idx int64 1 56k | question stringlengths 15 155 | answer stringlengths 2 29.2k ⌀ | question_cut stringlengths 15 100 | answer_cut stringlengths 2 200 ⌀ | conversation stringlengths 47 29.3k | conversation_cut stringlengths 47 301 |
|---|---|---|---|---|---|---|
37,201 | Mixed effects model or mixed design ANOVA in R | So I've done a lot of reading and chatting to people and I have a solution.
My experimental design is a split plot design, which is quite different from a nested or hierarchical design. I was originally confusing the terms. As Robert correctly states in his answer, what is needed is a mixed effects model. Thus:
Fi... | Mixed effects model or mixed design ANOVA in R | So I've done a lot of reading and chatting to people and I have a solution.
My experimental design is a split plot design, which is quite different from a nested or hierarchical design. I was origi | Mixed effects model or mixed design ANOVA in R
So I've done a lot of reading and chatting to people and I have a solution.
My experimental design is a split plot design, which is quite different from a nested or hierarchical design. I was originally confusing the terms. As Robert correctly states in his answer, wha... | Mixed effects model or mixed design ANOVA in R
So I've done a lot of reading and chatting to people and I have a solution.
My experimental design is a split plot design, which is quite different from a nested or hierarchical design. I was origi |
37,202 | Mixed effects model or mixed design ANOVA in R | My suggestion is to use a mixed effects model with
Treatment 1 and 2 as factors (fixed effects)
Year as an interval-scaled factor
Block as a random factor
Q: Should year be treated as a random effect?
A: Depends on what you expect based on your theory. I suppose the number of species might increase over time, and t... | Mixed effects model or mixed design ANOVA in R | My suggestion is to use a mixed effects model with
Treatment 1 and 2 as factors (fixed effects)
Year as an interval-scaled factor
Block as a random factor
Q: Should year be treated as a random effe | Mixed effects model or mixed design ANOVA in R
My suggestion is to use a mixed effects model with
Treatment 1 and 2 as factors (fixed effects)
Year as an interval-scaled factor
Block as a random factor
Q: Should year be treated as a random effect?
A: Depends on what you expect based on your theory. I suppose the nu... | Mixed effects model or mixed design ANOVA in R
My suggestion is to use a mixed effects model with
Treatment 1 and 2 as factors (fixed effects)
Year as an interval-scaled factor
Block as a random factor
Q: Should year be treated as a random effe |
37,203 | Bootstrap size and probability of drawing distinct observations | EDIT after seeing your code for the simulation
I think you did not consider the fact that a certain number can also occurr more than once within one sample. After accounting for that, we get the same results. Here is your modified code:
fx02<-function(ll,n,k){
a1<-matrix(0,n,2)
samp1 <- sample(1:n, k, replace=TRUE)... | Bootstrap size and probability of drawing distinct observations | EDIT after seeing your code for the simulation
I think you did not consider the fact that a certain number can also occurr more than once within one sample. After accounting for that, we get the same | Bootstrap size and probability of drawing distinct observations
EDIT after seeing your code for the simulation
I think you did not consider the fact that a certain number can also occurr more than once within one sample. After accounting for that, we get the same results. Here is your modified code:
fx02<-function(ll,n... | Bootstrap size and probability of drawing distinct observations
EDIT after seeing your code for the simulation
I think you did not consider the fact that a certain number can also occurr more than once within one sample. After accounting for that, we get the same |
37,204 | Pattern recognition techniques in spatial or spatio-temporal data? | I don't have a cookbook answer but here are some initial thoughts:
I think that you idea about Frobenius norm is not unreasonable and can serve as a first safe bet indeed. I think you can use quite a few different metrics for matrix distances but I will propose two based on you data's nature:
Given that what you are ... | Pattern recognition techniques in spatial or spatio-temporal data? | I don't have a cookbook answer but here are some initial thoughts:
I think that you idea about Frobenius norm is not unreasonable and can serve as a first safe bet indeed. I think you can use quite a | Pattern recognition techniques in spatial or spatio-temporal data?
I don't have a cookbook answer but here are some initial thoughts:
I think that you idea about Frobenius norm is not unreasonable and can serve as a first safe bet indeed. I think you can use quite a few different metrics for matrix distances but I wil... | Pattern recognition techniques in spatial or spatio-temporal data?
I don't have a cookbook answer but here are some initial thoughts:
I think that you idea about Frobenius norm is not unreasonable and can serve as a first safe bet indeed. I think you can use quite a |
37,205 | When and how to use weights for sequence analysis in social science? | I assume that you are using sampling weights to correct for representativity bias. Please note that some "data providers" require you to use the weights in your publications.
In my opinion, you should always use weights for descriptive analysis in order to get unbiased results. I think that there are more consensus for... | When and how to use weights for sequence analysis in social science? | I assume that you are using sampling weights to correct for representativity bias. Please note that some "data providers" require you to use the weights in your publications.
In my opinion, you should | When and how to use weights for sequence analysis in social science?
I assume that you are using sampling weights to correct for representativity bias. Please note that some "data providers" require you to use the weights in your publications.
In my opinion, you should always use weights for descriptive analysis in ord... | When and how to use weights for sequence analysis in social science?
I assume that you are using sampling weights to correct for representativity bias. Please note that some "data providers" require you to use the weights in your publications.
In my opinion, you should |
37,206 | Implementation of the cross validiation | I realize this is a somewhat older question now but perhaps this can shed some light. There are several things wrong with your code.
The code as it stands is NOT reproducible. At no point is h defined which is the exact parameter you wish to tune.
You aren't iterating over different bandwidths. If you are using cro... | Implementation of the cross validiation | I realize this is a somewhat older question now but perhaps this can shed some light. There are several things wrong with your code.
The code as it stands is NOT reproducible. At no point is h defi | Implementation of the cross validiation
I realize this is a somewhat older question now but perhaps this can shed some light. There are several things wrong with your code.
The code as it stands is NOT reproducible. At no point is h defined which is the exact parameter you wish to tune.
You aren't iterating over dif... | Implementation of the cross validiation
I realize this is a somewhat older question now but perhaps this can shed some light. There are several things wrong with your code.
The code as it stands is NOT reproducible. At no point is h defi |
37,207 | Given that one can sample $X \sim f(x)$, is there an easy way to sample $Y \sim k \cdot f(g(y))$ (such as $k \cdot f(e^y)$)? | If the inverse of $g(y)$, i.e. $g^{-1}(x)$, is relatively linear for the most probable values drawn from $f(x)$, then the following method should have a reasonable acceptance rate. I'm assuming $g(y)$ is strictly monotonic - in order that it have an inverse.
This is Metropolis-Hastings. We make a proposal, and then a... | Given that one can sample $X \sim f(x)$, is there an easy way to sample $Y \sim k \cdot f(g(y))$ (su | If the inverse of $g(y)$, i.e. $g^{-1}(x)$, is relatively linear for the most probable values drawn from $f(x)$, then the following method should have a reasonable acceptance rate. I'm assuming $g(y) | Given that one can sample $X \sim f(x)$, is there an easy way to sample $Y \sim k \cdot f(g(y))$ (such as $k \cdot f(e^y)$)?
If the inverse of $g(y)$, i.e. $g^{-1}(x)$, is relatively linear for the most probable values drawn from $f(x)$, then the following method should have a reasonable acceptance rate. I'm assuming ... | Given that one can sample $X \sim f(x)$, is there an easy way to sample $Y \sim k \cdot f(g(y))$ (su
If the inverse of $g(y)$, i.e. $g^{-1}(x)$, is relatively linear for the most probable values drawn from $f(x)$, then the following method should have a reasonable acceptance rate. I'm assuming $g(y) |
37,208 | Does every log-linear model have a perfectly equivalent logistic regression? | The answer is 'no'. The loglinear model is more general than the logistic regression model. See Fienberg, 1980, Analysis of Cross-Classified Categorical Data, section 6.2 on how to specify a loglinear model so that it corresponds to logistic regression.
Actually the reverse is true: If all variables are categorical, t... | Does every log-linear model have a perfectly equivalent logistic regression? | The answer is 'no'. The loglinear model is more general than the logistic regression model. See Fienberg, 1980, Analysis of Cross-Classified Categorical Data, section 6.2 on how to specify a loglinear | Does every log-linear model have a perfectly equivalent logistic regression?
The answer is 'no'. The loglinear model is more general than the logistic regression model. See Fienberg, 1980, Analysis of Cross-Classified Categorical Data, section 6.2 on how to specify a loglinear model so that it corresponds to logistic r... | Does every log-linear model have a perfectly equivalent logistic regression?
The answer is 'no'. The loglinear model is more general than the logistic regression model. See Fienberg, 1980, Analysis of Cross-Classified Categorical Data, section 6.2 on how to specify a loglinear |
37,209 | regression with non-independent data | I assume what you have in mind is score as the response and then some player attributes as the predictors. E.g find out if blonds score higher.
Why not perform the regression with game as your sample unit. A game of N points must distribute those points between A and B so you can just take player A score for each game... | regression with non-independent data | I assume what you have in mind is score as the response and then some player attributes as the predictors. E.g find out if blonds score higher.
Why not perform the regression with game as your sample | regression with non-independent data
I assume what you have in mind is score as the response and then some player attributes as the predictors. E.g find out if blonds score higher.
Why not perform the regression with game as your sample unit. A game of N points must distribute those points between A and B so you can j... | regression with non-independent data
I assume what you have in mind is score as the response and then some player attributes as the predictors. E.g find out if blonds score higher.
Why not perform the regression with game as your sample |
37,210 | regression with non-independent data | You have a system of simultaneous equations to deal with, which should have been talked about in your econometrics class (you are an economist, right?) You will be estimating the system using 2SLS or 3SLS methods, provided that you have decent exogeneous variables that affect only one of the outcomes, i.e., demographic... | regression with non-independent data | You have a system of simultaneous equations to deal with, which should have been talked about in your econometrics class (you are an economist, right?) You will be estimating the system using 2SLS or | regression with non-independent data
You have a system of simultaneous equations to deal with, which should have been talked about in your econometrics class (you are an economist, right?) You will be estimating the system using 2SLS or 3SLS methods, provided that you have decent exogeneous variables that affect only o... | regression with non-independent data
You have a system of simultaneous equations to deal with, which should have been talked about in your econometrics class (you are an economist, right?) You will be estimating the system using 2SLS or |
37,211 | regression with non-independent data | Model the actions of the players instead of the payoffs. That is, predict the probability that a player selects to cooperate at a particular round as a function of previous rounds (if the game is repeated in your setting) and your covariates. I think this makes more causal sense, as the players actually select the acti... | regression with non-independent data | Model the actions of the players instead of the payoffs. That is, predict the probability that a player selects to cooperate at a particular round as a function of previous rounds (if the game is repe | regression with non-independent data
Model the actions of the players instead of the payoffs. That is, predict the probability that a player selects to cooperate at a particular round as a function of previous rounds (if the game is repeated in your setting) and your covariates. I think this makes more causal sense, as... | regression with non-independent data
Model the actions of the players instead of the payoffs. That is, predict the probability that a player selects to cooperate at a particular round as a function of previous rounds (if the game is repe |
37,212 | Evaluate $\lim_{n \to \infty} \sum_{j=0}^{n}{{j+n-1} \choose j}\frac{1}{2^{j+n}}$ | Another way is to use the combinatorial identity $\displaystyle \sum_{j=0}^m \binom{m+j}{j} 2^{m-j}= 4^m$. (See end of post for a proof.)
Dividing by $4^m$, setting $m = n-1$, and extracting the last term, the OP's sum becomes $$ \binom{2n-1}{n} \frac{1}{4^n} + \frac{1}{2} \sum_{j=0}^{n-1}{{j+n-1} \choose j}\frac{1}{2... | Evaluate $\lim_{n \to \infty} \sum_{j=0}^{n}{{j+n-1} \choose j}\frac{1}{2^{j+n}}$ | Another way is to use the combinatorial identity $\displaystyle \sum_{j=0}^m \binom{m+j}{j} 2^{m-j}= 4^m$. (See end of post for a proof.)
Dividing by $4^m$, setting $m = n-1$, and extracting the last | Evaluate $\lim_{n \to \infty} \sum_{j=0}^{n}{{j+n-1} \choose j}\frac{1}{2^{j+n}}$
Another way is to use the combinatorial identity $\displaystyle \sum_{j=0}^m \binom{m+j}{j} 2^{m-j}= 4^m$. (See end of post for a proof.)
Dividing by $4^m$, setting $m = n-1$, and extracting the last term, the OP's sum becomes $$ \binom{... | Evaluate $\lim_{n \to \infty} \sum_{j=0}^{n}{{j+n-1} \choose j}\frac{1}{2^{j+n}}$
Another way is to use the combinatorial identity $\displaystyle \sum_{j=0}^m \binom{m+j}{j} 2^{m-j}= 4^m$. (See end of post for a proof.)
Dividing by $4^m$, setting $m = n-1$, and extracting the last |
37,213 | Post hoc test in a 2x3 mixed design ANOVA using SPSS? | Answer edited to implement encouraging and constructive comment by @Ferdi
I would like to:
provide an answer with a full contained script
mention one can also test more general custom contrasts using the /TEST command
argue this is necessary in some cases (ie the EMMEANS COMPARE combination is not enough)
I assume to... | Post hoc test in a 2x3 mixed design ANOVA using SPSS? | Answer edited to implement encouraging and constructive comment by @Ferdi
I would like to:
provide an answer with a full contained script
mention one can also test more general custom contrasts using | Post hoc test in a 2x3 mixed design ANOVA using SPSS?
Answer edited to implement encouraging and constructive comment by @Ferdi
I would like to:
provide an answer with a full contained script
mention one can also test more general custom contrasts using the /TEST command
argue this is necessary in some cases (ie the E... | Post hoc test in a 2x3 mixed design ANOVA using SPSS?
Answer edited to implement encouraging and constructive comment by @Ferdi
I would like to:
provide an answer with a full contained script
mention one can also test more general custom contrasts using |
37,214 | Post hoc test in a 2x3 mixed design ANOVA using SPSS? | I don't know SPSS syntax particularly well, but, if I understand your situation correctly, the significant interaction means that, in order to adequately assess the significance of your main effects, you'll need to do separate analyses. I think the best way to proceed is to do separate repeated measure analyses for eac... | Post hoc test in a 2x3 mixed design ANOVA using SPSS? | I don't know SPSS syntax particularly well, but, if I understand your situation correctly, the significant interaction means that, in order to adequately assess the significance of your main effects, | Post hoc test in a 2x3 mixed design ANOVA using SPSS?
I don't know SPSS syntax particularly well, but, if I understand your situation correctly, the significant interaction means that, in order to adequately assess the significance of your main effects, you'll need to do separate analyses. I think the best way to proce... | Post hoc test in a 2x3 mixed design ANOVA using SPSS?
I don't know SPSS syntax particularly well, but, if I understand your situation correctly, the significant interaction means that, in order to adequately assess the significance of your main effects, |
37,215 | Post hoc test in a 2x3 mixed design ANOVA using SPSS? | In short. There is no globally accepted convention for these situations. Some will use Bonferroni corrections. Some will force the Tukey HSD framework to dance for them (e.g. Maxwell & Delaney). In contrast...
COMPARE(time) ADJ(BONFERRONI)", just after "/EMMEANS=TABLES(newgroup*time)
... does seem to use the Bonfe... | Post hoc test in a 2x3 mixed design ANOVA using SPSS? | In short. There is no globally accepted convention for these situations. Some will use Bonferroni corrections. Some will force the Tukey HSD framework to dance for them (e.g. Maxwell & Delaney). I | Post hoc test in a 2x3 mixed design ANOVA using SPSS?
In short. There is no globally accepted convention for these situations. Some will use Bonferroni corrections. Some will force the Tukey HSD framework to dance for them (e.g. Maxwell & Delaney). In contrast...
COMPARE(time) ADJ(BONFERRONI)", just after "/EMMEANS... | Post hoc test in a 2x3 mixed design ANOVA using SPSS?
In short. There is no globally accepted convention for these situations. Some will use Bonferroni corrections. Some will force the Tukey HSD framework to dance for them (e.g. Maxwell & Delaney). I |
37,216 | LARS - LASSO with weights | The glmnet Package solves the lasso problem using coordinate descent. It also provides features for adding in weights | LARS - LASSO with weights | The glmnet Package solves the lasso problem using coordinate descent. It also provides features for adding in weights | LARS - LASSO with weights
The glmnet Package solves the lasso problem using coordinate descent. It also provides features for adding in weights | LARS - LASSO with weights
The glmnet Package solves the lasso problem using coordinate descent. It also provides features for adding in weights |
37,217 | Why are there so many random generators in R? | One case where this RNG cornucopia is handy is when you're rewriting or comparing software that rely on different RNGs. One example might be porting R code to C++. You want to pin down why you're getting different results and it helps to hold as many things constant as possible. | Why are there so many random generators in R? | One case where this RNG cornucopia is handy is when you're rewriting or comparing software that rely on different RNGs. One example might be porting R code to C++. You want to pin down why you're gett | Why are there so many random generators in R?
One case where this RNG cornucopia is handy is when you're rewriting or comparing software that rely on different RNGs. One example might be porting R code to C++. You want to pin down why you're getting different results and it helps to hold as many things constant as poss... | Why are there so many random generators in R?
One case where this RNG cornucopia is handy is when you're rewriting or comparing software that rely on different RNGs. One example might be porting R code to C++. You want to pin down why you're gett |
37,218 | Variables for post-stratification weights? | It is an interesting twist to find a case where the demographic data will be seen as less reliable as the behavioral data. There isn't much good advice on how to select the calibration variables, other than they should correlate with both the (non-)response process and the variables of interest. The reasoning behind th... | Variables for post-stratification weights? | It is an interesting twist to find a case where the demographic data will be seen as less reliable as the behavioral data. There isn't much good advice on how to select the calibration variables, othe | Variables for post-stratification weights?
It is an interesting twist to find a case where the demographic data will be seen as less reliable as the behavioral data. There isn't much good advice on how to select the calibration variables, other than they should correlate with both the (non-)response process and the var... | Variables for post-stratification weights?
It is an interesting twist to find a case where the demographic data will be seen as less reliable as the behavioral data. There isn't much good advice on how to select the calibration variables, othe |
37,219 | Can you reproduce this chi-squared test result? | It seems to me that there are three things wrong with the conclusion.
First, as @caracal said: They are reporting "significance" using a one-tailed test, without saying that they are doing so. Most people, I think, recommend using two-tailed tests almost always. Certainly it is not ok to use a one-tail test without sa... | Can you reproduce this chi-squared test result? | It seems to me that there are three things wrong with the conclusion.
First, as @caracal said: They are reporting "significance" using a one-tailed test, without saying that they are doing so. Most p | Can you reproduce this chi-squared test result?
It seems to me that there are three things wrong with the conclusion.
First, as @caracal said: They are reporting "significance" using a one-tailed test, without saying that they are doing so. Most people, I think, recommend using two-tailed tests almost always. Certainl... | Can you reproduce this chi-squared test result?
It seems to me that there are three things wrong with the conclusion.
First, as @caracal said: They are reporting "significance" using a one-tailed test, without saying that they are doing so. Most p |
37,220 | Can you reproduce this chi-squared test result? | A Fisher exact test on the given table gives, per this code
actual <- c(rep("Y", 32), rep("N", 19), rep("Y", 261), rep("N", 274))
det <- c(rep("Y", 51), rep("N", 535))
table(det,actual)
fisher.test(det,actual)
a p = 0.08 | Can you reproduce this chi-squared test result? | A Fisher exact test on the given table gives, per this code
actual <- c(rep("Y", 32), rep("N", 19), rep("Y", 261), rep("N", 274))
det <- c(rep("Y", 51), rep("N", 535))
table(det,actual)
fisher.test(d | Can you reproduce this chi-squared test result?
A Fisher exact test on the given table gives, per this code
actual <- c(rep("Y", 32), rep("N", 19), rep("Y", 261), rep("N", 274))
det <- c(rep("Y", 51), rep("N", 535))
table(det,actual)
fisher.test(det,actual)
a p = 0.08 | Can you reproduce this chi-squared test result?
A Fisher exact test on the given table gives, per this code
actual <- c(rep("Y", 32), rep("N", 19), rep("Y", 261), rep("N", 274))
det <- c(rep("Y", 51), rep("N", 535))
table(det,actual)
fisher.test(d |
37,221 | Is it possible to interpret standardized beta coefficients for quantile regression? | Yes, that is the interpretation. One way in which you can see this is by predicting the median for different values of your standardized, each 1 unit (in this case standard deviation) appart. Than you can look at how much these predicted medians differ, and you will see that that is exactly the same number as your stan... | Is it possible to interpret standardized beta coefficients for quantile regression? | Yes, that is the interpretation. One way in which you can see this is by predicting the median for different values of your standardized, each 1 unit (in this case standard deviation) appart. Than you | Is it possible to interpret standardized beta coefficients for quantile regression?
Yes, that is the interpretation. One way in which you can see this is by predicting the median for different values of your standardized, each 1 unit (in this case standard deviation) appart. Than you can look at how much these predicte... | Is it possible to interpret standardized beta coefficients for quantile regression?
Yes, that is the interpretation. One way in which you can see this is by predicting the median for different values of your standardized, each 1 unit (in this case standard deviation) appart. Than you |
37,222 | Combination of variational methods and empirical Bayes | One way of deciding how to run variational MLE is to look at how the experts do it.
In Blei's LDA code (http://www.cs.princeton.edu/~blei/lda-c/lda-c-dist.tgz), within the "run_em" function, the "lda_inference" function (inside "doc_e_step") repeatedly maximizes with respect to each $q$ distribution until convergence. ... | Combination of variational methods and empirical Bayes | One way of deciding how to run variational MLE is to look at how the experts do it.
In Blei's LDA code (http://www.cs.princeton.edu/~blei/lda-c/lda-c-dist.tgz), within the "run_em" function, the "lda_ | Combination of variational methods and empirical Bayes
One way of deciding how to run variational MLE is to look at how the experts do it.
In Blei's LDA code (http://www.cs.princeton.edu/~blei/lda-c/lda-c-dist.tgz), within the "run_em" function, the "lda_inference" function (inside "doc_e_step") repeatedly maximizes wi... | Combination of variational methods and empirical Bayes
One way of deciding how to run variational MLE is to look at how the experts do it.
In Blei's LDA code (http://www.cs.princeton.edu/~blei/lda-c/lda-c-dist.tgz), within the "run_em" function, the "lda_ |
37,223 | Combination of variational methods and empirical Bayes | Generally, in empirical Bayes, you maximise the marginal likelihood (also called model evidence, or the normalising constant of the posterior) with respect to the hyperparameters and plug this estimate of the hyperparameters into the posterior.
In Casella (2001) there is a derivation of an EM for empirical Bayes. Casel... | Combination of variational methods and empirical Bayes | Generally, in empirical Bayes, you maximise the marginal likelihood (also called model evidence, or the normalising constant of the posterior) with respect to the hyperparameters and plug this estimat | Combination of variational methods and empirical Bayes
Generally, in empirical Bayes, you maximise the marginal likelihood (also called model evidence, or the normalising constant of the posterior) with respect to the hyperparameters and plug this estimate of the hyperparameters into the posterior.
In Casella (2001) th... | Combination of variational methods and empirical Bayes
Generally, in empirical Bayes, you maximise the marginal likelihood (also called model evidence, or the normalising constant of the posterior) with respect to the hyperparameters and plug this estimat |
37,224 | Getting probabilities over 1 in positive and unlabeled learning | I tried to follow authors' instructions with a very simple test case. Here is the R code that I used.
set.seed(123)
# Create the data according to authors' notations.
# For the first 100 observations y = 1, and for the last 100 y = 0.
# Only the first 25 obersvations are labelled, according to their
# "chosen completel... | Getting probabilities over 1 in positive and unlabeled learning | I tried to follow authors' instructions with a very simple test case. Here is the R code that I used.
set.seed(123)
# Create the data according to authors' notations.
# For the first 100 observations | Getting probabilities over 1 in positive and unlabeled learning
I tried to follow authors' instructions with a very simple test case. Here is the R code that I used.
set.seed(123)
# Create the data according to authors' notations.
# For the first 100 observations y = 1, and for the last 100 y = 0.
# Only the first 25 o... | Getting probabilities over 1 in positive and unlabeled learning
I tried to follow authors' instructions with a very simple test case. Here is the R code that I used.
set.seed(123)
# Create the data according to authors' notations.
# For the first 100 observations |
37,225 | How to generate nice summary table? | If you have the R package Hmisc and a working latex installation you can do:
x=rnorm(1000)
y=rnorm(1000)
lm1=lm(y~x)
slm1=summary(lm1)
latex(slm1)
It works the same with datasets,
latex(summary(cars)) | How to generate nice summary table? | If you have the R package Hmisc and a working latex installation you can do:
x=rnorm(1000)
y=rnorm(1000)
lm1=lm(y~x)
slm1=summary(lm1)
latex(slm1)
It works the same with datasets,
latex(summary(cars) | How to generate nice summary table?
If you have the R package Hmisc and a working latex installation you can do:
x=rnorm(1000)
y=rnorm(1000)
lm1=lm(y~x)
slm1=summary(lm1)
latex(slm1)
It works the same with datasets,
latex(summary(cars)) | How to generate nice summary table?
If you have the R package Hmisc and a working latex installation you can do:
x=rnorm(1000)
y=rnorm(1000)
lm1=lm(y~x)
slm1=summary(lm1)
latex(slm1)
It works the same with datasets,
latex(summary(cars) |
37,226 | Why do we need sparsity for auto-encoders? | Remember that auto-encoders are trying to come up with the best summarized/compressed (hidden/laten) representation of the data such that the reconstruction error is minimized. This can be expressed in equations as follow:
$$ \min_{\hat{x} \in \mathcal{F}} \frac{1}{n} \sum^{n}_{t=1} cost(x^{(t)}, \hat{x}^{(t)} )$$
wher... | Why do we need sparsity for auto-encoders? | Remember that auto-encoders are trying to come up with the best summarized/compressed (hidden/laten) representation of the data such that the reconstruction error is minimized. This can be expressed i | Why do we need sparsity for auto-encoders?
Remember that auto-encoders are trying to come up with the best summarized/compressed (hidden/laten) representation of the data such that the reconstruction error is minimized. This can be expressed in equations as follow:
$$ \min_{\hat{x} \in \mathcal{F}} \frac{1}{n} \sum^{n}... | Why do we need sparsity for auto-encoders?
Remember that auto-encoders are trying to come up with the best summarized/compressed (hidden/laten) representation of the data such that the reconstruction error is minimized. This can be expressed i |
37,227 | Does using box-cox transformation on individual data sets prevent these data from being comparable? | Yes, if they are on different scales you logically cannot compare them. Had the transformations all been the same you could, since the power transform is monotonic. However, the sample variance changes because of the transformation and that would need to be accounted for. But in your situation, you cannot compare th... | Does using box-cox transformation on individual data sets prevent these data from being comparable? | Yes, if they are on different scales you logically cannot compare them. Had the transformations all been the same you could, since the power transform is monotonic. However, the sample variance chan | Does using box-cox transformation on individual data sets prevent these data from being comparable?
Yes, if they are on different scales you logically cannot compare them. Had the transformations all been the same you could, since the power transform is monotonic. However, the sample variance changes because of the t... | Does using box-cox transformation on individual data sets prevent these data from being comparable?
Yes, if they are on different scales you logically cannot compare them. Had the transformations all been the same you could, since the power transform is monotonic. However, the sample variance chan |
37,228 | Posterior simulations of the variances with the mcmcsamp function | The short(ish) answer is that
as.data.frame(mm,type="varcov")
should extract the chains for the fixed effects and for the random-effect and residual variances in the form of a data frame.
For example:
library(lme4.0) ## I am using the r-forge version
fm2 <- lmer(Reaction ~ Days + (1|Subject) +
(0+Days|Subject), ... | Posterior simulations of the variances with the mcmcsamp function | The short(ish) answer is that
as.data.frame(mm,type="varcov")
should extract the chains for the fixed effects and for the random-effect and residual variances in the form of a data frame.
For exampl | Posterior simulations of the variances with the mcmcsamp function
The short(ish) answer is that
as.data.frame(mm,type="varcov")
should extract the chains for the fixed effects and for the random-effect and residual variances in the form of a data frame.
For example:
library(lme4.0) ## I am using the r-forge version
f... | Posterior simulations of the variances with the mcmcsamp function
The short(ish) answer is that
as.data.frame(mm,type="varcov")
should extract the chains for the fixed effects and for the random-effect and residual variances in the form of a data frame.
For exampl |
37,229 | Jack-knife with time series models | I don't understand why you think $q>0$ is a problem for prediction. It is easy enough to forecast using an ARIMA model with MA terms and you don't need to use the innovations algorithm of Brockwell and Davis. That algorithm is useful for estimation; in particular, in getting starting values when optimizing the likeliho... | Jack-knife with time series models | I don't understand why you think $q>0$ is a problem for prediction. It is easy enough to forecast using an ARIMA model with MA terms and you don't need to use the innovations algorithm of Brockwell an | Jack-knife with time series models
I don't understand why you think $q>0$ is a problem for prediction. It is easy enough to forecast using an ARIMA model with MA terms and you don't need to use the innovations algorithm of Brockwell and Davis. That algorithm is useful for estimation; in particular, in getting starting ... | Jack-knife with time series models
I don't understand why you think $q>0$ is a problem for prediction. It is easy enough to forecast using an ARIMA model with MA terms and you don't need to use the innovations algorithm of Brockwell an |
37,230 | How to analyse a ranking and rating scale together? | I assume you can't just ask them if they prefer a laptop or a tablet; or you want to check what they think they prefer with what you think they should prefer...
There are a number of ways to do this. This is in fact a version of the very common real life problem of evaluating job applicants, or tenders for contracting... | How to analyse a ranking and rating scale together? | I assume you can't just ask them if they prefer a laptop or a tablet; or you want to check what they think they prefer with what you think they should prefer...
There are a number of ways to do this. | How to analyse a ranking and rating scale together?
I assume you can't just ask them if they prefer a laptop or a tablet; or you want to check what they think they prefer with what you think they should prefer...
There are a number of ways to do this. This is in fact a version of the very common real life problem of e... | How to analyse a ranking and rating scale together?
I assume you can't just ask them if they prefer a laptop or a tablet; or you want to check what they think they prefer with what you think they should prefer...
There are a number of ways to do this. |
37,231 | How to analyse a ranking and rating scale together? | To think that you can learn what is important in people's decisions simply by asking expresses unjustified optimism. But there are some sound methods of "deriving" the importance of different factors. Years and years of research in psychology and behavioural economics have borne this out. A colleague and I summarize... | How to analyse a ranking and rating scale together? | To think that you can learn what is important in people's decisions simply by asking expresses unjustified optimism. But there are some sound methods of "deriving" the importance of different factors | How to analyse a ranking and rating scale together?
To think that you can learn what is important in people's decisions simply by asking expresses unjustified optimism. But there are some sound methods of "deriving" the importance of different factors. Years and years of research in psychology and behavioural economi... | How to analyse a ranking and rating scale together?
To think that you can learn what is important in people's decisions simply by asking expresses unjustified optimism. But there are some sound methods of "deriving" the importance of different factors |
37,232 | How to analyse a ranking and rating scale together? | This is an unsupervised learning task. Here is a very simple idea which if incorrect I hope someone else points out. Feed your ten variables into a PCA to extract 2 PCs. Use the two principal components in a 2-mean clustering algorithm to define boundaries for the assignment to each of two groups. Examine the PCs, and ... | How to analyse a ranking and rating scale together? | This is an unsupervised learning task. Here is a very simple idea which if incorrect I hope someone else points out. Feed your ten variables into a PCA to extract 2 PCs. Use the two principal componen | How to analyse a ranking and rating scale together?
This is an unsupervised learning task. Here is a very simple idea which if incorrect I hope someone else points out. Feed your ten variables into a PCA to extract 2 PCs. Use the two principal components in a 2-mean clustering algorithm to define boundaries for the ass... | How to analyse a ranking and rating scale together?
This is an unsupervised learning task. Here is a very simple idea which if incorrect I hope someone else points out. Feed your ten variables into a PCA to extract 2 PCs. Use the two principal componen |
37,233 | Tracking down the assumptions made by SciPy's ttest_ind() function | By using the SciPy built-in function source(), I could see a printout of the source code for the function ttest_ind(). Based on the source code, the SciPy built-in is performing the t-test assuming that the variances of the two samples are equal. It is not using the Welch-Satterthwaite degrees of freedom.
I just want t... | Tracking down the assumptions made by SciPy's ttest_ind() function | By using the SciPy built-in function source(), I could see a printout of the source code for the function ttest_ind(). Based on the source code, the SciPy built-in is performing the t-test assuming th | Tracking down the assumptions made by SciPy's ttest_ind() function
By using the SciPy built-in function source(), I could see a printout of the source code for the function ttest_ind(). Based on the source code, the SciPy built-in is performing the t-test assuming that the variances of the two samples are equal. It is ... | Tracking down the assumptions made by SciPy's ttest_ind() function
By using the SciPy built-in function source(), I could see a printout of the source code for the function ttest_ind(). Based on the source code, the SciPy built-in is performing the t-test assuming th |
37,234 | Relationship between correlation and sample variance | This can be explained as follows. Mathematically, given two variables X and Y, their Correlation is defined as the
covariance(X,Y)/(Standard Deviation(X)*Standard Deviation(Y)).
In other words, the correlation is proportional to the the covariance of the two variables. The divisor in the equation acts has a scaling ... | Relationship between correlation and sample variance | This can be explained as follows. Mathematically, given two variables X and Y, their Correlation is defined as the
covariance(X,Y)/(Standard Deviation(X)*Standard Deviation(Y)).
In other words, the | Relationship between correlation and sample variance
This can be explained as follows. Mathematically, given two variables X and Y, their Correlation is defined as the
covariance(X,Y)/(Standard Deviation(X)*Standard Deviation(Y)).
In other words, the correlation is proportional to the the covariance of the two varia... | Relationship between correlation and sample variance
This can be explained as follows. Mathematically, given two variables X and Y, their Correlation is defined as the
covariance(X,Y)/(Standard Deviation(X)*Standard Deviation(Y)).
In other words, the |
37,235 | Relationship between correlation and sample variance | Yes, there is a mathematical although rather conceptual explanation. I was puzzled by the same question until now.
First, why we were puzzled:
1) If you are calculating the correlation coefficient in a sample with lower variance (e.g. all with similar scholar achievements) BUT which truly and perfectly represents the ... | Relationship between correlation and sample variance | Yes, there is a mathematical although rather conceptual explanation. I was puzzled by the same question until now.
First, why we were puzzled:
1) If you are calculating the correlation coefficient in | Relationship between correlation and sample variance
Yes, there is a mathematical although rather conceptual explanation. I was puzzled by the same question until now.
First, why we were puzzled:
1) If you are calculating the correlation coefficient in a sample with lower variance (e.g. all with similar scholar achiev... | Relationship between correlation and sample variance
Yes, there is a mathematical although rather conceptual explanation. I was puzzled by the same question until now.
First, why we were puzzled:
1) If you are calculating the correlation coefficient in |
37,236 | Relationship between correlation and sample variance | The correlation coefficient (I frequently use the intraclass as a measure of test-retest reliability) is often defined as the ratio of between-subject variation to the total variation (between-subject + within-subject). If the between-subject variation is high (e.g., persons with very different school types) compared t... | Relationship between correlation and sample variance | The correlation coefficient (I frequently use the intraclass as a measure of test-retest reliability) is often defined as the ratio of between-subject variation to the total variation (between-subject | Relationship between correlation and sample variance
The correlation coefficient (I frequently use the intraclass as a measure of test-retest reliability) is often defined as the ratio of between-subject variation to the total variation (between-subject + within-subject). If the between-subject variation is high (e.g.,... | Relationship between correlation and sample variance
The correlation coefficient (I frequently use the intraclass as a measure of test-retest reliability) is often defined as the ratio of between-subject variation to the total variation (between-subject |
37,237 | Calculate average of a set numbers with reported standard errors | "The variance of the sums is the sum of the variances". So:
Square each of the 365 standard errors so they become variances. Add them together; this will give you the variance of the annual total. Divide that variance by 365^2; this will give you the variance of the annual average. Take the square root of that vari... | Calculate average of a set numbers with reported standard errors | "The variance of the sums is the sum of the variances". So:
Square each of the 365 standard errors so they become variances. Add them together; this will give you the variance of the annual total. | Calculate average of a set numbers with reported standard errors
"The variance of the sums is the sum of the variances". So:
Square each of the 365 standard errors so they become variances. Add them together; this will give you the variance of the annual total. Divide that variance by 365^2; this will give you the v... | Calculate average of a set numbers with reported standard errors
"The variance of the sums is the sum of the variances". So:
Square each of the 365 standard errors so they become variances. Add them together; this will give you the variance of the annual total. |
37,238 | Calculate average of a set numbers with reported standard errors | In Ken Tatebe’s “Combining Multiple Averaged Data Points And Their Errors” (PDF—linked in Steven Howell’s answer), Tatebe shows that given two "bins" of averaged data points $a$ and $b$, each reported as an average ($\bar a$, $\bar b$) and an error ($\varepsilon_a$, $\varepsilon_b$), with bin sizes $n_a$ and $n_b$ (whe... | Calculate average of a set numbers with reported standard errors | In Ken Tatebe’s “Combining Multiple Averaged Data Points And Their Errors” (PDF—linked in Steven Howell’s answer), Tatebe shows that given two "bins" of averaged data points $a$ and $b$, each reported | Calculate average of a set numbers with reported standard errors
In Ken Tatebe’s “Combining Multiple Averaged Data Points And Their Errors” (PDF—linked in Steven Howell’s answer), Tatebe shows that given two "bins" of averaged data points $a$ and $b$, each reported as an average ($\bar a$, $\bar b$) and an error ($\var... | Calculate average of a set numbers with reported standard errors
In Ken Tatebe’s “Combining Multiple Averaged Data Points And Their Errors” (PDF—linked in Steven Howell’s answer), Tatebe shows that given two "bins" of averaged data points $a$ and $b$, each reported |
37,239 | How to find implementation details for a SAS procedure? | This information is not documented because SAS is a proprietary statistical software suite. Sharing such info (from their perspective) would compromise the integrity of their license. Because statistics lack any kind of IEEE-like standard for numerical routines, nothing can be inferred about the methods used without in... | How to find implementation details for a SAS procedure? | This information is not documented because SAS is a proprietary statistical software suite. Sharing such info (from their perspective) would compromise the integrity of their license. Because statisti | How to find implementation details for a SAS procedure?
This information is not documented because SAS is a proprietary statistical software suite. Sharing such info (from their perspective) would compromise the integrity of their license. Because statistics lack any kind of IEEE-like standard for numerical routines, n... | How to find implementation details for a SAS procedure?
This information is not documented because SAS is a proprietary statistical software suite. Sharing such info (from their perspective) would compromise the integrity of their license. Because statisti |
37,240 | Accuracy of a random classifier | I am not sure I understand the last part of your question
But, how can I compare the accuracy of my classifier without citing a test set?
but I think I understand your concern. A given binary classifier's accuracy of 90% may be misleading if the natural frequency of one case vs the other is 90/100. If the classifier ... | Accuracy of a random classifier | I am not sure I understand the last part of your question
But, how can I compare the accuracy of my classifier without citing a test set?
but I think I understand your concern. A given binary classi | Accuracy of a random classifier
I am not sure I understand the last part of your question
But, how can I compare the accuracy of my classifier without citing a test set?
but I think I understand your concern. A given binary classifier's accuracy of 90% may be misleading if the natural frequency of one case vs the oth... | Accuracy of a random classifier
I am not sure I understand the last part of your question
But, how can I compare the accuracy of my classifier without citing a test set?
but I think I understand your concern. A given binary classi |
37,241 | Will quantum computing allow new statistical techniques? | Frankly I doubt this would ever work -- IMO every more complex structure will just melt from decoherence.
Nevertheless probably the most obvious use is doing complete combinatorical sweeps for larger number of variables or huge Monte Carlo simulations.
Yet those are things achievable by molecular computers -- imagine $... | Will quantum computing allow new statistical techniques? | Frankly I doubt this would ever work -- IMO every more complex structure will just melt from decoherence.
Nevertheless probably the most obvious use is doing complete combinatorical sweeps for larger | Will quantum computing allow new statistical techniques?
Frankly I doubt this would ever work -- IMO every more complex structure will just melt from decoherence.
Nevertheless probably the most obvious use is doing complete combinatorical sweeps for larger number of variables or huge Monte Carlo simulations.
Yet those ... | Will quantum computing allow new statistical techniques?
Frankly I doubt this would ever work -- IMO every more complex structure will just melt from decoherence.
Nevertheless probably the most obvious use is doing complete combinatorical sweeps for larger |
37,242 | Will quantum computing allow new statistical techniques? | If it actually worked, and was something you could implement statistical code on in one way or another? Absolutely. There are undoubtedly new techniques that could emerge from throwing yet more computational firepower at something. Or, as importantly, making currently bleeding edge, computationally intensive techniques... | Will quantum computing allow new statistical techniques? | If it actually worked, and was something you could implement statistical code on in one way or another? Absolutely. There are undoubtedly new techniques that could emerge from throwing yet more comput | Will quantum computing allow new statistical techniques?
If it actually worked, and was something you could implement statistical code on in one way or another? Absolutely. There are undoubtedly new techniques that could emerge from throwing yet more computational firepower at something. Or, as importantly, making curr... | Will quantum computing allow new statistical techniques?
If it actually worked, and was something you could implement statistical code on in one way or another? Absolutely. There are undoubtedly new techniques that could emerge from throwing yet more comput |
37,243 | Bootstrapped parameter and fit estimates with non-normality for structural equation models | The following are just a few points:
If you have departure from normality then bootstrapping is often a good idea.
You mention using "1000" replicates. Increasing the number of replicates increases computational time and accuracy. Thus, sometimes when first setting up your model, you'll set the number of replicates a... | Bootstrapped parameter and fit estimates with non-normality for structural equation models | The following are just a few points:
If you have departure from normality then bootstrapping is often a good idea.
You mention using "1000" replicates. Increasing the number of replicates increases | Bootstrapped parameter and fit estimates with non-normality for structural equation models
The following are just a few points:
If you have departure from normality then bootstrapping is often a good idea.
You mention using "1000" replicates. Increasing the number of replicates increases computational time and accura... | Bootstrapped parameter and fit estimates with non-normality for structural equation models
The following are just a few points:
If you have departure from normality then bootstrapping is often a good idea.
You mention using "1000" replicates. Increasing the number of replicates increases |
37,244 | Unexpected singularities in the Hessian matrix error in multinomial logistic regression | I the key you may be looking for can be found on the UCLA website for Multinomial Logistic Regression where it states:
Perfect prediction: Perfect
prediction means that only one value
of a predictor variable is associated
with only one value of the response
variable. You can tell from the output
of the regr... | Unexpected singularities in the Hessian matrix error in multinomial logistic regression | I the key you may be looking for can be found on the UCLA website for Multinomial Logistic Regression where it states:
Perfect prediction: Perfect
prediction means that only one value
of a predi | Unexpected singularities in the Hessian matrix error in multinomial logistic regression
I the key you may be looking for can be found on the UCLA website for Multinomial Logistic Regression where it states:
Perfect prediction: Perfect
prediction means that only one value
of a predictor variable is associated
wi... | Unexpected singularities in the Hessian matrix error in multinomial logistic regression
I the key you may be looking for can be found on the UCLA website for Multinomial Logistic Regression where it states:
Perfect prediction: Perfect
prediction means that only one value
of a predi |
37,245 | How to perform text mining, sentiment mining, and business category identification, and where to obtain a categorization library | One solution mentioned by Jeffrey Breen is to use Lu and Hiu's lexicon. He also gives a cool tutorial for sentiment mining on Twitter. | How to perform text mining, sentiment mining, and business category identification, and where to obt | One solution mentioned by Jeffrey Breen is to use Lu and Hiu's lexicon. He also gives a cool tutorial for sentiment mining on Twitter. | How to perform text mining, sentiment mining, and business category identification, and where to obtain a categorization library
One solution mentioned by Jeffrey Breen is to use Lu and Hiu's lexicon. He also gives a cool tutorial for sentiment mining on Twitter. | How to perform text mining, sentiment mining, and business category identification, and where to obt
One solution mentioned by Jeffrey Breen is to use Lu and Hiu's lexicon. He also gives a cool tutorial for sentiment mining on Twitter. |
37,246 | How to perform text mining, sentiment mining, and business category identification, and where to obtain a categorization library | A few alternatives
1) Supervised learning: Ideally you'd want to have in your data the text and a label, where the label refers to the category you are interested. For this you'd need to manually label the data.
Then you can train a statistical/machine learning algorithm in order to classify the categories you've label... | How to perform text mining, sentiment mining, and business category identification, and where to obt | A few alternatives
1) Supervised learning: Ideally you'd want to have in your data the text and a label, where the label refers to the category you are interested. For this you'd need to manually labe | How to perform text mining, sentiment mining, and business category identification, and where to obtain a categorization library
A few alternatives
1) Supervised learning: Ideally you'd want to have in your data the text and a label, where the label refers to the category you are interested. For this you'd need to manu... | How to perform text mining, sentiment mining, and business category identification, and where to obt
A few alternatives
1) Supervised learning: Ideally you'd want to have in your data the text and a label, where the label refers to the category you are interested. For this you'd need to manually labe |
37,247 | Help in drawing confidence ellipse | An ellipse can be parametrized as the affine image of any given circle. If we consider the unit circle:
$$x=a \cos (t)$$
$$y=b \sin (t)$$
ellipse(center, shape, radius, log="", center.pch=19, center.cex=1.5,
segments=51, add=TRUE, xlab="", ylab="",
col=palette()[2], lwd=2, fill=FALSE, fill.alpha=0.3, grid=TRUE, ... | Help in drawing confidence ellipse | An ellipse can be parametrized as the affine image of any given circle. If we consider the unit circle:
$$x=a \cos (t)$$
$$y=b \sin (t)$$
ellipse(center, shape, radius, log="", center.pch=19, center.c | Help in drawing confidence ellipse
An ellipse can be parametrized as the affine image of any given circle. If we consider the unit circle:
$$x=a \cos (t)$$
$$y=b \sin (t)$$
ellipse(center, shape, radius, log="", center.pch=19, center.cex=1.5,
segments=51, add=TRUE, xlab="", ylab="",
col=palette()[2], lwd=2, fill... | Help in drawing confidence ellipse
An ellipse can be parametrized as the affine image of any given circle. If we consider the unit circle:
$$x=a \cos (t)$$
$$y=b \sin (t)$$
ellipse(center, shape, radius, log="", center.pch=19, center.c |
37,248 | Scalable multinomial regression implementation | I've had good experiences with Madigan's and Lewis's BMR and BBR packages for multiple category dependent variables, lasso or ridge priors on parameters, and high dimensional input data. Not quite as high as yours, but it might still be worth a look. Instructions are here: http://bayesianregression.com/bmr.html | Scalable multinomial regression implementation | I've had good experiences with Madigan's and Lewis's BMR and BBR packages for multiple category dependent variables, lasso or ridge priors on parameters, and high dimensional input data. Not quite as | Scalable multinomial regression implementation
I've had good experiences with Madigan's and Lewis's BMR and BBR packages for multiple category dependent variables, lasso or ridge priors on parameters, and high dimensional input data. Not quite as high as yours, but it might still be worth a look. Instructions are her... | Scalable multinomial regression implementation
I've had good experiences with Madigan's and Lewis's BMR and BBR packages for multiple category dependent variables, lasso or ridge priors on parameters, and high dimensional input data. Not quite as |
37,249 | Are there bounds on the Spearman correlation of a sum of two variables? | Spearman's rank correlation is just the Pearson product-moment correlation between the ranks of the variables. Shabbychef's extra constraint means that $y_1$ and $y_2$ are the same as their ranks and that there are no ties, so they have equal standard deviation $\sigma_y$ (say). If we also replace x by its ranks, the p... | Are there bounds on the Spearman correlation of a sum of two variables? | Spearman's rank correlation is just the Pearson product-moment correlation between the ranks of the variables. Shabbychef's extra constraint means that $y_1$ and $y_2$ are the same as their ranks and | Are there bounds on the Spearman correlation of a sum of two variables?
Spearman's rank correlation is just the Pearson product-moment correlation between the ranks of the variables. Shabbychef's extra constraint means that $y_1$ and $y_2$ are the same as their ranks and that there are no ties, so they have equal stand... | Are there bounds on the Spearman correlation of a sum of two variables?
Spearman's rank correlation is just the Pearson product-moment correlation between the ranks of the variables. Shabbychef's extra constraint means that $y_1$ and $y_2$ are the same as their ranks and |
37,250 | Brown-Forsythe and Welch f-ratios in two-way ANOVAs? | I found this article by Algina & Olejnik (1984).
The abstract:
The Welch-James procedure may be used
to test hypotheses on means, when
independent samples from populations
with heterogeneous variances are
available. Until recently the
complexity of the available
presentations of this procedure
limited t... | Brown-Forsythe and Welch f-ratios in two-way ANOVAs? | I found this article by Algina & Olejnik (1984).
The abstract:
The Welch-James procedure may be used
to test hypotheses on means, when
independent samples from populations
with heterogeneous v | Brown-Forsythe and Welch f-ratios in two-way ANOVAs?
I found this article by Algina & Olejnik (1984).
The abstract:
The Welch-James procedure may be used
to test hypotheses on means, when
independent samples from populations
with heterogeneous variances are
available. Until recently the
complexity of the av... | Brown-Forsythe and Welch f-ratios in two-way ANOVAs?
I found this article by Algina & Olejnik (1984).
The abstract:
The Welch-James procedure may be used
to test hypotheses on means, when
independent samples from populations
with heterogeneous v |
37,251 | Brown-Forsythe and Welch f-ratios in two-way ANOVAs? | The Brown-Forsythe F* can be used even in two-way ANOVAs. From what I can tell the F statistic is the same as for classic two-way ANOVA, the only difference is in how the degrees of freedom are calculated. Of course it gets more complicated for unbalanced factorial designs. (the original Brown & Forsythe's paper is ava... | Brown-Forsythe and Welch f-ratios in two-way ANOVAs? | The Brown-Forsythe F* can be used even in two-way ANOVAs. From what I can tell the F statistic is the same as for classic two-way ANOVA, the only difference is in how the degrees of freedom are calcul | Brown-Forsythe and Welch f-ratios in two-way ANOVAs?
The Brown-Forsythe F* can be used even in two-way ANOVAs. From what I can tell the F statistic is the same as for classic two-way ANOVA, the only difference is in how the degrees of freedom are calculated. Of course it gets more complicated for unbalanced factorial d... | Brown-Forsythe and Welch f-ratios in two-way ANOVAs?
The Brown-Forsythe F* can be used even in two-way ANOVAs. From what I can tell the F statistic is the same as for classic two-way ANOVA, the only difference is in how the degrees of freedom are calcul |
37,252 | How can one extract meaningful factors from a sparse matrix? | I might suggest non-negative matrix factorization. The iterative algorithm of Lee and Seung is easy to implement and should be amenable to sparse matrices (although it involves Hadamard products, which some sparse matrix packages may not support.). | How can one extract meaningful factors from a sparse matrix? | I might suggest non-negative matrix factorization. The iterative algorithm of Lee and Seung is easy to implement and should be amenable to sparse matrices (although it involves Hadamard products, whic | How can one extract meaningful factors from a sparse matrix?
I might suggest non-negative matrix factorization. The iterative algorithm of Lee and Seung is easy to implement and should be amenable to sparse matrices (although it involves Hadamard products, which some sparse matrix packages may not support.). | How can one extract meaningful factors from a sparse matrix?
I might suggest non-negative matrix factorization. The iterative algorithm of Lee and Seung is easy to implement and should be amenable to sparse matrices (although it involves Hadamard products, whic |
37,253 | How can one extract meaningful factors from a sparse matrix? | One has to be careful about the meaning of the word sparse. Your matrix contains many zeroes and one may represent such a matrix in a sparse way (to save on storage). But since the figures represent co-occurrences these zeroes are still to be considered informative (they are not missing; they are not structurally zero)... | How can one extract meaningful factors from a sparse matrix? | One has to be careful about the meaning of the word sparse. Your matrix contains many zeroes and one may represent such a matrix in a sparse way (to save on storage). But since the figures represent c | How can one extract meaningful factors from a sparse matrix?
One has to be careful about the meaning of the word sparse. Your matrix contains many zeroes and one may represent such a matrix in a sparse way (to save on storage). But since the figures represent co-occurrences these zeroes are still to be considered infor... | How can one extract meaningful factors from a sparse matrix?
One has to be careful about the meaning of the word sparse. Your matrix contains many zeroes and one may represent such a matrix in a sparse way (to save on storage). But since the figures represent c |
37,254 | How can one extract meaningful factors from a sparse matrix? | I had the same problem with a sparce matrix in NLP and what we did was select the columns that where more useful to clasify our rows (that gave more information for discerning the result), if you want I can explain it to you in more detail but it is really simple you can figure it out.
But your problem does not seem t... | How can one extract meaningful factors from a sparse matrix? | I had the same problem with a sparce matrix in NLP and what we did was select the columns that where more useful to clasify our rows (that gave more information for discerning the result), if you want | How can one extract meaningful factors from a sparse matrix?
I had the same problem with a sparce matrix in NLP and what we did was select the columns that where more useful to clasify our rows (that gave more information for discerning the result), if you want I can explain it to you in more detail but it is really si... | How can one extract meaningful factors from a sparse matrix?
I had the same problem with a sparce matrix in NLP and what we did was select the columns that where more useful to clasify our rows (that gave more information for discerning the result), if you want |
37,255 | How can one extract meaningful factors from a sparse matrix? | I suggest that you look at the 2009 paper by Leng and Wang in JCGS:
http://pubs.amstat.org/toc/jcgs/18/1
If this is what you want, the authors supply R code in the supplementary materials. | How can one extract meaningful factors from a sparse matrix? | I suggest that you look at the 2009 paper by Leng and Wang in JCGS:
http://pubs.amstat.org/toc/jcgs/18/1
If this is what you want, the authors supply R code in the supplementary materials. | How can one extract meaningful factors from a sparse matrix?
I suggest that you look at the 2009 paper by Leng and Wang in JCGS:
http://pubs.amstat.org/toc/jcgs/18/1
If this is what you want, the authors supply R code in the supplementary materials. | How can one extract meaningful factors from a sparse matrix?
I suggest that you look at the 2009 paper by Leng and Wang in JCGS:
http://pubs.amstat.org/toc/jcgs/18/1
If this is what you want, the authors supply R code in the supplementary materials. |
37,256 | Random generation of scores similar to those of a classification model | Some time has passed and I think I might have a solution at hand. I will describe my approach briefly to give you the general idea. The code should be enough to figure out the details. I like to attach code here, but it is a lot and stackexchange makes it not easy to do so. I am of course happy to answer any comments, ... | Random generation of scores similar to those of a classification model | Some time has passed and I think I might have a solution at hand. I will describe my approach briefly to give you the general idea. The code should be enough to figure out the details. I like to attac | Random generation of scores similar to those of a classification model
Some time has passed and I think I might have a solution at hand. I will describe my approach briefly to give you the general idea. The code should be enough to figure out the details. I like to attach code here, but it is a lot and stackexchange ma... | Random generation of scores similar to those of a classification model
Some time has passed and I think I might have a solution at hand. I will describe my approach briefly to give you the general idea. The code should be enough to figure out the details. I like to attac |
37,257 | How to explain null hypothesis testing using Bayesian terms? | ...the idea to describe NHST as something like a posterior predictive check, but with a "null hypothesis" pseudo-posterior that is a Dirac $\delta$ density about $H_0$. Does that make sense...?
Yes. I'm not sure whether to call NHST a prior or posterior predictive check, but it is fair to see it as a form of model che... | How to explain null hypothesis testing using Bayesian terms? | ...the idea to describe NHST as something like a posterior predictive check, but with a "null hypothesis" pseudo-posterior that is a Dirac $\delta$ density about $H_0$. Does that make sense...?
Yes. | How to explain null hypothesis testing using Bayesian terms?
...the idea to describe NHST as something like a posterior predictive check, but with a "null hypothesis" pseudo-posterior that is a Dirac $\delta$ density about $H_0$. Does that make sense...?
Yes. I'm not sure whether to call NHST a prior or posterior pred... | How to explain null hypothesis testing using Bayesian terms?
...the idea to describe NHST as something like a posterior predictive check, but with a "null hypothesis" pseudo-posterior that is a Dirac $\delta$ density about $H_0$. Does that make sense...?
Yes. |
37,258 | How to explain null hypothesis testing using Bayesian terms? | Null hypothesis significance testing, NHST, is expressing an observed effect in terms of a probabilistic comparison with the hypothesis of an absence of the effect. An observation is statistically significant if there is a clear distinction in the support of the data for absence versus presence of an effect.
An example... | How to explain null hypothesis testing using Bayesian terms? | Null hypothesis significance testing, NHST, is expressing an observed effect in terms of a probabilistic comparison with the hypothesis of an absence of the effect. An observation is statistically sig | How to explain null hypothesis testing using Bayesian terms?
Null hypothesis significance testing, NHST, is expressing an observed effect in terms of a probabilistic comparison with the hypothesis of an absence of the effect. An observation is statistically significant if there is a clear distinction in the support of ... | How to explain null hypothesis testing using Bayesian terms?
Null hypothesis significance testing, NHST, is expressing an observed effect in terms of a probabilistic comparison with the hypothesis of an absence of the effect. An observation is statistically sig |
37,259 | Why does collider adjustment in a shielded triplet tend to cause independence? | Here you can find a formal example of linear causal model that share your DAG.
Which OLS assumptions are colliders violating?
I consider (there and here) the case where all noises are independent each others. Moreover now I consider here the particular case where noises are standard Normal. Moreover, like in your examp... | Why does collider adjustment in a shielded triplet tend to cause independence? | Here you can find a formal example of linear causal model that share your DAG.
Which OLS assumptions are colliders violating?
I consider (there and here) the case where all noises are independent each | Why does collider adjustment in a shielded triplet tend to cause independence?
Here you can find a formal example of linear causal model that share your DAG.
Which OLS assumptions are colliders violating?
I consider (there and here) the case where all noises are independent each others. Moreover now I consider here the... | Why does collider adjustment in a shielded triplet tend to cause independence?
Here you can find a formal example of linear causal model that share your DAG.
Which OLS assumptions are colliders violating?
I consider (there and here) the case where all noises are independent each |
37,260 | Why does collider adjustment in a shielded triplet tend to cause independence? | This is called colliding bias, also called Berkson's paradox, if the relationship between X and Y conditions on Z. Conditioning on Z will induce negative association between X and Y, so if X affects Y positively, then this positive causation will be reduced, even to 0, as you showed. | Why does collider adjustment in a shielded triplet tend to cause independence? | This is called colliding bias, also called Berkson's paradox, if the relationship between X and Y conditions on Z. Conditioning on Z will induce negative association between X and Y, so if X affects Y | Why does collider adjustment in a shielded triplet tend to cause independence?
This is called colliding bias, also called Berkson's paradox, if the relationship between X and Y conditions on Z. Conditioning on Z will induce negative association between X and Y, so if X affects Y positively, then this positive causation... | Why does collider adjustment in a shielded triplet tend to cause independence?
This is called colliding bias, also called Berkson's paradox, if the relationship between X and Y conditions on Z. Conditioning on Z will induce negative association between X and Y, so if X affects Y |
37,261 | How to design experiment and holdout for two types of treatment at the same time | OP mentioned that they ended up selecting control groups for the treatments independently.
In this case, if there is no clear bias in the assignment mechanisms of treatment A and treatment B (e.g. somehow applying treatment B also increases probability of treatment A), the subtraction in the calculation of average trea... | How to design experiment and holdout for two types of treatment at the same time | OP mentioned that they ended up selecting control groups for the treatments independently.
In this case, if there is no clear bias in the assignment mechanisms of treatment A and treatment B (e.g. som | How to design experiment and holdout for two types of treatment at the same time
OP mentioned that they ended up selecting control groups for the treatments independently.
In this case, if there is no clear bias in the assignment mechanisms of treatment A and treatment B (e.g. somehow applying treatment B also increase... | How to design experiment and holdout for two types of treatment at the same time
OP mentioned that they ended up selecting control groups for the treatments independently.
In this case, if there is no clear bias in the assignment mechanisms of treatment A and treatment B (e.g. som |
37,262 | How to design experiment and holdout for two types of treatment at the same time | When conducting these kinds of experiments there is a natural control-group for each marginal and conditional effect in the experiment. The figure below shows an experimental flowchart for the possible categories of each participant. The "No Treat" category acts as the control group for determining the marginal effec... | How to design experiment and holdout for two types of treatment at the same time | When conducting these kinds of experiments there is a natural control-group for each marginal and conditional effect in the experiment. The figure below shows an experimental flowchart for the possib | How to design experiment and holdout for two types of treatment at the same time
When conducting these kinds of experiments there is a natural control-group for each marginal and conditional effect in the experiment. The figure below shows an experimental flowchart for the possible categories of each participant. The... | How to design experiment and holdout for two types of treatment at the same time
When conducting these kinds of experiments there is a natural control-group for each marginal and conditional effect in the experiment. The figure below shows an experimental flowchart for the possib |
37,263 | How to design experiment and holdout for two types of treatment at the same time | I opted to construct control groups for treatment A and treatment B independently. Each control group is randomly selected. It allowed the two teams at my work to save time and effort for communications.
I used matching to adjust for any potential bias in the measurement of treatment effect of A and B introduced by the... | How to design experiment and holdout for two types of treatment at the same time | I opted to construct control groups for treatment A and treatment B independently. Each control group is randomly selected. It allowed the two teams at my work to save time and effort for communicatio | How to design experiment and holdout for two types of treatment at the same time
I opted to construct control groups for treatment A and treatment B independently. Each control group is randomly selected. It allowed the two teams at my work to save time and effort for communications.
I used matching to adjust for any p... | How to design experiment and holdout for two types of treatment at the same time
I opted to construct control groups for treatment A and treatment B independently. Each control group is randomly selected. It allowed the two teams at my work to save time and effort for communicatio |
37,264 | The law of total probability: $P(T > t, Z = 1) = \int_t^\infty P(\cap_{j = 2}^k \{ T_j > x \} ) \lambda_1 e^{- \lambda_1 x} \ dx$? | The notation here is more complicated than it needs to be. A simpler way to frame this is to say that:
$$\mathbb{P}(T>t, Z=1) = \mathbb{P}(t<T_1< \min(T_2,...,T_k)).$$
Now, for all values $r \in \mathbb{R}$ we clearly have the event equivalence:
$$\{ r< \min(T_2,...,T_k) \} = \bigcap_{i=2}^k \{ T_i > r \}.$$
Thus, app... | The law of total probability: $P(T > t, Z = 1) = \int_t^\infty P(\cap_{j = 2}^k \{ T_j > x \} ) \lam | The notation here is more complicated than it needs to be. A simpler way to frame this is to say that:
$$\mathbb{P}(T>t, Z=1) = \mathbb{P}(t<T_1< \min(T_2,...,T_k)).$$
Now, for all values $r \in \mat | The law of total probability: $P(T > t, Z = 1) = \int_t^\infty P(\cap_{j = 2}^k \{ T_j > x \} ) \lambda_1 e^{- \lambda_1 x} \ dx$?
The notation here is more complicated than it needs to be. A simpler way to frame this is to say that:
$$\mathbb{P}(T>t, Z=1) = \mathbb{P}(t<T_1< \min(T_2,...,T_k)).$$
Now, for all values ... | The law of total probability: $P(T > t, Z = 1) = \int_t^\infty P(\cap_{j = 2}^k \{ T_j > x \} ) \lam
The notation here is more complicated than it needs to be. A simpler way to frame this is to say that:
$$\mathbb{P}(T>t, Z=1) = \mathbb{P}(t<T_1< \min(T_2,...,T_k)).$$
Now, for all values $r \in \mat |
37,265 | The law of total probability: $P(T > t, Z = 1) = \int_t^\infty P(\cap_{j = 2}^k \{ T_j > x \} ) \lambda_1 e^{- \lambda_1 x} \ dx$? | Since no one has attempted an answer, I will say that if $X,Y$ are random variables $P(t < X < Y) = P(X > t, X < Y) = \int_t^\infty P(X < Y \mid X = x)f(x) \ dx$ by an adjusted version of law of total probability (adjusting the limits of $X$). Here we have $P(t < T_1 < T_j ,j = 2 ,\dots, k) = \int_t^\infty P(\cap_{j = ... | The law of total probability: $P(T > t, Z = 1) = \int_t^\infty P(\cap_{j = 2}^k \{ T_j > x \} ) \lam | Since no one has attempted an answer, I will say that if $X,Y$ are random variables $P(t < X < Y) = P(X > t, X < Y) = \int_t^\infty P(X < Y \mid X = x)f(x) \ dx$ by an adjusted version of law of total | The law of total probability: $P(T > t, Z = 1) = \int_t^\infty P(\cap_{j = 2}^k \{ T_j > x \} ) \lambda_1 e^{- \lambda_1 x} \ dx$?
Since no one has attempted an answer, I will say that if $X,Y$ are random variables $P(t < X < Y) = P(X > t, X < Y) = \int_t^\infty P(X < Y \mid X = x)f(x) \ dx$ by an adjusted version of l... | The law of total probability: $P(T > t, Z = 1) = \int_t^\infty P(\cap_{j = 2}^k \{ T_j > x \} ) \lam
Since no one has attempted an answer, I will say that if $X,Y$ are random variables $P(t < X < Y) = P(X > t, X < Y) = \int_t^\infty P(X < Y \mid X = x)f(x) \ dx$ by an adjusted version of law of total |
37,266 | The law of total probability: $P(T > t, Z = 1) = \int_t^\infty P(\cap_{j = 2}^k \{ T_j > x \} ) \lambda_1 e^{- \lambda_1 x} \ dx$? | There is a good discussion of this theorem in Wikipedia / Exponential Distribution / Distribution of the minimum of exponential random variables.
How exactly was the law of total probability used ... ?
Total probability in the integral you provide sums over all possible outcomes ("total probability") of the other ind... | The law of total probability: $P(T > t, Z = 1) = \int_t^\infty P(\cap_{j = 2}^k \{ T_j > x \} ) \lam | There is a good discussion of this theorem in Wikipedia / Exponential Distribution / Distribution of the minimum of exponential random variables.
How exactly was the law of total probability used ... | The law of total probability: $P(T > t, Z = 1) = \int_t^\infty P(\cap_{j = 2}^k \{ T_j > x \} ) \lambda_1 e^{- \lambda_1 x} \ dx$?
There is a good discussion of this theorem in Wikipedia / Exponential Distribution / Distribution of the minimum of exponential random variables.
How exactly was the law of total probabili... | The law of total probability: $P(T > t, Z = 1) = \int_t^\infty P(\cap_{j = 2}^k \{ T_j > x \} ) \lam
There is a good discussion of this theorem in Wikipedia / Exponential Distribution / Distribution of the minimum of exponential random variables.
How exactly was the law of total probability used ... |
37,267 | The law of total probability: $P(T > t, Z = 1) = \int_t^\infty P(\cap_{j = 2}^k \{ T_j > x \} ) \lambda_1 e^{- \lambda_1 x} \ dx$? | The answer is in your question:
where the probability in the integrand is $P(T_1 > t \ \& \ T_1 < T_j, (j = 2, \dots, k) \mid T_1 = x)$.
With your notation, $A = T_1 > t \ \& \ T_1 < T_j, (j = 2, \dots, k)$.
So
$$
P(A\mid T_1 = x) = I(t >x)P(T_j > x, \,\,(j = 2, \dots, k))
$$
Thus,
$$
P(A) = \int_{-\infty}^{\infty}P(... | The law of total probability: $P(T > t, Z = 1) = \int_t^\infty P(\cap_{j = 2}^k \{ T_j > x \} ) \lam | The answer is in your question:
where the probability in the integrand is $P(T_1 > t \ \& \ T_1 < T_j, (j = 2, \dots, k) \mid T_1 = x)$.
With your notation, $A = T_1 > t \ \& \ T_1 < T_j, (j = 2, \d | The law of total probability: $P(T > t, Z = 1) = \int_t^\infty P(\cap_{j = 2}^k \{ T_j > x \} ) \lambda_1 e^{- \lambda_1 x} \ dx$?
The answer is in your question:
where the probability in the integrand is $P(T_1 > t \ \& \ T_1 < T_j, (j = 2, \dots, k) \mid T_1 = x)$.
With your notation, $A = T_1 > t \ \& \ T_1 < T_j,... | The law of total probability: $P(T > t, Z = 1) = \int_t^\infty P(\cap_{j = 2}^k \{ T_j > x \} ) \lam
The answer is in your question:
where the probability in the integrand is $P(T_1 > t \ \& \ T_1 < T_j, (j = 2, \dots, k) \mid T_1 = x)$.
With your notation, $A = T_1 > t \ \& \ T_1 < T_j, (j = 2, \d |
37,268 | What does non-linearity mean when using only binary predictors? | Aside from interactions, which could be vitally important, I do not see it, either.
Let's consider two features that are $0/1$ binary variables.
$$
x_{i1}\in\{0,1\}\\
x_{i2}\in\{0,1\}\\
$$
Now consider some functions $\phi_i:\rightarrow\mathbb R$ of those variables.
$$
\phi_1(x_{i1}) \in\{a_1, b_1\}\\
\phi_2(x_{i2}) \i... | What does non-linearity mean when using only binary predictors? | Aside from interactions, which could be vitally important, I do not see it, either.
Let's consider two features that are $0/1$ binary variables.
$$
x_{i1}\in\{0,1\}\\
x_{i2}\in\{0,1\}\\
$$
Now conside | What does non-linearity mean when using only binary predictors?
Aside from interactions, which could be vitally important, I do not see it, either.
Let's consider two features that are $0/1$ binary variables.
$$
x_{i1}\in\{0,1\}\\
x_{i2}\in\{0,1\}\\
$$
Now consider some functions $\phi_i:\rightarrow\mathbb R$ of those ... | What does non-linearity mean when using only binary predictors?
Aside from interactions, which could be vitally important, I do not see it, either.
Let's consider two features that are $0/1$ binary variables.
$$
x_{i1}\in\{0,1\}\\
x_{i2}\in\{0,1\}\\
$$
Now conside |
37,269 | Heterogeneous Treatment Effects with Continuous Treatment (e.g. using BART) | The first part is to identify what is the exact estimand you are interested in. In the context of $T \in \{0, 1\}$, things are fairly simple. However, you can picture different variations for a continuous $T$. For example, you can imagine 'shifting' all the observed $T$ values by some constant $\alpha$. See Dia-Munoz &... | Heterogeneous Treatment Effects with Continuous Treatment (e.g. using BART) | The first part is to identify what is the exact estimand you are interested in. In the context of $T \in \{0, 1\}$, things are fairly simple. However, you can picture different variations for a contin | Heterogeneous Treatment Effects with Continuous Treatment (e.g. using BART)
The first part is to identify what is the exact estimand you are interested in. In the context of $T \in \{0, 1\}$, things are fairly simple. However, you can picture different variations for a continuous $T$. For example, you can imagine 'shif... | Heterogeneous Treatment Effects with Continuous Treatment (e.g. using BART)
The first part is to identify what is the exact estimand you are interested in. In the context of $T \in \{0, 1\}$, things are fairly simple. However, you can picture different variations for a contin |
37,270 | Heterogeneous Treatment Effects with Continuous Treatment (e.g. using BART) | With respect to BART's ability to handle continuous treatments, I have found two useful references:
(Hill, 2011): Section 6 of the paper (named "Estimating Dosage Effects") uses BART to estimate the causal effect of getting a dosage level $d\in \mathbb{R}$ compared to getting a dosage of 0.
(Woody et al, 2020): The pa... | Heterogeneous Treatment Effects with Continuous Treatment (e.g. using BART) | With respect to BART's ability to handle continuous treatments, I have found two useful references:
(Hill, 2011): Section 6 of the paper (named "Estimating Dosage Effects") uses BART to estimate the | Heterogeneous Treatment Effects with Continuous Treatment (e.g. using BART)
With respect to BART's ability to handle continuous treatments, I have found two useful references:
(Hill, 2011): Section 6 of the paper (named "Estimating Dosage Effects") uses BART to estimate the causal effect of getting a dosage level $d\i... | Heterogeneous Treatment Effects with Continuous Treatment (e.g. using BART)
With respect to BART's ability to handle continuous treatments, I have found two useful references:
(Hill, 2011): Section 6 of the paper (named "Estimating Dosage Effects") uses BART to estimate the |
37,271 | On solving ode/pde with Neural Networks | The procedure presented in the paper seems to be slightly different from the one above. In the paper the authors make an ansatz that explicitely fulfills the initial conditions. For a second order differential equation of the form
$$
\Psi''(t)=f(t,\Psi(t),\Psi'(t))
$$
with $\Psi(0)=A$ and $\Psi'(0)=B$ they suggest to u... | On solving ode/pde with Neural Networks | The procedure presented in the paper seems to be slightly different from the one above. In the paper the authors make an ansatz that explicitely fulfills the initial conditions. For a second order dif | On solving ode/pde with Neural Networks
The procedure presented in the paper seems to be slightly different from the one above. In the paper the authors make an ansatz that explicitely fulfills the initial conditions. For a second order differential equation of the form
$$
\Psi''(t)=f(t,\Psi(t),\Psi'(t))
$$
with $\Psi(... | On solving ode/pde with Neural Networks
The procedure presented in the paper seems to be slightly different from the one above. In the paper the authors make an ansatz that explicitely fulfills the initial conditions. For a second order dif |
37,272 | Wikipedia Proof About Minimum of Exponential Random Variables | $P(X_k=x)=0$ for every $x$, but you can condition on $X_k=x$, $x \in [0,\infty)$:
\begin{align*}
P(I=k) &= P(X_i>X_k, i\ne k) \\
&= \int_0^\infty P(X_i>X_k, i\ne k\mid X_k=x)\lambda_ke^{-\lambda_k x}dx\\
&= \int_0^\infty P(X_i>x, i\ne k)\lambda_ke^{-\lambda_k x}dx \\
&= \int_0^\infty \lambda_ke^{-\lambda_k x}dx\left(\p... | Wikipedia Proof About Minimum of Exponential Random Variables | $P(X_k=x)=0$ for every $x$, but you can condition on $X_k=x$, $x \in [0,\infty)$:
\begin{align*}
P(I=k) &= P(X_i>X_k, i\ne k) \\
&= \int_0^\infty P(X_i>X_k, i\ne k\mid X_k=x)\lambda_ke^{-\lambda_k x}d | Wikipedia Proof About Minimum of Exponential Random Variables
$P(X_k=x)=0$ for every $x$, but you can condition on $X_k=x$, $x \in [0,\infty)$:
\begin{align*}
P(I=k) &= P(X_i>X_k, i\ne k) \\
&= \int_0^\infty P(X_i>X_k, i\ne k\mid X_k=x)\lambda_ke^{-\lambda_k x}dx\\
&= \int_0^\infty P(X_i>x, i\ne k)\lambda_ke^{-\lambda_... | Wikipedia Proof About Minimum of Exponential Random Variables
$P(X_k=x)=0$ for every $x$, but you can condition on $X_k=x$, $x \in [0,\infty)$:
\begin{align*}
P(I=k) &= P(X_i>X_k, i\ne k) \\
&= \int_0^\infty P(X_i>X_k, i\ne k\mid X_k=x)\lambda_ke^{-\lambda_k x}d |
37,273 | Should we really do Re-Sampling in Class Imbalance data? | In real world, many imbalanced class problems have heavy cost on misclassification. The minority class might be rare, but one occurrence of that class will have really great impact. The minority class is oftentimes "the goal/point" to avoid or to obtain, not "some useless noise class".
This is enough to justify resampl... | Should we really do Re-Sampling in Class Imbalance data? | In real world, many imbalanced class problems have heavy cost on misclassification. The minority class might be rare, but one occurrence of that class will have really great impact. The minority class | Should we really do Re-Sampling in Class Imbalance data?
In real world, many imbalanced class problems have heavy cost on misclassification. The minority class might be rare, but one occurrence of that class will have really great impact. The minority class is oftentimes "the goal/point" to avoid or to obtain, not "som... | Should we really do Re-Sampling in Class Imbalance data?
In real world, many imbalanced class problems have heavy cost on misclassification. The minority class might be rare, but one occurrence of that class will have really great impact. The minority class |
37,274 | Should we really do Re-Sampling in Class Imbalance data? | I'm not sure if this is an answer or not, but I'll throw in my two cents.
Real world test data is imbalanced. Shouldn’t be not modify the training data to make it balanced so that it mimics real world data still?
You're referring to the prevalence of classes in the real world. This is an important point to make when... | Should we really do Re-Sampling in Class Imbalance data? | I'm not sure if this is an answer or not, but I'll throw in my two cents.
Real world test data is imbalanced. Shouldn’t be not modify the training data to make it balanced so that it mimics real worl | Should we really do Re-Sampling in Class Imbalance data?
I'm not sure if this is an answer or not, but I'll throw in my two cents.
Real world test data is imbalanced. Shouldn’t be not modify the training data to make it balanced so that it mimics real world data still?
You're referring to the prevalence of classes in... | Should we really do Re-Sampling in Class Imbalance data?
I'm not sure if this is an answer or not, but I'll throw in my two cents.
Real world test data is imbalanced. Shouldn’t be not modify the training data to make it balanced so that it mimics real worl |
37,275 | Why does PCA often perform comparably well to nonlinear models on nonlinear problems? | The reason you are not breaking PCA is because your data is still "simple" and have strong "linear properties".
In your first example, the line example, we can summarize data as follows: the regression target will be larger, with respect x and y, i.e., in original feature space, the upper right corner.
In your second e... | Why does PCA often perform comparably well to nonlinear models on nonlinear problems? | The reason you are not breaking PCA is because your data is still "simple" and have strong "linear properties".
In your first example, the line example, we can summarize data as follows: the regressio | Why does PCA often perform comparably well to nonlinear models on nonlinear problems?
The reason you are not breaking PCA is because your data is still "simple" and have strong "linear properties".
In your first example, the line example, we can summarize data as follows: the regression target will be larger, with resp... | Why does PCA often perform comparably well to nonlinear models on nonlinear problems?
The reason you are not breaking PCA is because your data is still "simple" and have strong "linear properties".
In your first example, the line example, we can summarize data as follows: the regressio |
37,276 | Seeking an intuitive understanding of independence for random variables | Welcome to this community!
The following answer comes from the point of view of probability as a generalization of logic, and as an expression of a person's degrees of belief.
First of all I'd like to emphasize that independence is not a physical property of objects or quantities. It is a property of a person's degree ... | Seeking an intuitive understanding of independence for random variables | Welcome to this community!
The following answer comes from the point of view of probability as a generalization of logic, and as an expression of a person's degrees of belief.
First of all I'd like to | Seeking an intuitive understanding of independence for random variables
Welcome to this community!
The following answer comes from the point of view of probability as a generalization of logic, and as an expression of a person's degrees of belief.
First of all I'd like to emphasize that independence is not a physical p... | Seeking an intuitive understanding of independence for random variables
Welcome to this community!
The following answer comes from the point of view of probability as a generalization of logic, and as an expression of a person's degrees of belief.
First of all I'd like to |
37,277 | When and why would you not want to use a GAM? | You could take this to extreme and ask why wouldn't we use non-parametric model like $k$-NN regression? Actually, the opposite question Why would anyone use KNN for regression? was asked, and you can check it for more detailed discussion. You can also make the question more broad and ask why wouldn't we use more compli... | When and why would you not want to use a GAM? | You could take this to extreme and ask why wouldn't we use non-parametric model like $k$-NN regression? Actually, the opposite question Why would anyone use KNN for regression? was asked, and you can | When and why would you not want to use a GAM?
You could take this to extreme and ask why wouldn't we use non-parametric model like $k$-NN regression? Actually, the opposite question Why would anyone use KNN for regression? was asked, and you can check it for more detailed discussion. You can also make the question more... | When and why would you not want to use a GAM?
You could take this to extreme and ask why wouldn't we use non-parametric model like $k$-NN regression? Actually, the opposite question Why would anyone use KNN for regression? was asked, and you can |
37,278 | Why K and V are not the same in Transformer attention? | I guess the reason why the specific terms "query", "key" and "value" were chosen is that this attention mechanism resembles a memory access mechanism. The query is the specific element for which we seek a representation. The role of the keys is to respond more or less to the query and the values are here to compose an ... | Why K and V are not the same in Transformer attention? | I guess the reason why the specific terms "query", "key" and "value" were chosen is that this attention mechanism resembles a memory access mechanism. The query is the specific element for which we se | Why K and V are not the same in Transformer attention?
I guess the reason why the specific terms "query", "key" and "value" were chosen is that this attention mechanism resembles a memory access mechanism. The query is the specific element for which we seek a representation. The role of the keys is to respond more or l... | Why K and V are not the same in Transformer attention?
I guess the reason why the specific terms "query", "key" and "value" were chosen is that this attention mechanism resembles a memory access mechanism. The query is the specific element for which we se |
37,279 | Fractional un-differencing of time-series | This paper offers one way to integrate the fractional integrated process where $d\in(-1/2,1/2)$:
Reisen, V. A. and Lopes, S. (1999) Some simulations and applications of forecasting long-memory time series models; Journal of Statistical Planning and Inference, 80, 269–287
You can find it here.
The idea's that when you h... | Fractional un-differencing of time-series | This paper offers one way to integrate the fractional integrated process where $d\in(-1/2,1/2)$:
Reisen, V. A. and Lopes, S. (1999) Some simulations and applications of forecasting long-memory time se | Fractional un-differencing of time-series
This paper offers one way to integrate the fractional integrated process where $d\in(-1/2,1/2)$:
Reisen, V. A. and Lopes, S. (1999) Some simulations and applications of forecasting long-memory time series models; Journal of Statistical Planning and Inference, 80, 269–287
You ca... | Fractional un-differencing of time-series
This paper offers one way to integrate the fractional integrated process where $d\in(-1/2,1/2)$:
Reisen, V. A. and Lopes, S. (1999) Some simulations and applications of forecasting long-memory time se |
37,280 | Optimal scaling of the Random Walk Metroplis-Hastings algorithm and the speed measure of the limiting diffusion | The Langevin diffusion is a process $(X_t)_{t \ge 0}$ satisfying the SDE:
\begin{align*}
d X_t = -\nabla h(X_t) + \sqrt{2} dW_t
\end{align*}
where $(W_t)_{t \ge 0}$ is the standard Brownian motion in $\mathbb R^d$. Under mild conditions on $h$, the above has a unique solution which is a Markov process. Also, the distri... | Optimal scaling of the Random Walk Metroplis-Hastings algorithm and the speed measure of the limitin | The Langevin diffusion is a process $(X_t)_{t \ge 0}$ satisfying the SDE:
\begin{align*}
d X_t = -\nabla h(X_t) + \sqrt{2} dW_t
\end{align*}
where $(W_t)_{t \ge 0}$ is the standard Brownian motion in | Optimal scaling of the Random Walk Metroplis-Hastings algorithm and the speed measure of the limiting diffusion
The Langevin diffusion is a process $(X_t)_{t \ge 0}$ satisfying the SDE:
\begin{align*}
d X_t = -\nabla h(X_t) + \sqrt{2} dW_t
\end{align*}
where $(W_t)_{t \ge 0}$ is the standard Brownian motion in $\mathbb... | Optimal scaling of the Random Walk Metroplis-Hastings algorithm and the speed measure of the limitin
The Langevin diffusion is a process $(X_t)_{t \ge 0}$ satisfying the SDE:
\begin{align*}
d X_t = -\nabla h(X_t) + \sqrt{2} dW_t
\end{align*}
where $(W_t)_{t \ge 0}$ is the standard Brownian motion in |
37,281 | Clarification: Are Generative Adversarial Networks an alternative to MCMC sampling? | Both Markov Chain Monte Carlo (MCMC) and the generator network from a Generative Adversarial Network (GAN) return samples from a probability distribution.
However, they solve different problems:
MCMC works when known the formula for the probability of each configuration (it does not need to be normalized). A classic ex... | Clarification: Are Generative Adversarial Networks an alternative to MCMC sampling? | Both Markov Chain Monte Carlo (MCMC) and the generator network from a Generative Adversarial Network (GAN) return samples from a probability distribution.
However, they solve different problems:
MCMC | Clarification: Are Generative Adversarial Networks an alternative to MCMC sampling?
Both Markov Chain Monte Carlo (MCMC) and the generator network from a Generative Adversarial Network (GAN) return samples from a probability distribution.
However, they solve different problems:
MCMC works when known the formula for the... | Clarification: Are Generative Adversarial Networks an alternative to MCMC sampling?
Both Markov Chain Monte Carlo (MCMC) and the generator network from a Generative Adversarial Network (GAN) return samples from a probability distribution.
However, they solve different problems:
MCMC |
37,282 | Is a visual estimate of homoscedasticity rigorous enough? | I would say that (concentrating on the second plot) that heteroskedasticity is not clear, the spread (vertical) seems larger where the density of points is higher. So to evaluate that, maybe add a local smooth of the residual standard deviation. That could be very informative.
Also answered by comments:
I'm usually gr... | Is a visual estimate of homoscedasticity rigorous enough? | I would say that (concentrating on the second plot) that heteroskedasticity is not clear, the spread (vertical) seems larger where the density of points is higher. So to evaluate that, maybe add a loc | Is a visual estimate of homoscedasticity rigorous enough?
I would say that (concentrating on the second plot) that heteroskedasticity is not clear, the spread (vertical) seems larger where the density of points is higher. So to evaluate that, maybe add a local smooth of the residual standard deviation. That could be ve... | Is a visual estimate of homoscedasticity rigorous enough?
I would say that (concentrating on the second plot) that heteroskedasticity is not clear, the spread (vertical) seems larger where the density of points is higher. So to evaluate that, maybe add a loc |
37,283 | What exactly should be called "projection matrix" in the context of PCA? | $U U^T$ is the projection operator. I believe calling $z = U^T x$ a projection is an abuse of terminology. It is actually a coordinate transformation, where each value in the new coordinates is computed by a scalar projection onto the principal vectors. $U U^T x$ is the orthogonal projection of the data onto the princi... | What exactly should be called "projection matrix" in the context of PCA? | $U U^T$ is the projection operator. I believe calling $z = U^T x$ a projection is an abuse of terminology. It is actually a coordinate transformation, where each value in the new coordinates is comput | What exactly should be called "projection matrix" in the context of PCA?
$U U^T$ is the projection operator. I believe calling $z = U^T x$ a projection is an abuse of terminology. It is actually a coordinate transformation, where each value in the new coordinates is computed by a scalar projection onto the principal ve... | What exactly should be called "projection matrix" in the context of PCA?
$U U^T$ is the projection operator. I believe calling $z = U^T x$ a projection is an abuse of terminology. It is actually a coordinate transformation, where each value in the new coordinates is comput |
37,284 | Analytically solving sampling with or without replacement after Poisson/Negative binomial | The case without replacement
If you have $n$ independent Poisson distributed variables
$$Y_i \sim \text{Pois$(\lambda_i)$}$$
and condition on
$$\sum_{j=i}^n Y_j = K$$
then
$$\lbrace Y_i \rbrace \sim \text{Multinom} \left(K,\left(\frac{\lambda_i}{\sum_{j=1}^n \lambda_j} \right)\right)$$
So you could fill your urn wi... | Analytically solving sampling with or without replacement after Poisson/Negative binomial | The case without replacement
If you have $n$ independent Poisson distributed variables
$$Y_i \sim \text{Pois$(\lambda_i)$}$$
and condition on
$$\sum_{j=i}^n Y_j = K$$
then
$$\lbrace Y_i \rbrace \si | Analytically solving sampling with or without replacement after Poisson/Negative binomial
The case without replacement
If you have $n$ independent Poisson distributed variables
$$Y_i \sim \text{Pois$(\lambda_i)$}$$
and condition on
$$\sum_{j=i}^n Y_j = K$$
then
$$\lbrace Y_i \rbrace \sim \text{Multinom} \left(K,\lef... | Analytically solving sampling with or without replacement after Poisson/Negative binomial
The case without replacement
If you have $n$ independent Poisson distributed variables
$$Y_i \sim \text{Pois$(\lambda_i)$}$$
and condition on
$$\sum_{j=i}^n Y_j = K$$
then
$$\lbrace Y_i \rbrace \si |
37,285 | Is there any such thing as "polar regression"? | There is an enormous amount of statistics related to this under the name circular or directional statistics.
Your case is not so well described though.
What is the 'switch' that you were thinking of by introducing polar coordinates?
Do you mean to solve a situation of a non-negative variable, e.g. some count, as funct... | Is there any such thing as "polar regression"? | There is an enormous amount of statistics related to this under the name circular or directional statistics.
Your case is not so well described though.
What is the 'switch' that you were thinking of | Is there any such thing as "polar regression"?
There is an enormous amount of statistics related to this under the name circular or directional statistics.
Your case is not so well described though.
What is the 'switch' that you were thinking of by introducing polar coordinates?
Do you mean to solve a situation of a n... | Is there any such thing as "polar regression"?
There is an enormous amount of statistics related to this under the name circular or directional statistics.
Your case is not so well described though.
What is the 'switch' that you were thinking of |
37,286 | What are the recent works and research scope in asymptotic inference (large sample theory)? | I am probably less up-to-date than you in this field, so rather than giving you some fish, I am going to try to teach you to fish. I also hope that this answer might be more broadly interesting to readers that also want to look up statistical literature, but are interested in a different topic than you. Please forgi... | What are the recent works and research scope in asymptotic inference (large sample theory)? | I am probably less up-to-date than you in this field, so rather than giving you some fish, I am going to try to teach you to fish. I also hope that this answer might be more broadly interesting to r | What are the recent works and research scope in asymptotic inference (large sample theory)?
I am probably less up-to-date than you in this field, so rather than giving you some fish, I am going to try to teach you to fish. I also hope that this answer might be more broadly interesting to readers that also want to loo... | What are the recent works and research scope in asymptotic inference (large sample theory)?
I am probably less up-to-date than you in this field, so rather than giving you some fish, I am going to try to teach you to fish. I also hope that this answer might be more broadly interesting to r |
37,287 | What are the recent works and research scope in asymptotic inference (large sample theory)? | I would point out that "Asymptotics/Limit Theory" is the general term covering all cases where we study Approximation theory, while the "sample size goes to infinity Asymptotics" is just a particular subfield in there.
Viewing the field as a user of its results, I would not say that major things and breakthroughs are ... | What are the recent works and research scope in asymptotic inference (large sample theory)? | I would point out that "Asymptotics/Limit Theory" is the general term covering all cases where we study Approximation theory, while the "sample size goes to infinity Asymptotics" is just a particular | What are the recent works and research scope in asymptotic inference (large sample theory)?
I would point out that "Asymptotics/Limit Theory" is the general term covering all cases where we study Approximation theory, while the "sample size goes to infinity Asymptotics" is just a particular subfield in there.
Viewing ... | What are the recent works and research scope in asymptotic inference (large sample theory)?
I would point out that "Asymptotics/Limit Theory" is the general term covering all cases where we study Approximation theory, while the "sample size goes to infinity Asymptotics" is just a particular |
37,288 | Standardized and unstandardized variables yield different results for mixed regression model | As pointed out by @BenBolker uncorrelated random slopes are independent terms. Because the random effects are uncorrelated an additive transformation does and will result in a change in estimated correlations as well as the likelihood and predictions of the resulting model (Bates, Mächler, Bolker, & Walker, 2015).
Edit... | Standardized and unstandardized variables yield different results for mixed regression model | As pointed out by @BenBolker uncorrelated random slopes are independent terms. Because the random effects are uncorrelated an additive transformation does and will result in a change in estimated corr | Standardized and unstandardized variables yield different results for mixed regression model
As pointed out by @BenBolker uncorrelated random slopes are independent terms. Because the random effects are uncorrelated an additive transformation does and will result in a change in estimated correlations as well as the lik... | Standardized and unstandardized variables yield different results for mixed regression model
As pointed out by @BenBolker uncorrelated random slopes are independent terms. Because the random effects are uncorrelated an additive transformation does and will result in a change in estimated corr |
37,289 | Definition of softmax function | Yes, you are correct that there is a lack of identifiability unless one of the coefficent vectors is fixed. There are some reasons that don't mention this. I can't speak to why they omit this detail, but here's an explanation of what it is and how to fix it.
Description
Say you have observations $y_i \in \{0, 1, 2, \l... | Definition of softmax function | Yes, you are correct that there is a lack of identifiability unless one of the coefficent vectors is fixed. There are some reasons that don't mention this. I can't speak to why they omit this detail, | Definition of softmax function
Yes, you are correct that there is a lack of identifiability unless one of the coefficent vectors is fixed. There are some reasons that don't mention this. I can't speak to why they omit this detail, but here's an explanation of what it is and how to fix it.
Description
Say you have obse... | Definition of softmax function
Yes, you are correct that there is a lack of identifiability unless one of the coefficent vectors is fixed. There are some reasons that don't mention this. I can't speak to why they omit this detail, |
37,290 | Whether to use EFA or CFA to predict latent variables scores? | As Jeremy pointed out, EFA, CFA, and IRT models scores would usually be in close agreement. This is especially true in the case of unidimensional scales, or 2nd-order factor models (since this will take you back to almost the same configuration when working on the higher-order factor). Moreover, PCA, which does not tak... | Whether to use EFA or CFA to predict latent variables scores? | As Jeremy pointed out, EFA, CFA, and IRT models scores would usually be in close agreement. This is especially true in the case of unidimensional scales, or 2nd-order factor models (since this will ta | Whether to use EFA or CFA to predict latent variables scores?
As Jeremy pointed out, EFA, CFA, and IRT models scores would usually be in close agreement. This is especially true in the case of unidimensional scales, or 2nd-order factor models (since this will take you back to almost the same configuration when working ... | Whether to use EFA or CFA to predict latent variables scores?
As Jeremy pointed out, EFA, CFA, and IRT models scores would usually be in close agreement. This is especially true in the case of unidimensional scales, or 2nd-order factor models (since this will ta |
37,291 | Whether to use EFA or CFA to predict latent variables scores? | It looks as though you are interested in extracting (i.e., observing) latent variable scores for prediction purposes (i.e., not necessarily to make inferences). Given this, I would not rule out PCA either (while dually noting its similarity to EFA; see link below for more details). Also, since your goal prediction, I w... | Whether to use EFA or CFA to predict latent variables scores? | It looks as though you are interested in extracting (i.e., observing) latent variable scores for prediction purposes (i.e., not necessarily to make inferences). Given this, I would not rule out PCA ei | Whether to use EFA or CFA to predict latent variables scores?
It looks as though you are interested in extracting (i.e., observing) latent variable scores for prediction purposes (i.e., not necessarily to make inferences). Given this, I would not rule out PCA either (while dually noting its similarity to EFA; see link ... | Whether to use EFA or CFA to predict latent variables scores?
It looks as though you are interested in extracting (i.e., observing) latent variable scores for prediction purposes (i.e., not necessarily to make inferences). Given this, I would not rule out PCA ei |
37,292 | Post-hoc test to determine difference in variance | I worked on a project not too long ago where I approached this type of problem within the framework of generalized least squares regression. In other words, I fitted a model to my data which estimated the means of the groups while allowing the standard deviations of groups 2, 3, ..., 4 to be equal to:
the standard d... | Post-hoc test to determine difference in variance | I worked on a project not too long ago where I approached this type of problem within the framework of generalized least squares regression. In other words, I fitted a model to my data which estimate | Post-hoc test to determine difference in variance
I worked on a project not too long ago where I approached this type of problem within the framework of generalized least squares regression. In other words, I fitted a model to my data which estimated the means of the groups while allowing the standard deviations of gr... | Post-hoc test to determine difference in variance
I worked on a project not too long ago where I approached this type of problem within the framework of generalized least squares regression. In other words, I fitted a model to my data which estimate |
37,293 | If I have a vector of $N$ correlated probabilities. How can I turn them into binary $0,1$ without destroying the correlation? | I don't understand Gaussian Copula enough to know what is the problem. But I found a way to generate correlated Bernoulli vectors.
Following https://mathoverflow.net/a/19436/105908 if we take a set of fixed vectors $v_1 ... v_n$ and a random vector on the unit sphere $u$, we can transform $u$ into binary $X$ where $X_i... | If I have a vector of $N$ correlated probabilities. How can I turn them into binary $0,1$ without de | I don't understand Gaussian Copula enough to know what is the problem. But I found a way to generate correlated Bernoulli vectors.
Following https://mathoverflow.net/a/19436/105908 if we take a set of | If I have a vector of $N$ correlated probabilities. How can I turn them into binary $0,1$ without destroying the correlation?
I don't understand Gaussian Copula enough to know what is the problem. But I found a way to generate correlated Bernoulli vectors.
Following https://mathoverflow.net/a/19436/105908 if we take a ... | If I have a vector of $N$ correlated probabilities. How can I turn them into binary $0,1$ without de
I don't understand Gaussian Copula enough to know what is the problem. But I found a way to generate correlated Bernoulli vectors.
Following https://mathoverflow.net/a/19436/105908 if we take a set of |
37,294 | Invertibility in Reinsch form Derivation (Smoothing Splines) | I was hoping to find a more intuitive proof, but the matrix can be shown to be invertible by directly showing that its determinant is nonzero.
First note that the knots are located at the $K$ unique values of $\mathbf{x}$. Let $\boldsymbol{\xi}$ represent these knots, in ascending order.
Also, $d_j(\xi_i) = 0$ if $i \... | Invertibility in Reinsch form Derivation (Smoothing Splines) | I was hoping to find a more intuitive proof, but the matrix can be shown to be invertible by directly showing that its determinant is nonzero.
First note that the knots are located at the $K$ unique v | Invertibility in Reinsch form Derivation (Smoothing Splines)
I was hoping to find a more intuitive proof, but the matrix can be shown to be invertible by directly showing that its determinant is nonzero.
First note that the knots are located at the $K$ unique values of $\mathbf{x}$. Let $\boldsymbol{\xi}$ represent the... | Invertibility in Reinsch form Derivation (Smoothing Splines)
I was hoping to find a more intuitive proof, but the matrix can be shown to be invertible by directly showing that its determinant is nonzero.
First note that the knots are located at the $K$ unique v |
37,295 | Would you flag this data as fraudulent? | The ethical issue is paramount here. I'd agree on this information in regarding the data as highly suspect and report it as such; I would never call "fraudulence" because that's for others to determine after investigation and in some countries could lay you open to legal action or its threat. As for attaching a probabi... | Would you flag this data as fraudulent? | The ethical issue is paramount here. I'd agree on this information in regarding the data as highly suspect and report it as such; I would never call "fraudulence" because that's for others to determin | Would you flag this data as fraudulent?
The ethical issue is paramount here. I'd agree on this information in regarding the data as highly suspect and report it as such; I would never call "fraudulence" because that's for others to determine after investigation and in some countries could lay you open to legal action o... | Would you flag this data as fraudulent?
The ethical issue is paramount here. I'd agree on this information in regarding the data as highly suspect and report it as such; I would never call "fraudulence" because that's for others to determin |
37,296 | Fitting Gaussian mixture models with dirac delta functions | I am confused why EM doesn't encouter this problem, as fitting GMM
with Dirac delta functions is not typically discussed in textbooks.
The unboundedness of the likelihood of a Gaussian mixture model is discussed in many textbooks (incl. mine). It is rarely a problem for EM as the corresponding modes are very narrow ... | Fitting Gaussian mixture models with dirac delta functions | I am confused why EM doesn't encouter this problem, as fitting GMM
with Dirac delta functions is not typically discussed in textbooks.
The unboundedness of the likelihood of a Gaussian mixture mode | Fitting Gaussian mixture models with dirac delta functions
I am confused why EM doesn't encouter this problem, as fitting GMM
with Dirac delta functions is not typically discussed in textbooks.
The unboundedness of the likelihood of a Gaussian mixture model is discussed in many textbooks (incl. mine). It is rarely a... | Fitting Gaussian mixture models with dirac delta functions
I am confused why EM doesn't encouter this problem, as fitting GMM
with Dirac delta functions is not typically discussed in textbooks.
The unboundedness of the likelihood of a Gaussian mixture mode |
37,297 | Sum of linear combination of product of exponentials is exponential | Not a complete answer, sorry, but a few ideas (to long for a comment). Note that what you have is a product of $K+1$ iid random variables, where $K$ is a random variable (rv) with a poisson distribution with parameter $\lambda$. That can be used for another "sanity check", a simulation (using exponentials of rate 1): ... | Sum of linear combination of product of exponentials is exponential | Not a complete answer, sorry, but a few ideas (to long for a comment). Note that what you have is a product of $K+1$ iid random variables, where $K$ is a random variable (rv) with a poisson distributi | Sum of linear combination of product of exponentials is exponential
Not a complete answer, sorry, but a few ideas (to long for a comment). Note that what you have is a product of $K+1$ iid random variables, where $K$ is a random variable (rv) with a poisson distribution with parameter $\lambda$. That can be used for a... | Sum of linear combination of product of exponentials is exponential
Not a complete answer, sorry, but a few ideas (to long for a comment). Note that what you have is a product of $K+1$ iid random variables, where $K$ is a random variable (rv) with a poisson distributi |
37,298 | Confidence Interval Widths as Measure for Variability | In brief, it's not a bad measure, but there are some things to be aware of.
For (almost) any given data generating process, increasing the number of data will decrease the width of the confidence interval. Under some extra assumptions (those necessary for the Central Limit Theorem), the width will, asymptotically, foll... | Confidence Interval Widths as Measure for Variability | In brief, it's not a bad measure, but there are some things to be aware of.
For (almost) any given data generating process, increasing the number of data will decrease the width of the confidence inte | Confidence Interval Widths as Measure for Variability
In brief, it's not a bad measure, but there are some things to be aware of.
For (almost) any given data generating process, increasing the number of data will decrease the width of the confidence interval. Under some extra assumptions (those necessary for the Centra... | Confidence Interval Widths as Measure for Variability
In brief, it's not a bad measure, but there are some things to be aware of.
For (almost) any given data generating process, increasing the number of data will decrease the width of the confidence inte |
37,299 | Relationship between variance of mean and mean variance | $$\newcommand{\Var}{\operatorname{Var}}$$
The article compares two different estimates for the true population mean, $\mu$.
The mean computed from five random samples $x_i$
$$\hat{\mu}_x = \frac{x_1 + x_2 + x_3 + x_4 + x_5}{5}$$
and the mean computed from five random quintiles $y_i$ (5 quintiles selected by five times... | Relationship between variance of mean and mean variance | $$\newcommand{\Var}{\operatorname{Var}}$$
The article compares two different estimates for the true population mean, $\mu$.
The mean computed from five random samples $x_i$
$$\hat{\mu}_x = \frac{x_1 | Relationship between variance of mean and mean variance
$$\newcommand{\Var}{\operatorname{Var}}$$
The article compares two different estimates for the true population mean, $\mu$.
The mean computed from five random samples $x_i$
$$\hat{\mu}_x = \frac{x_1 + x_2 + x_3 + x_4 + x_5}{5}$$
and the mean computed from five ra... | Relationship between variance of mean and mean variance
$$\newcommand{\Var}{\operatorname{Var}}$$
The article compares two different estimates for the true population mean, $\mu$.
The mean computed from five random samples $x_i$
$$\hat{\mu}_x = \frac{x_1 |
37,300 | Calculating Probability of x1 > x2 | The setting is conventionally expressed in the form
$$y = X\beta + \varepsilon$$
for an $n$-vector $y$ of responses, an $n\times k$ model matrix $X$, and a $k$-vector of parameters $\beta$, under the assumptions that the random errors $\varepsilon = (\varepsilon_i)$ are uncorrelated with equal variances $\sigma^2$ and ... | Calculating Probability of x1 > x2 | The setting is conventionally expressed in the form
$$y = X\beta + \varepsilon$$
for an $n$-vector $y$ of responses, an $n\times k$ model matrix $X$, and a $k$-vector of parameters $\beta$, under the | Calculating Probability of x1 > x2
The setting is conventionally expressed in the form
$$y = X\beta + \varepsilon$$
for an $n$-vector $y$ of responses, an $n\times k$ model matrix $X$, and a $k$-vector of parameters $\beta$, under the assumptions that the random errors $\varepsilon = (\varepsilon_i)$ are uncorrelated w... | Calculating Probability of x1 > x2
The setting is conventionally expressed in the form
$$y = X\beta + \varepsilon$$
for an $n$-vector $y$ of responses, an $n\times k$ model matrix $X$, and a $k$-vector of parameters $\beta$, under the |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.