bit on model assumptions here and here.
Just to add a general remark to the discussion: Statistical model assumptions are required for proving mathematical theorems regarding the quality of a method. In case model assumptions are violate... | Why Do Residuals Need To Be Homoscedastic (Equal Variance)?
I have written quite a bit on model assumptions here and here.
Just to add a general remark to the discussion: Statistical model assumptions are required for proving mathematical theorems regarding th |
41,353 | How to extract coefficients corresponding to data from each time in a mixed effect model in R? | Context: Since it is known that vaccine A induces higher antibody levels than vaccine B, I interpret the question to mean: How do we use visit 1 and visit 2 data to test that A has the same efficacy on the second visit no matter which vaccine a subject receives on the first visit? I describe two ways to do it, with and... | How to extract coefficients corresponding to data from each time in a mixed effect model in R? | Context: Since it is known that vaccine A induces higher antibody levels than vaccine B, I interpret the question to mean: How do we use visit 1 and visit 2 data to test that A has the same efficacy o | How to extract coefficients corresponding to data from each time in a mixed effect model in R?
Context: Since it is known that vaccine A induces higher antibody levels than vaccine B, I interpret the question to mean: How do we use visit 1 and visit 2 data to test that A has the same efficacy on the second visit no mat... | How to extract coefficients corresponding to data from each time in a mixed effect model in R?
Context: Since it is known that vaccine A induces higher antibody levels than vaccine B, I interpret the question to mean: How do we use visit 1 and visit 2 data to test that A has the same efficacy o |
41,354 | What is Galton's paradox? | The "paradox" here arises from sneaking in an implicit insinuation of independence that does not actually hold, which allows the argument to lead you to a wrong answer with a series of plausible-sounding steps. As you can see from your enumeration of the possible outcomes, every possible outcome is one where "at least... | What is Galton's paradox? | The "paradox" here arises from sneaking in an implicit insinuation of independence that does not actually hold, which allows the argument to lead you to a wrong answer with a series of plausible-sound | What is Galton's paradox?
The "paradox" here arises from sneaking in an implicit insinuation of independence that does not actually hold, which allows the argument to lead you to a wrong answer with a series of plausible-sounding steps. As you can see from your enumeration of the possible outcomes, every possible outc... | What is Galton's paradox?
The "paradox" here arises from sneaking in an implicit insinuation of independence that does not actually hold, which allows the argument to lead you to a wrong answer with a series of plausible-sound |
41,355 | How to choose $\gamma$ parameter in Focal Loss? | The parameter $\gamma$ smoothly adjusts the rate at which easy examples are down-weighted and that is quite dataset and application dependent. In the paper, the focal loss is actually given as: $−\alpha (1 − p_t)^\gamma \log(p_t)$ which is a reformulated view of the standard cross-entropy loss and the class imbalance i... | How to choose $\gamma$ parameter in Focal Loss? | The parameter $\gamma$ smoothly adjusts the rate at which easy examples are down-weighted and that is quite dataset and application dependent. In the paper, the focal loss is actually given as: $−\alp | How to choose $\gamma$ parameter in Focal Loss?
The parameter $\gamma$ smoothly adjusts the rate at which easy examples are down-weighted and that is quite dataset and application dependent. In the paper, the focal loss is actually given as: $−\alpha (1 − p_t)^\gamma \log(p_t)$ which is a reformulated view of the stand... | How to choose $\gamma$ parameter in Focal Loss?
The parameter $\gamma$ smoothly adjusts the rate at which easy examples are down-weighted and that is quite dataset and application dependent. In the paper, the focal loss is actually given as: $−\alp |
41,356 | How to choose $\gamma$ parameter in Focal Loss? | On page 3, the authors write "we found $\gamma = 2$ to work best in our experiments." This tells us that they chose $\gamma$ experimentally by training models with different values and then choosing the $\gamma$ from the best model. Because this value was chosen experimentally, it may not be the best choice across all ... | How to choose $\gamma$ parameter in Focal Loss? | On page 3, the authors write "we found $\gamma = 2$ to work best in our experiments." This tells us that they chose $\gamma$ experimentally by training models with different values and then choosing t | How to choose $\gamma$ parameter in Focal Loss?
On page 3, the authors write "we found $\gamma = 2$ to work best in our experiments." This tells us that they chose $\gamma$ experimentally by training models with different values and then choosing the $\gamma$ from the best model. Because this value was chosen experimen... | How to choose $\gamma$ parameter in Focal Loss?
On page 3, the authors write "we found $\gamma = 2$ to work best in our experiments." This tells us that they chose $\gamma$ experimentally by training models with different values and then choosing t |
41,357 | Fast likelihood evaluation for Gaussian distribution with diagonal plus low rank covariance | $\newcommand{\L}{\Lambda}$We need to be able to efficiently evaluate $y^T(\Sigma + \L\L^T)^{-1} y$ and $\det (\Sigma + \L\L^T)$. The standard approach here is to use the Woodbury matrix identity and matrix determinant lemma to change our hard operations from being on $p\times p$ matrices to being on $d\times d$ matrice... | Fast likelihood evaluation for Gaussian distribution with diagonal plus low rank covariance | $\newcommand{\L}{\Lambda}$We need to be able to efficiently evaluate $y^T(\Sigma + \L\L^T)^{-1} y$ and $\det (\Sigma + \L\L^T)$. The standard approach here is to use the Woodbury matrix identity and m | Fast likelihood evaluation for Gaussian distribution with diagonal plus low rank covariance
$\newcommand{\L}{\Lambda}$We need to be able to efficiently evaluate $y^T(\Sigma + \L\L^T)^{-1} y$ and $\det (\Sigma + \L\L^T)$. The standard approach here is to use the Woodbury matrix identity and matrix determinant lemma to c... | Fast likelihood evaluation for Gaussian distribution with diagonal plus low rank covariance
$\newcommand{\L}{\Lambda}$We need to be able to efficiently evaluate $y^T(\Sigma + \L\L^T)^{-1} y$ and $\det (\Sigma + \L\L^T)$. The standard approach here is to use the Woodbury matrix identity and m |
41,358 | Difference between splines from different packages (mgcv, rms etc.) | The main difference is the choice of knots and penalization. To start, let's focus on cubic splines for x, y data.*
I find it useful to start from the extreme situation, an interpolating spline that connects all data points with a smooth curve. Then each x-axis value is a knot at which two cubic functions interpolating... | Difference between splines from different packages (mgcv, rms etc.) | The main difference is the choice of knots and penalization. To start, let's focus on cubic splines for x, y data.*
I find it useful to start from the extreme situation, an interpolating spline that c | Difference between splines from different packages (mgcv, rms etc.)
The main difference is the choice of knots and penalization. To start, let's focus on cubic splines for x, y data.*
I find it useful to start from the extreme situation, an interpolating spline that connects all data points with a smooth curve. Then ea... | Difference between splines from different packages (mgcv, rms etc.)
The main difference is the choice of knots and penalization. To start, let's focus on cubic splines for x, y data.*
I find it useful to start from the extreme situation, an interpolating spline that c |
41,359 | Please clarify Bayesian calibration of the posterior mean | It may be confusing that the $\hat \theta = E[\theta \mid y]$ seems to use the chosen prior and the posterior distribution then implied by the observation, while the $E\left[\theta \mid \hat \theta\right]-\hat \theta$ in the miscalibration calculation seems to use the actual (though presumably unknown) distribution for... | Please clarify Bayesian calibration of the posterior mean | It may be confusing that the $\hat \theta = E[\theta \mid y]$ seems to use the chosen prior and the posterior distribution then implied by the observation, while the $E\left[\theta \mid \hat \theta\ri | Please clarify Bayesian calibration of the posterior mean
It may be confusing that the $\hat \theta = E[\theta \mid y]$ seems to use the chosen prior and the posterior distribution then implied by the observation, while the $E\left[\theta \mid \hat \theta\right]-\hat \theta$ in the miscalibration calculation seems to u... | Please clarify Bayesian calibration of the posterior mean
It may be confusing that the $\hat \theta = E[\theta \mid y]$ seems to use the chosen prior and the posterior distribution then implied by the observation, while the $E\left[\theta \mid \hat \theta\ri |
41,360 | Understand the idea of margin in contrastive loss for siamese networks | The best explanation is given in A Tutorial on Energy-Based Learning by LeCun et al, concretely in section 5. Also, Learning a Similarity Metric Discriminatively, with Application to Face Verification by Chopra et al. provides a detailed analysis for the case of face verification. The motivation for introducing the mar... | Understand the idea of margin in contrastive loss for siamese networks | The best explanation is given in A Tutorial on Energy-Based Learning by LeCun et al, concretely in section 5. Also, Learning a Similarity Metric Discriminatively, with Application to Face Verification | Understand the idea of margin in contrastive loss for siamese networks
The best explanation is given in A Tutorial on Energy-Based Learning by LeCun et al, concretely in section 5. Also, Learning a Similarity Metric Discriminatively, with Application to Face Verification by Chopra et al. provides a detailed analysis fo... | Understand the idea of margin in contrastive loss for siamese networks
The best explanation is given in A Tutorial on Energy-Based Learning by LeCun et al, concretely in section 5. Also, Learning a Similarity Metric Discriminatively, with Application to Face Verification |
41,361 | Understand the idea of margin in contrastive loss for siamese networks | If you look at the Loss it is composed of two parts, 1st the loss when they are similar and second the loss when they are dissimilar.
If model works very well, observation which are similar should have very small distance. Using Sqaure distance in first ensure that model is penalized if its gives high distance for sim... | Understand the idea of margin in contrastive loss for siamese networks | If you look at the Loss it is composed of two parts, 1st the loss when they are similar and second the loss when they are dissimilar.
If model works very well, observation which are similar should ha | Understand the idea of margin in contrastive loss for siamese networks
If you look at the Loss it is composed of two parts, 1st the loss when they are similar and second the loss when they are dissimilar.
If model works very well, observation which are similar should have very small distance. Using Sqaure distance in ... | Understand the idea of margin in contrastive loss for siamese networks
If you look at the Loss it is composed of two parts, 1st the loss when they are similar and second the loss when they are dissimilar.
If model works very well, observation which are similar should ha |
41,362 | How can I learn statistical a/b testing? | Two books come to mind:
Trustworthy Online Controlled Experiments by Kohavi, Tang, and
Xu
Statistical Methods in Online A/B Testing by Georgi Georgiev
The first book collects a great deal of wisdom distilled from years of experience that was scattered in obscure field journals and touched only briefly in textbooks on... | How can I learn statistical a/b testing? | Two books come to mind:
Trustworthy Online Controlled Experiments by Kohavi, Tang, and
Xu
Statistical Methods in Online A/B Testing by Georgi Georgiev
The first book collects a great deal of wisdom | How can I learn statistical a/b testing?
Two books come to mind:
Trustworthy Online Controlled Experiments by Kohavi, Tang, and
Xu
Statistical Methods in Online A/B Testing by Georgi Georgiev
The first book collects a great deal of wisdom distilled from years of experience that was scattered in obscure field journals... | How can I learn statistical a/b testing?
Two books come to mind:
Trustworthy Online Controlled Experiments by Kohavi, Tang, and
Xu
Statistical Methods in Online A/B Testing by Georgi Georgiev
The first book collects a great deal of wisdom |
41,363 | Interpretation of regression coefficients with multiple categorical predictors | I think your question fundamentally goes back to the difference between the interpretation of main-effects in main-effect-only (y ~ cat1 + cat2) vs. interactive (y ~ cat1 * cat2) regression models.
When your model is of the form: y ~ sex + schoolgend. Then, YES, .175 has no choice but to represent both the:
diff. bet.... | Interpretation of regression coefficients with multiple categorical predictors | I think your question fundamentally goes back to the difference between the interpretation of main-effects in main-effect-only (y ~ cat1 + cat2) vs. interactive (y ~ cat1 * cat2) regression models.
Wh | Interpretation of regression coefficients with multiple categorical predictors
I think your question fundamentally goes back to the difference between the interpretation of main-effects in main-effect-only (y ~ cat1 + cat2) vs. interactive (y ~ cat1 * cat2) regression models.
When your model is of the form: y ~ sex + s... | Interpretation of regression coefficients with multiple categorical predictors
I think your question fundamentally goes back to the difference between the interpretation of main-effects in main-effect-only (y ~ cat1 + cat2) vs. interactive (y ~ cat1 * cat2) regression models.
Wh |
41,364 | Interpretation of regression coefficients with multiple categorical predictors | It's the difference between the (predicted) mean of girls in girls-only schools and the (predicted) mean of girls in mixed schools. You can see this by looking at the design matrix or solving for a predicted value using the fitted regression equation. Let's make some simple data and work through this.
d = expand.grid... | Interpretation of regression coefficients with multiple categorical predictors | It's the difference between the (predicted) mean of girls in girls-only schools and the (predicted) mean of girls in mixed schools. You can see this by looking at the design matrix or solving for a p | Interpretation of regression coefficients with multiple categorical predictors
It's the difference between the (predicted) mean of girls in girls-only schools and the (predicted) mean of girls in mixed schools. You can see this by looking at the design matrix or solving for a predicted value using the fitted regressio... | Interpretation of regression coefficients with multiple categorical predictors
It's the difference between the (predicted) mean of girls in girls-only schools and the (predicted) mean of girls in mixed schools. You can see this by looking at the design matrix or solving for a p |
41,365 | Interpretation of regression coefficients with multiple categorical predictors | The answers so far address interpretations that implicitly ignore the multilevel nature of the model. They are all correct though, that you don't have interactions, so the interpretations hinge on the tricky issue of boys-only or girls-only schools not having the other sex. The R code is helpful but let's put this in t... | Interpretation of regression coefficients with multiple categorical predictors | The answers so far address interpretations that implicitly ignore the multilevel nature of the model. They are all correct though, that you don't have interactions, so the interpretations hinge on the | Interpretation of regression coefficients with multiple categorical predictors
The answers so far address interpretations that implicitly ignore the multilevel nature of the model. They are all correct though, that you don't have interactions, so the interpretations hinge on the tricky issue of boys-only or girls-only ... | Interpretation of regression coefficients with multiple categorical predictors
The answers so far address interpretations that implicitly ignore the multilevel nature of the model. They are all correct though, that you don't have interactions, so the interpretations hinge on the |
41,366 | causal graph - counting the number of backdoor paths in a DAG | For Example 1, you are correct. $A\leftarrow Z\to W\to M\to Y$ is a valid backdoor path with no colliders in it (which would stop the backdoor path from being a problem).
In Example 2, you are incorrect. The definition of a backdoor path implies that the first arrow has to go into $G$ (in this case), or it's not a back... | causal graph - counting the number of backdoor paths in a DAG | For Example 1, you are correct. $A\leftarrow Z\to W\to M\to Y$ is a valid backdoor path with no colliders in it (which would stop the backdoor path from being a problem).
In Example 2, you are incorre | causal graph - counting the number of backdoor paths in a DAG
For Example 1, you are correct. $A\leftarrow Z\to W\to M\to Y$ is a valid backdoor path with no colliders in it (which would stop the backdoor path from being a problem).
In Example 2, you are incorrect. The definition of a backdoor path implies that the fir... | causal graph - counting the number of backdoor paths in a DAG
For Example 1, you are correct. $A\leftarrow Z\to W\to M\to Y$ is a valid backdoor path with no colliders in it (which would stop the backdoor path from being a problem).
In Example 2, you are incorre |
41,367 | Understanding the pdf of a truncated normal distribution | Perhaps a more general notation will uncover the basic concepts and help you answer your question. There's little more to the following analysis than using mathematical notation carefully. Because that makes it abstract, I rephrase the key results in English: look for the quoted passages.
When there are $m$ random va... | Understanding the pdf of a truncated normal distribution | Perhaps a more general notation will uncover the basic concepts and help you answer your question. There's little more to the following analysis than using mathematical notation carefully. Because t | Understanding the pdf of a truncated normal distribution
Perhaps a more general notation will uncover the basic concepts and help you answer your question. There's little more to the following analysis than using mathematical notation carefully. Because that makes it abstract, I rephrase the key results in English: l... | Understanding the pdf of a truncated normal distribution
Perhaps a more general notation will uncover the basic concepts and help you answer your question. There's little more to the following analysis than using mathematical notation carefully. Because t |
41,368 | Distribution of $\frac{X}{X+Y}$ if $X,Y$ are independent Beta random variables | This situation is described by T. Pham-Gia in 'Distributions of the ratios of independent beta variables and applications' in Communications in Statistics - Theory and Methods Volume 29, 2000 - Issue 12 https://doi.org/10.1080/03610920008832632
For the variable $T = \frac{X_1}{X_1+X_2}$ you get
$$f(t) = \begin{cases}
... | Distribution of $\frac{X}{X+Y}$ if $X,Y$ are independent Beta random variables | This situation is described by T. Pham-Gia in 'Distributions of the ratios of independent beta variables and applications' in Communications in Statistics - Theory and Methods Volume 29, 2000 - Issue | Distribution of $\frac{X}{X+Y}$ if $X,Y$ are independent Beta random variables
This situation is described by T. Pham-Gia in 'Distributions of the ratios of independent beta variables and applications' in Communications in Statistics - Theory and Methods Volume 29, 2000 - Issue 12 https://doi.org/10.1080/03610920008832... | Distribution of $\frac{X}{X+Y}$ if $X,Y$ are independent Beta random variables
This situation is described by T. Pham-Gia in 'Distributions of the ratios of independent beta variables and applications' in Communications in Statistics - Theory and Methods Volume 29, 2000 - Issue |
41,369 | Subgroups in meta-analysis | For simplicity let us assume there are two groups although the issues are the same for multiple groups. The choices are (a) to run an analysis on each group separately (b) to run an analysis on the whole data-set with a two-level factor as a moderator.
The advantage of option (b) is that you have more data and hence yo... | Subgroups in meta-analysis | For simplicity let us assume there are two groups although the issues are the same for multiple groups. The choices are (a) to run an analysis on each group separately (b) to run an analysis on the wh | Subgroups in meta-analysis
For simplicity let us assume there are two groups although the issues are the same for multiple groups. The choices are (a) to run an analysis on each group separately (b) to run an analysis on the whole data-set with a two-level factor as a moderator.
The advantage of option (b) is that you ... | Subgroups in meta-analysis
For simplicity let us assume there are two groups although the issues are the same for multiple groups. The choices are (a) to run an analysis on each group separately (b) to run an analysis on the wh |
41,370 | Subgroups in meta-analysis | There definitely should be a multiple comparison correction.
Meta-analyses are...generally not of the highest quality, with regards to statistical soundness. | Subgroups in meta-analysis | There definitely should be a multiple comparison correction.
Meta-analyses are...generally not of the highest quality, with regards to statistical soundness. | Subgroups in meta-analysis
There definitely should be a multiple comparison correction.
Meta-analyses are...generally not of the highest quality, with regards to statistical soundness. | Subgroups in meta-analysis
There definitely should be a multiple comparison correction.
Meta-analyses are...generally not of the highest quality, with regards to statistical soundness. |
41,371 | Subgroups in meta-analysis | It depends whether the data obtained using different methodologies can be statistically compared. Normally in a MA you first show the results overall and then you run a sensitivity analysis e.g. stratified analysis. | Subgroups in meta-analysis | It depends whether the data obtained using different methodologies can be statistically compared. Normally in a MA you first show the results overall and then you run a sensitivity analysis e.g. strat | Subgroups in meta-analysis
It depends whether the data obtained using different methodologies can be statistically compared. Normally in a MA you first show the results overall and then you run a sensitivity analysis e.g. stratified analysis. | Subgroups in meta-analysis
It depends whether the data obtained using different methodologies can be statistically compared. Normally in a MA you first show the results overall and then you run a sensitivity analysis e.g. strat |
41,372 | Why are Transformers "suboptimal" for language modeling but not for translation? | I think I acquired some insights into this question after posting it 1.5 months ago, and since there are no other answers, I'll share them:
Plain RNNs are, in practice, incapable of learning long-term dependencies, and while LSTMs can do it, they are still focused on recent inputs. This suits LMs just fine, because LMs... | Why are Transformers "suboptimal" for language modeling but not for translation? | I think I acquired some insights into this question after posting it 1.5 months ago, and since there are no other answers, I'll share them:
Plain RNNs are, in practice, incapable of learning long-term | Why are Transformers "suboptimal" for language modeling but not for translation?
I think I acquired some insights into this question after posting it 1.5 months ago, and since there are no other answers, I'll share them:
Plain RNNs are, in practice, incapable of learning long-term dependencies, and while LSTMs can do i... | Why are Transformers "suboptimal" for language modeling but not for translation?
I think I acquired some insights into this question after posting it 1.5 months ago, and since there are no other answers, I'll share them:
Plain RNNs are, in practice, incapable of learning long-term |
41,373 | Estimate Ratio of Normalizing Constants from two datasets | [Warning: the following proposals, except one, assume $f$ can be evaluated at arbitrary values. If the only inputs are the sets $A$ and $B$, and the samples $\mathbf x$ and $\mathbf y$, the problem has no solution since any combination $\alpha f_A(x)+(1-\alpha) f_B(x)$ could produce exactly the same samples $\mathbf x$... | Estimate Ratio of Normalizing Constants from two datasets | [Warning: the following proposals, except one, assume $f$ can be evaluated at arbitrary values. If the only inputs are the sets $A$ and $B$, and the samples $\mathbf x$ and $\mathbf y$, the problem ha | Estimate Ratio of Normalizing Constants from two datasets
[Warning: the following proposals, except one, assume $f$ can be evaluated at arbitrary values. If the only inputs are the sets $A$ and $B$, and the samples $\mathbf x$ and $\mathbf y$, the problem has no solution since any combination $\alpha f_A(x)+(1-\alpha) ... | Estimate Ratio of Normalizing Constants from two datasets
[Warning: the following proposals, except one, assume $f$ can be evaluated at arbitrary values. If the only inputs are the sets $A$ and $B$, and the samples $\mathbf x$ and $\mathbf y$, the problem ha |
41,374 | LightGBM model improvement when the focus is on probability prediction | Using the binary log-loss classification as an objective is a good move in this situation (and in most situations). We might want to point Optuna (or our general hyper-parameter search framework) to minimise the Brier score of the predictions if we care about how much the probabilities might be off; the AUC-ROC is a ra... | LightGBM model improvement when the focus is on probability prediction | Using the binary log-loss classification as an objective is a good move in this situation (and in most situations). We might want to point Optuna (or our general hyper-parameter search framework) to m | LightGBM model improvement when the focus is on probability prediction
Using the binary log-loss classification as an objective is a good move in this situation (and in most situations). We might want to point Optuna (or our general hyper-parameter search framework) to minimise the Brier score of the predictions if we ... | LightGBM model improvement when the focus is on probability prediction
Using the binary log-loss classification as an objective is a good move in this situation (and in most situations). We might want to point Optuna (or our general hyper-parameter search framework) to m |
41,375 | Best way to combine MCMC inference with multiple imputation? [duplicate] | One well-known approach is exactly what you describe (if I understood correctly): i.e. combine the inferences from the analyses of a large number of imputed datasets (each analyzed separately) by just using the equally weighted mixture distribution of the posterior distributions as the combined posterior distribution. ... | Best way to combine MCMC inference with multiple imputation? [duplicate] | One well-known approach is exactly what you describe (if I understood correctly): i.e. combine the inferences from the analyses of a large number of imputed datasets (each analyzed separately) by just | Best way to combine MCMC inference with multiple imputation? [duplicate]
One well-known approach is exactly what you describe (if I understood correctly): i.e. combine the inferences from the analyses of a large number of imputed datasets (each analyzed separately) by just using the equally weighted mixture distributio... | Best way to combine MCMC inference with multiple imputation? [duplicate]
One well-known approach is exactly what you describe (if I understood correctly): i.e. combine the inferences from the analyses of a large number of imputed datasets (each analyzed separately) by just |
41,376 | Best way to combine MCMC inference with multiple imputation? [duplicate] | (Thanks for the reminder! The answer has been revised to focus more on the originally posted question)
I think the paper by Zhou, as recommended above by @Björn, specifically discussed about Bayesian inference after multiple imputation.
Recently, I am also applying Bayesian conditional logistic regression after multipl... | Best way to combine MCMC inference with multiple imputation? [duplicate] | (Thanks for the reminder! The answer has been revised to focus more on the originally posted question)
I think the paper by Zhou, as recommended above by @Björn, specifically discussed about Bayesian | Best way to combine MCMC inference with multiple imputation? [duplicate]
(Thanks for the reminder! The answer has been revised to focus more on the originally posted question)
I think the paper by Zhou, as recommended above by @Björn, specifically discussed about Bayesian inference after multiple imputation.
Recently, ... | Best way to combine MCMC inference with multiple imputation? [duplicate]
(Thanks for the reminder! The answer has been revised to focus more on the originally posted question)
I think the paper by Zhou, as recommended above by @Björn, specifically discussed about Bayesian |
41,377 | Best way to combine MCMC inference with multiple imputation? [duplicate] | Are you familiar with censorship in survival analysis modeling? Censorship means that a patient was removed from the study without explicitly dying (at least in the context of survival analysis.) There are appropriate architectures to handle censorship; however, it's more a question of model architecture than the under... | Best way to combine MCMC inference with multiple imputation? [duplicate] | Are you familiar with censorship in survival analysis modeling? Censorship means that a patient was removed from the study without explicitly dying (at least in the context of survival analysis.) Ther | Best way to combine MCMC inference with multiple imputation? [duplicate]
Are you familiar with censorship in survival analysis modeling? Censorship means that a patient was removed from the study without explicitly dying (at least in the context of survival analysis.) There are appropriate architectures to handle censo... | Best way to combine MCMC inference with multiple imputation? [duplicate]
Are you familiar with censorship in survival analysis modeling? Censorship means that a patient was removed from the study without explicitly dying (at least in the context of survival analysis.) Ther |
41,378 | Best way to combine MCMC inference with multiple imputation? [duplicate] | I wrote a paper arxiv.org/abs/1907.09090 that describes how the pseudo-marginal approach can impute missing data. 400 covariates sounds tough, though, to be completely honest. Depends on what kind of distributions you want to put on the columns, the number of rows, how you program everything. Intractable in your case? ... | Best way to combine MCMC inference with multiple imputation? [duplicate] | I wrote a paper arxiv.org/abs/1907.09090 that describes how the pseudo-marginal approach can impute missing data. 400 covariates sounds tough, though, to be completely honest. Depends on what kind of | Best way to combine MCMC inference with multiple imputation? [duplicate]
I wrote a paper arxiv.org/abs/1907.09090 that describes how the pseudo-marginal approach can impute missing data. 400 covariates sounds tough, though, to be completely honest. Depends on what kind of distributions you want to put on the columns, t... | Best way to combine MCMC inference with multiple imputation? [duplicate]
I wrote a paper arxiv.org/abs/1907.09090 that describes how the pseudo-marginal approach can impute missing data. 400 covariates sounds tough, though, to be completely honest. Depends on what kind of |
41,379 | Feature Interaction and its applications? | Quoted from the OP's link:
5.4 Feature Interaction
When features interact with each other in a prediction model, the prediction cannot be expressed as the sum of the feature effects, because the effect of one feature depends on the value of the other feature. Aristotle's predicate "The whole is greater than the sum of... | Feature Interaction and its applications? | Quoted from the OP's link:
5.4 Feature Interaction
When features interact with each other in a prediction model, the prediction cannot be expressed as the sum of the feature effects, because the effe | Feature Interaction and its applications?
Quoted from the OP's link:
5.4 Feature Interaction
When features interact with each other in a prediction model, the prediction cannot be expressed as the sum of the feature effects, because the effect of one feature depends on the value of the other feature. Aristotle's predi... | Feature Interaction and its applications?
Quoted from the OP's link:
5.4 Feature Interaction
When features interact with each other in a prediction model, the prediction cannot be expressed as the sum of the feature effects, because the effe |
41,380 | Feature Interaction and its applications? | Feature interaction seems to be just new (machine learning?) terminology for plain old interaction. As such there is already many posts at this site, see this list. | Feature Interaction and its applications? | Feature interaction seems to be just new (machine learning?) terminology for plain old interaction. As such there is already many posts at this site, see this list. | Feature Interaction and its applications?
Feature interaction seems to be just new (machine learning?) terminology for plain old interaction. As such there is already many posts at this site, see this list. | Feature Interaction and its applications?
Feature interaction seems to be just new (machine learning?) terminology for plain old interaction. As such there is already many posts at this site, see this list. |
41,381 | If $X_n - \mu = O_p(a_n)$ does that imply that $X_n^{-1} - \mu^{-1} = O_p(a_n)$? | You mention convergence in probability, but note that $X_n - \mu = O_p(a_n)$ does not imply that $\frac{X_n - \mu}{a_n}$ converges in probability to $0$. Wikipedia has the relevant definition.
The implication does not hold. As a counterexample, suppose $\mu = 1$, every $a_n = 1$, and $P(X_n = \frac{1}{n}) = 1$.
Then $P... | If $X_n - \mu = O_p(a_n)$ does that imply that $X_n^{-1} - \mu^{-1} = O_p(a_n)$? | You mention convergence in probability, but note that $X_n - \mu = O_p(a_n)$ does not imply that $\frac{X_n - \mu}{a_n}$ converges in probability to $0$. Wikipedia has the relevant definition.
The imp | If $X_n - \mu = O_p(a_n)$ does that imply that $X_n^{-1} - \mu^{-1} = O_p(a_n)$?
You mention convergence in probability, but note that $X_n - \mu = O_p(a_n)$ does not imply that $\frac{X_n - \mu}{a_n}$ converges in probability to $0$. Wikipedia has the relevant definition.
The implication does not hold. As a counterexa... | If $X_n - \mu = O_p(a_n)$ does that imply that $X_n^{-1} - \mu^{-1} = O_p(a_n)$?
You mention convergence in probability, but note that $X_n - \mu = O_p(a_n)$ does not imply that $\frac{X_n - \mu}{a_n}$ converges in probability to $0$. Wikipedia has the relevant definition.
The imp |
41,382 | If $X_n - \mu = O_p(a_n)$ does that imply that $X_n^{-1} - \mu^{-1} = O_p(a_n)$? | Your question relates to the continuous mapping theorem which states
$$X_n \xrightarrow[]{p} a \implies g(X_n) \xrightarrow[]{p} g(a)$$
But this convergence in probability relates to small $o$ notation and not big $O$. | If $X_n - \mu = O_p(a_n)$ does that imply that $X_n^{-1} - \mu^{-1} = O_p(a_n)$? | Your question relates to the continuous mapping theorem which states
$$X_n \xrightarrow[]{p} a \implies g(X_n) \xrightarrow[]{p} g(a)$$
But this convergence in probability relates to small $o$ notatio | If $X_n - \mu = O_p(a_n)$ does that imply that $X_n^{-1} - \mu^{-1} = O_p(a_n)$?
Your question relates to the continuous mapping theorem which states
$$X_n \xrightarrow[]{p} a \implies g(X_n) \xrightarrow[]{p} g(a)$$
But this convergence in probability relates to small $o$ notation and not big $O$. | If $X_n - \mu = O_p(a_n)$ does that imply that $X_n^{-1} - \mu^{-1} = O_p(a_n)$?
Your question relates to the continuous mapping theorem which states
$$X_n \xrightarrow[]{p} a \implies g(X_n) \xrightarrow[]{p} g(a)$$
But this convergence in probability relates to small $o$ notatio |
41,383 | Normalized Cross Entropy | First note that the denominator does not depend on the model, so it is only a linear transform of the LLH.
Unless your model is worse than predicting a constant, the denominator should be higher than the numerator, so it is usually between 0 and 1
Typically, when the label is difficult to predict accurately, the LLH is... | Normalized Cross Entropy | First note that the denominator does not depend on the model, so it is only a linear transform of the LLH.
Unless your model is worse than predicting a constant, the denominator should be higher than | Normalized Cross Entropy
First note that the denominator does not depend on the model, so it is only a linear transform of the LLH.
Unless your model is worse than predicting a constant, the denominator should be higher than the numerator, so it is usually between 0 and 1
Typically, when the label is difficult to predi... | Normalized Cross Entropy
First note that the denominator does not depend on the model, so it is only a linear transform of the LLH.
Unless your model is worse than predicting a constant, the denominator should be higher than |
41,384 | Normalized Cross Entropy | I think what the author meant was that the denominator (log loss from the background CTR) will be close to 0 when the background CTR p is close to either 0 or 1. This can be easily verified by plotting a graph. It does not look like the sentence was referring to the numerator. | Normalized Cross Entropy | I think what the author meant was that the denominator (log loss from the background CTR) will be close to 0 when the background CTR p is close to either 0 or 1. This can be easily verified by plottin | Normalized Cross Entropy
I think what the author meant was that the denominator (log loss from the background CTR) will be close to 0 when the background CTR p is close to either 0 or 1. This can be easily verified by plotting a graph. It does not look like the sentence was referring to the numerator. | Normalized Cross Entropy
I think what the author meant was that the denominator (log loss from the background CTR) will be close to 0 when the background CTR p is close to either 0 or 1. This can be easily verified by plottin |
41,385 | Normalized Cross Entropy | Simply speaking, one wants to compare his model accuracy versus a 'free' vanilla model (that outputs always the majority class).
How? create a ratio and put the entropy of the free model into denominator.
Why? for extremely unbalanced data with 99% majority class, even 'free' vanilla model claims high accuracy, which i... | Normalized Cross Entropy | Simply speaking, one wants to compare his model accuracy versus a 'free' vanilla model (that outputs always the majority class).
How? create a ratio and put the entropy of the free model into denomina | Normalized Cross Entropy
Simply speaking, one wants to compare his model accuracy versus a 'free' vanilla model (that outputs always the majority class).
How? create a ratio and put the entropy of the free model into denominator.
Why? for extremely unbalanced data with 99% majority class, even 'free' vanilla model clai... | Normalized Cross Entropy
Simply speaking, one wants to compare his model accuracy versus a 'free' vanilla model (that outputs always the majority class).
How? create a ratio and put the entropy of the free model into denomina |
41,386 | Normalized Cross Entropy | the closer p is to 0 or 1, the easier it is to achieve a better log loss (i.e. cross entropy, i.e. numerator).
If almost all of the cases are of one category, then we can always predict a high probability of that category and get a fairly small log loss, since extreme probabilities will be close to almost all of the c... | Normalized Cross Entropy | the closer p is to 0 or 1, the easier it is to achieve a better log loss (i.e. cross entropy, i.e. numerator).
If almost all of the cases are of one category, then we can always predict a high probab | Normalized Cross Entropy
the closer p is to 0 or 1, the easier it is to achieve a better log loss (i.e. cross entropy, i.e. numerator).
If almost all of the cases are of one category, then we can always predict a high probability of that category and get a fairly small log loss, since extreme probabilities will be clo... | Normalized Cross Entropy
the closer p is to 0 or 1, the easier it is to achieve a better log loss (i.e. cross entropy, i.e. numerator).
If almost all of the cases are of one category, then we can always predict a high probab |
41,387 | Terminology: unconditional heteroskedasticity | You can treat it as a shorthand for "heteroskedasticity that does not depend on variables explicitly recognized by the model".
In a more practical sense, it is "heteroskedasticity that does not depend on variables on which we have data".
So "conditional heteroskedasticity" would be "heteroskedasticity that does depend... | Terminology: unconditional heteroskedasticity | You can treat it as a shorthand for "heteroskedasticity that does not depend on variables explicitly recognized by the model".
In a more practical sense, it is "heteroskedasticity that does not depen | Terminology: unconditional heteroskedasticity
You can treat it as a shorthand for "heteroskedasticity that does not depend on variables explicitly recognized by the model".
In a more practical sense, it is "heteroskedasticity that does not depend on variables on which we have data".
So "conditional heteroskedasticity"... | Terminology: unconditional heteroskedasticity
You can treat it as a shorthand for "heteroskedasticity that does not depend on variables explicitly recognized by the model".
In a more practical sense, it is "heteroskedasticity that does not depen |
41,388 | What is the specific issue with using count data for ANOVA tests | Count data cannot really have a normal distribution, except as an approximation in the case of large counts. But that is not the main reason:
Count data do not have constant variance. For the most used model, the Poisson distribution, the variance equals the mean, for many other reasonable models (cluster processes, l... | What is the specific issue with using count data for ANOVA tests | Count data cannot really have a normal distribution, except as an approximation in the case of large counts. But that is not the main reason:
Count data do not have constant variance. For the most us | What is the specific issue with using count data for ANOVA tests
Count data cannot really have a normal distribution, except as an approximation in the case of large counts. But that is not the main reason:
Count data do not have constant variance. For the most used model, the Poisson distribution, the variance equals... | What is the specific issue with using count data for ANOVA tests
Count data cannot really have a normal distribution, except as an approximation in the case of large counts. But that is not the main reason:
Count data do not have constant variance. For the most us |
41,389 | Multiplying vectors by the covariance matrix? | They're not exactly on a line, but yes, they generally follow the main eigenvector because the projected point has the following coordinates (assuming $x$ with dimensions $2\times 1$):$$\Sigma x=\sigma_1u_1u_1^Tx+\sigma_2u_2u_2^Tx=(\sigma_1<u_1,x>)u_1+(\sigma_2<u_2,x>)u_2$$
Here, $u_i$ are eigenvectors, and $\sigma_i$ ... | Multiplying vectors by the covariance matrix? | They're not exactly on a line, but yes, they generally follow the main eigenvector because the projected point has the following coordinates (assuming $x$ with dimensions $2\times 1$):$$\Sigma x=\sigm | Multiplying vectors by the covariance matrix?
They're not exactly on a line, but yes, they generally follow the main eigenvector because the projected point has the following coordinates (assuming $x$ with dimensions $2\times 1$):$$\Sigma x=\sigma_1u_1u_1^Tx+\sigma_2u_2u_2^Tx=(\sigma_1<u_1,x>)u_1+(\sigma_2<u_2,x>)u_2$$... | Multiplying vectors by the covariance matrix?
They're not exactly on a line, but yes, they generally follow the main eigenvector because the projected point has the following coordinates (assuming $x$ with dimensions $2\times 1$):$$\Sigma x=\sigm |
41,390 | Should we center original data if we want to get principal component? | While it is true that your original data can be reconstructed from the principal components, even if you didn't center the data when calculating them, part of what one is usually trying to do in principal components analysis is dimensionality reduction. That is you want to find a subset of the principal components tha... | Should we center original data if we want to get principal component? | While it is true that your original data can be reconstructed from the principal components, even if you didn't center the data when calculating them, part of what one is usually trying to do in princ | Should we center original data if we want to get principal component?
While it is true that your original data can be reconstructed from the principal components, even if you didn't center the data when calculating them, part of what one is usually trying to do in principal components analysis is dimensionality reducti... | Should we center original data if we want to get principal component?
While it is true that your original data can be reconstructed from the principal components, even if you didn't center the data when calculating them, part of what one is usually trying to do in princ |
41,391 | Should we center original data if we want to get principal component? | PCA is done on the centered data matrix in the first place (because $X^TX$ is the (scaled) covariance estimate if $X$ is centered). So, while fitting, $X$ is centered internally. The same mathematical operation takes place while transforming new data points. | Should we center original data if we want to get principal component? | PCA is done on the centered data matrix in the first place (because $X^TX$ is the (scaled) covariance estimate if $X$ is centered). So, while fitting, $X$ is centered internally. The same mathematical | Should we center original data if we want to get principal component?
PCA is done on the centered data matrix in the first place (because $X^TX$ is the (scaled) covariance estimate if $X$ is centered). So, while fitting, $X$ is centered internally. The same mathematical operation takes place while transforming new data... | Should we center original data if we want to get principal component?
PCA is done on the centered data matrix in the first place (because $X^TX$ is the (scaled) covariance estimate if $X$ is centered). So, while fitting, $X$ is centered internally. The same mathematical |
41,392 | When should I do train test split? | Your procedure is correct generally. In a more complex loop, additional operations may include validation, hyper-parameter optimisation, feature selection etc.
Typically, feature extraction follows exploratory data analysis (EDA), where you get to know your data, analyse/summarise it, draw intuitive conclusions. In EDA... | When should I do train test split? | Your procedure is correct generally. In a more complex loop, additional operations may include validation, hyper-parameter optimisation, feature selection etc.
Typically, feature extraction follows ex | When should I do train test split?
Your procedure is correct generally. In a more complex loop, additional operations may include validation, hyper-parameter optimisation, feature selection etc.
Typically, feature extraction follows exploratory data analysis (EDA), where you get to know your data, analyse/summarise it,... | When should I do train test split?
Your procedure is correct generally. In a more complex loop, additional operations may include validation, hyper-parameter optimisation, feature selection etc.
Typically, feature extraction follows ex |
41,393 | Likelihood ratio test for mixed effects model | My first hint is to use lmer from the lme4 package, not lme. When the variance components approach zero it will be more likely to converge without errors, although it may (and should) give a singular fit warning.
My second hint is to simulate $b_i$ with $\sigma_b^2$ not as identically zero, but just very small. | Likelihood ratio test for mixed effects model | My first hint is to use lmer from the lme4 package, not lme. When the variance components approach zero it will be more likely to converge without errors, although it may (and should) give a singular | Likelihood ratio test for mixed effects model
My first hint is to use lmer from the lme4 package, not lme. When the variance components approach zero it will be more likely to converge without errors, although it may (and should) give a singular fit warning.
My second hint is to simulate $b_i$ with $\sigma_b^2$ not as ... | Likelihood ratio test for mixed effects model
My first hint is to use lmer from the lme4 package, not lme. When the variance components approach zero it will be more likely to converge without errors, although it may (and should) give a singular |
41,394 | Batch normalization and the need for bias in neural networks | Check your software, but broadly the answer to your question is: yes, using batch normalization obviates the need for a bias in the preceding linear layer. Your question does a good job of laying out where you are confused, so let me speak to it: the shift term in batch normalization is also a vector, for instance the ... | Batch normalization and the need for bias in neural networks | Check your software, but broadly the answer to your question is: yes, using batch normalization obviates the need for a bias in the preceding linear layer. Your question does a good job of laying out | Batch normalization and the need for bias in neural networks
Check your software, but broadly the answer to your question is: yes, using batch normalization obviates the need for a bias in the preceding linear layer. Your question does a good job of laying out where you are confused, so let me speak to it: the shift te... | Batch normalization and the need for bias in neural networks
Check your software, but broadly the answer to your question is: yes, using batch normalization obviates the need for a bias in the preceding linear layer. Your question does a good job of laying out |
41,395 | Batch normalization and the need for bias in neural networks | Here's a quote from the original BN paper that should answer your question:
i.e. each activation is shifted by its own shift parameter (beta). So yes, the batch normalization eliminates the need for a bias vector.
Just a side note: in Pytorch the BN's betas are all initialized to zero by default, whereas the biases in... | Batch normalization and the need for bias in neural networks | Here's a quote from the original BN paper that should answer your question:
i.e. each activation is shifted by its own shift parameter (beta). So yes, the batch normalization eliminates the need for | Batch normalization and the need for bias in neural networks
Here's a quote from the original BN paper that should answer your question:
i.e. each activation is shifted by its own shift parameter (beta). So yes, the batch normalization eliminates the need for a bias vector.
Just a side note: in Pytorch the BN's betas ... | Batch normalization and the need for bias in neural networks
Here's a quote from the original BN paper that should answer your question:
i.e. each activation is shifted by its own shift parameter (beta). So yes, the batch normalization eliminates the need for |
41,396 | Is it better to compute Average Precision using the trapezoidal rule or the rectangle method? | UPDATE
This journal article explains why linear interpolation is both "too optimist" and is also "incorrect," due to the non-linear properties of the Precision-Recall curve: https://www.biostat.wisc.edu/~page/rocpr.pdf
Due to the non-linear nature of the precision-response curve, linear interpolation results in errone... | Is it better to compute Average Precision using the trapezoidal rule or the rectangle method? | UPDATE
This journal article explains why linear interpolation is both "too optimist" and is also "incorrect," due to the non-linear properties of the Precision-Recall curve: https://www.biostat.wisc.e | Is it better to compute Average Precision using the trapezoidal rule or the rectangle method?
UPDATE
This journal article explains why linear interpolation is both "too optimist" and is also "incorrect," due to the non-linear properties of the Precision-Recall curve: https://www.biostat.wisc.edu/~page/rocpr.pdf
Due to... | Is it better to compute Average Precision using the trapezoidal rule or the rectangle method?
UPDATE
This journal article explains why linear interpolation is both "too optimist" and is also "incorrect," due to the non-linear properties of the Precision-Recall curve: https://www.biostat.wisc.e |
41,397 | Is it better to compute Average Precision using the trapezoidal rule or the rectangle method? | For a piecewise linear function, using the trapezoidal rule with endpoints on each of the ends of the "pieces" will yield the exact area under the curve --- i.e., it is equivalent to integration under the curve. This occurs when the trapezoids correspond exactly with the lines in the piecewise linear function. (Of co... | Is it better to compute Average Precision using the trapezoidal rule or the rectangle method? | For a piecewise linear function, using the trapezoidal rule with endpoints on each of the ends of the "pieces" will yield the exact area under the curve --- i.e., it is equivalent to integration under | Is it better to compute Average Precision using the trapezoidal rule or the rectangle method?
For a piecewise linear function, using the trapezoidal rule with endpoints on each of the ends of the "pieces" will yield the exact area under the curve --- i.e., it is equivalent to integration under the curve. This occurs w... | Is it better to compute Average Precision using the trapezoidal rule or the rectangle method?
For a piecewise linear function, using the trapezoidal rule with endpoints on each of the ends of the "pieces" will yield the exact area under the curve --- i.e., it is equivalent to integration under |
41,398 | Does sample size affect choice between fixed and random effect | Some care is needed when talking about samples size in the context of mixed models.
First, there is the overall (total) sample size, let's call it $N$
Then there is the number of subjects (cities in the case of your example), let's call it $n$
Then there is the number of observations within each subject (city). In obse... | Does sample size affect choice between fixed and random effect | Some care is needed when talking about samples size in the context of mixed models.
First, there is the overall (total) sample size, let's call it $N$
Then there is the number of subjects (cities in t | Does sample size affect choice between fixed and random effect
Some care is needed when talking about samples size in the context of mixed models.
First, there is the overall (total) sample size, let's call it $N$
Then there is the number of subjects (cities in the case of your example), let's call it $n$
Then there is... | Does sample size affect choice between fixed and random effect
Some care is needed when talking about samples size in the context of mixed models.
First, there is the overall (total) sample size, let's call it $N$
Then there is the number of subjects (cities in t |
41,399 | Demonstrating complete-pooling, no-pooling, and partial-pooling regression in R | So I went ahead and generated some data to demonstrate that these work as expected.
library(tidyverse)
library(lme4)
if(!require(modelr)){
install.packages('modelr')
}
library(modelr)
pop_mean<-10
n_groups<-4
groups<-gl(n_groups, 20)
Z<-model.matrix(~groups-1)
group_means<-rnorm(n_groups, 0, 2.5)
y<- pop_mean + Z%... | Demonstrating complete-pooling, no-pooling, and partial-pooling regression in R | So I went ahead and generated some data to demonstrate that these work as expected.
library(tidyverse)
library(lme4)
if(!require(modelr)){
install.packages('modelr')
}
library(modelr)
pop_mean<-10 | Demonstrating complete-pooling, no-pooling, and partial-pooling regression in R
So I went ahead and generated some data to demonstrate that these work as expected.
library(tidyverse)
library(lme4)
if(!require(modelr)){
install.packages('modelr')
}
library(modelr)
pop_mean<-10
n_groups<-4
groups<-gl(n_groups, 20)
Z<... | Demonstrating complete-pooling, no-pooling, and partial-pooling regression in R
So I went ahead and generated some data to demonstrate that these work as expected.
library(tidyverse)
library(lme4)
if(!require(modelr)){
install.packages('modelr')
}
library(modelr)
pop_mean<-10 |
41,400 | Why does the posterior predictive distribution involve an integral? | You don't exactly know $\omega$ but you have some idea, a distribution based on the previous data you've seen, which is described by $p(\omega|X,Y)$. If you had a constant $\omega_0$, the posterior predictive distribution would be $p(y^*|x^*,\omega_0)$, but the integral is basically an expected value (i.e. a weighted a... | Why does the posterior predictive distribution involve an integral? | You don't exactly know $\omega$ but you have some idea, a distribution based on the previous data you've seen, which is described by $p(\omega|X,Y)$. If you had a constant $\omega_0$, the posterior pr | Why does the posterior predictive distribution involve an integral?
You don't exactly know $\omega$ but you have some idea, a distribution based on the previous data you've seen, which is described by $p(\omega|X,Y)$. If you had a constant $\omega_0$, the posterior predictive distribution would be $p(y^*|x^*,\omega_0)$... | Why does the posterior predictive distribution involve an integral?
You don't exactly know $\omega$ but you have some idea, a distribution based on the previous data you've seen, which is described by $p(\omega|X,Y)$. If you had a constant $\omega_0$, the posterior pr |
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