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 |
|---|---|---|---|---|---|---|
49,501 | Observed vs predicted values from a logit model | It sounds as if you are wanting to check the calibration of a model on the same dataset used to build the model. This will require the use of the bootstrap to re-fit the model 300 times. You can use a bootstrap overfitting-corrected nonparametric calibration curve with a nonparametric smoother. It is not a good idea... | Observed vs predicted values from a logit model | It sounds as if you are wanting to check the calibration of a model on the same dataset used to build the model. This will require the use of the bootstrap to re-fit the model 300 times. You can use | Observed vs predicted values from a logit model
It sounds as if you are wanting to check the calibration of a model on the same dataset used to build the model. This will require the use of the bootstrap to re-fit the model 300 times. You can use a bootstrap overfitting-corrected nonparametric calibration curve with ... | Observed vs predicted values from a logit model
It sounds as if you are wanting to check the calibration of a model on the same dataset used to build the model. This will require the use of the bootstrap to re-fit the model 300 times. You can use |
49,502 | What is the correct way to choose tests for pairwise comparison after ANOVA? | When choosing a test you have to consider two important things:
A: is the test reliable when the ANOVA assumption have been violated;
the question is if the test performs well when the group sizes are different and when the population variances are very different or you have not normally distributed data;
B: does the t... | What is the correct way to choose tests for pairwise comparison after ANOVA? | When choosing a test you have to consider two important things:
A: is the test reliable when the ANOVA assumption have been violated;
the question is if the test performs well when the group sizes are | What is the correct way to choose tests for pairwise comparison after ANOVA?
When choosing a test you have to consider two important things:
A: is the test reliable when the ANOVA assumption have been violated;
the question is if the test performs well when the group sizes are different and when the population variance... | What is the correct way to choose tests for pairwise comparison after ANOVA?
When choosing a test you have to consider two important things:
A: is the test reliable when the ANOVA assumption have been violated;
the question is if the test performs well when the group sizes are |
49,503 | What is the correct way to choose tests for pairwise comparison after ANOVA? | I will recommend you to have a read at BIOMETRY of Sokal and Rholf (old one, but with clear concepts for starting) and Experimental Design and Data Analysis for Biologists by Quinn and Keough. This last one is available in pdf on the web. | What is the correct way to choose tests for pairwise comparison after ANOVA? | I will recommend you to have a read at BIOMETRY of Sokal and Rholf (old one, but with clear concepts for starting) and Experimental Design and Data Analysis for Biologists by Quinn and Keough. This la | What is the correct way to choose tests for pairwise comparison after ANOVA?
I will recommend you to have a read at BIOMETRY of Sokal and Rholf (old one, but with clear concepts for starting) and Experimental Design and Data Analysis for Biologists by Quinn and Keough. This last one is available in pdf on the web. | What is the correct way to choose tests for pairwise comparison after ANOVA?
I will recommend you to have a read at BIOMETRY of Sokal and Rholf (old one, but with clear concepts for starting) and Experimental Design and Data Analysis for Biologists by Quinn and Keough. This la |
49,504 | Power calculations, logistic regression with continuous exposure--cohort [duplicate] | I'm skirting around the question on your simulation set up, and addressing the wider question of determining sample size in this scenario.
You could turn the question on its head (as I understand your question -- a binomial outcome, one continuous predictor) and then determine the power to detect a difference in means ... | Power calculations, logistic regression with continuous exposure--cohort [duplicate] | I'm skirting around the question on your simulation set up, and addressing the wider question of determining sample size in this scenario.
You could turn the question on its head (as I understand your | Power calculations, logistic regression with continuous exposure--cohort [duplicate]
I'm skirting around the question on your simulation set up, and addressing the wider question of determining sample size in this scenario.
You could turn the question on its head (as I understand your question -- a binomial outcome, on... | Power calculations, logistic regression with continuous exposure--cohort [duplicate]
I'm skirting around the question on your simulation set up, and addressing the wider question of determining sample size in this scenario.
You could turn the question on its head (as I understand your |
49,505 | Number of interactions in ANOVA with 4 independent variables | This is a relatively simple application of combinatorical calculations. The total number of combinations is given as $2^k$ where $k$ is the number of variables in the ANOVA ($k=4$ in your case). The logic behind this is that each variable can be either included or not included in each interaction term (eg the main ef... | Number of interactions in ANOVA with 4 independent variables | This is a relatively simple application of combinatorical calculations. The total number of combinations is given as $2^k$ where $k$ is the number of variables in the ANOVA ($k=4$ in your case). The | Number of interactions in ANOVA with 4 independent variables
This is a relatively simple application of combinatorical calculations. The total number of combinations is given as $2^k$ where $k$ is the number of variables in the ANOVA ($k=4$ in your case). The logic behind this is that each variable can be either incl... | Number of interactions in ANOVA with 4 independent variables
This is a relatively simple application of combinatorical calculations. The total number of combinations is given as $2^k$ where $k$ is the number of variables in the ANOVA ($k=4$ in your case). The |
49,506 | Number of interactions in ANOVA with 4 independent variables | These are the possible interactions between the 4 IV's:
1x2
1x3
1x4
2x3
2x4
3x4
1x2x3
1x2x4
1x3x4
2x3x4
1x2x3x4
Which comes to a total of 11. | Number of interactions in ANOVA with 4 independent variables | These are the possible interactions between the 4 IV's:
1x2
1x3
1x4
2x3
2x4
3x4
1x2x3
1x2x4
1x3x4
2x3x4
1x2x3x4
Which comes to a total of 11. | Number of interactions in ANOVA with 4 independent variables
These are the possible interactions between the 4 IV's:
1x2
1x3
1x4
2x3
2x4
3x4
1x2x3
1x2x4
1x3x4
2x3x4
1x2x3x4
Which comes to a total of 11. | Number of interactions in ANOVA with 4 independent variables
These are the possible interactions between the 4 IV's:
1x2
1x3
1x4
2x3
2x4
3x4
1x2x3
1x2x4
1x3x4
2x3x4
1x2x3x4
Which comes to a total of 11. |
49,507 | t-test when observations are years | Many years late, but:
This is not a good idea. Profitability of companies is likely to be autocorrelated. This means that observations are not independent, which is a basic assumption of t-tests. The autocorrelation structure can be accounted for in other analytical approaches. | t-test when observations are years | Many years late, but:
This is not a good idea. Profitability of companies is likely to be autocorrelated. This means that observations are not independent, which is a basic assumption of t-tests. The | t-test when observations are years
Many years late, but:
This is not a good idea. Profitability of companies is likely to be autocorrelated. This means that observations are not independent, which is a basic assumption of t-tests. The autocorrelation structure can be accounted for in other analytical approaches. | t-test when observations are years
Many years late, but:
This is not a good idea. Profitability of companies is likely to be autocorrelated. This means that observations are not independent, which is a basic assumption of t-tests. The |
49,508 | What is the difference between using the multiplication rule or using Venn diagram subtraction for probability? | Let's draw pictures in which regions depict events (such as "the first light is red") and their areas are proportional to the probabilities of those events. Taking care to show areas accurately extends the Venn diagram metaphor in a useful quantitative way.
For the traffic light problem, I will divide a unit square (r... | What is the difference between using the multiplication rule or using Venn diagram subtraction for p | Let's draw pictures in which regions depict events (such as "the first light is red") and their areas are proportional to the probabilities of those events. Taking care to show areas accurately exten | What is the difference between using the multiplication rule or using Venn diagram subtraction for probability?
Let's draw pictures in which regions depict events (such as "the first light is red") and their areas are proportional to the probabilities of those events. Taking care to show areas accurately extends the V... | What is the difference between using the multiplication rule or using Venn diagram subtraction for p
Let's draw pictures in which regions depict events (such as "the first light is red") and their areas are proportional to the probabilities of those events. Taking care to show areas accurately exten |
49,509 | What is the difference between using the multiplication rule or using Venn diagram subtraction for probability? | In problems like this it is important that you read specifically which information is given to you and which is the problem. So let's start with assignment 1.
The probability that Andrew is still alive - let's call that $P(A)$ and the probability that Ellen is still alive is $P(B)$.
What we are looking for is the event... | What is the difference between using the multiplication rule or using Venn diagram subtraction for p | In problems like this it is important that you read specifically which information is given to you and which is the problem. So let's start with assignment 1.
The probability that Andrew is still aliv | What is the difference between using the multiplication rule or using Venn diagram subtraction for probability?
In problems like this it is important that you read specifically which information is given to you and which is the problem. So let's start with assignment 1.
The probability that Andrew is still alive - let'... | What is the difference between using the multiplication rule or using Venn diagram subtraction for p
In problems like this it is important that you read specifically which information is given to you and which is the problem. So let's start with assignment 1.
The probability that Andrew is still aliv |
49,510 | Using a particle filter for robot localization | The Kalman filter is optimal when the system is linear and the noises are Gaussian, so if that's the case there is no reason to switch to a particle filter (which, apart from being suboptimal for linear systems, takes much more time to run). | Using a particle filter for robot localization | The Kalman filter is optimal when the system is linear and the noises are Gaussian, so if that's the case there is no reason to switch to a particle filter (which, apart from being suboptimal for line | Using a particle filter for robot localization
The Kalman filter is optimal when the system is linear and the noises are Gaussian, so if that's the case there is no reason to switch to a particle filter (which, apart from being suboptimal for linear systems, takes much more time to run). | Using a particle filter for robot localization
The Kalman filter is optimal when the system is linear and the noises are Gaussian, so if that's the case there is no reason to switch to a particle filter (which, apart from being suboptimal for line |
49,511 | How to get the standardized beta coefficients from glm.nb regression in R? | A quick way to get at the standardized beta coefficients directly from any lm (or glm) model in R, try using lm.beta(model). In the example provided, this would be:
library("MASS")
nb = glm.nb(responseCountVar ~ predictor1 + predictor2 +
predictor3 + predictor4 + predictor5 + predictor6 +
predictor7 + predict... | How to get the standardized beta coefficients from glm.nb regression in R? | A quick way to get at the standardized beta coefficients directly from any lm (or glm) model in R, try using lm.beta(model). In the example provided, this would be:
library("MASS")
nb = glm.nb(respons | How to get the standardized beta coefficients from glm.nb regression in R?
A quick way to get at the standardized beta coefficients directly from any lm (or glm) model in R, try using lm.beta(model). In the example provided, this would be:
library("MASS")
nb = glm.nb(responseCountVar ~ predictor1 + predictor2 +
pr... | How to get the standardized beta coefficients from glm.nb regression in R?
A quick way to get at the standardized beta coefficients directly from any lm (or glm) model in R, try using lm.beta(model). In the example provided, this would be:
library("MASS")
nb = glm.nb(respons |
49,512 | Clustering high-dimensional sparse binary data | Consider using a graph based approach.
Try to find a threshold to define when users are "somewhat similar". It can be quite low. Build a graph of these somewhat similar users.
Then use a Clique detection approach to find groups in this graph. | Clustering high-dimensional sparse binary data | Consider using a graph based approach.
Try to find a threshold to define when users are "somewhat similar". It can be quite low. Build a graph of these somewhat similar users.
Then use a Clique detect | Clustering high-dimensional sparse binary data
Consider using a graph based approach.
Try to find a threshold to define when users are "somewhat similar". It can be quite low. Build a graph of these somewhat similar users.
Then use a Clique detection approach to find groups in this graph. | Clustering high-dimensional sparse binary data
Consider using a graph based approach.
Try to find a threshold to define when users are "somewhat similar". It can be quite low. Build a graph of these somewhat similar users.
Then use a Clique detect |
49,513 | Clustering high-dimensional sparse binary data | I suggest a cluster analysis. Joachim Bacher discusses the different dissimilarity coefficients in depth in his script about cluster analysis, in particular the effects of treating the absence of a treat. For instance : are two items correlated when both show zero ? I remember that he also works with a multiple-respons... | Clustering high-dimensional sparse binary data | I suggest a cluster analysis. Joachim Bacher discusses the different dissimilarity coefficients in depth in his script about cluster analysis, in particular the effects of treating the absence of a tr | Clustering high-dimensional sparse binary data
I suggest a cluster analysis. Joachim Bacher discusses the different dissimilarity coefficients in depth in his script about cluster analysis, in particular the effects of treating the absence of a treat. For instance : are two items correlated when both show zero ? I reme... | Clustering high-dimensional sparse binary data
I suggest a cluster analysis. Joachim Bacher discusses the different dissimilarity coefficients in depth in his script about cluster analysis, in particular the effects of treating the absence of a tr |
49,514 | Two-level hierarchical model using time-series cross sectional data? | I'm not 100% sure, so check carefully, and you'll probably want to put priors on the variances instead of the 1.0E-12, but maybe something like this?
model {
for( i in 1 : nData ) {
crime[i] ~ dbern( mu[i] )
logit(mu[i]) <- base + b0[counties[i], period[i]] + b1[counties[i], period[i]] * police[i]
}
base ... | Two-level hierarchical model using time-series cross sectional data? | I'm not 100% sure, so check carefully, and you'll probably want to put priors on the variances instead of the 1.0E-12, but maybe something like this?
model {
for( i in 1 : nData ) {
crime[i] ~ d | Two-level hierarchical model using time-series cross sectional data?
I'm not 100% sure, so check carefully, and you'll probably want to put priors on the variances instead of the 1.0E-12, but maybe something like this?
model {
for( i in 1 : nData ) {
crime[i] ~ dbern( mu[i] )
logit(mu[i]) <- base + b0[countie... | Two-level hierarchical model using time-series cross sectional data?
I'm not 100% sure, so check carefully, and you'll probably want to put priors on the variances instead of the 1.0E-12, but maybe something like this?
model {
for( i in 1 : nData ) {
crime[i] ~ d |
49,515 | Adversarial noise in PCA | Here is one for you: the 10 percent of outliers have so
much influenced the PCA that the 1st principal component
is now nearly orthogonal to its true value.
library(MASS)
n<-50
p<-100
eps<-0.1
x0<-mvrnorm(n-floor(n*eps),rep(0,p),diag(p))
x1<-mvrnorm(floor(n*eps),rep(100,p),diag(p)/100)
O0<-prcomp(x0)
O1<-prcomp(rbind... | Adversarial noise in PCA | Here is one for you: the 10 percent of outliers have so
much influenced the PCA that the 1st principal component
is now nearly orthogonal to its true value.
library(MASS)
n<-50
p<-100
eps<-0.1
x0<-m | Adversarial noise in PCA
Here is one for you: the 10 percent of outliers have so
much influenced the PCA that the 1st principal component
is now nearly orthogonal to its true value.
library(MASS)
n<-50
p<-100
eps<-0.1
x0<-mvrnorm(n-floor(n*eps),rep(0,p),diag(p))
x1<-mvrnorm(floor(n*eps),rep(100,p),diag(p)/100)
O0<-pr... | Adversarial noise in PCA
Here is one for you: the 10 percent of outliers have so
much influenced the PCA that the 1st principal component
is now nearly orthogonal to its true value.
library(MASS)
n<-50
p<-100
eps<-0.1
x0<-m |
49,516 | Tolerance interval for Deming regression | Below is the code. Not very pretty, but (as said in the update of my question) it works well.
# returns estimates
deming.estim <- function(x,y,lambda=1){ # lambda=sigmay²/sigmax²
n <- length(x)
my <- mean(y)
mx <- mean(x)
SSDy <- crossprod(y-my)[,]
SSDx <- crossprod(x-mx)[,]
SPDxy <- crossprod(x-mx,y-my)... | Tolerance interval for Deming regression | Below is the code. Not very pretty, but (as said in the update of my question) it works well.
# returns estimates
deming.estim <- function(x,y,lambda=1){ # lambda=sigmay²/sigmax²
n <- length(x)
| Tolerance interval for Deming regression
Below is the code. Not very pretty, but (as said in the update of my question) it works well.
# returns estimates
deming.estim <- function(x,y,lambda=1){ # lambda=sigmay²/sigmax²
n <- length(x)
my <- mean(y)
mx <- mean(x)
SSDy <- crossprod(y-my)[,]
SSDx <- crossprod... | Tolerance interval for Deming regression
Below is the code. Not very pretty, but (as said in the update of my question) it works well.
# returns estimates
deming.estim <- function(x,y,lambda=1){ # lambda=sigmay²/sigmax²
n <- length(x)
|
49,517 | How to perform unsupervised Random Forest classification using R? | Over classification may be caused by prediction bias, which is a problem for the canonical RF method and for which a number of modifications have been researched. Probably the principal approach to mitigating bias is to utilise randomised split thresholds, sometimes referred to as 'extreme' random forest. I'm not sure ... | How to perform unsupervised Random Forest classification using R? | Over classification may be caused by prediction bias, which is a problem for the canonical RF method and for which a number of modifications have been researched. Probably the principal approach to mi | How to perform unsupervised Random Forest classification using R?
Over classification may be caused by prediction bias, which is a problem for the canonical RF method and for which a number of modifications have been researched. Probably the principal approach to mitigating bias is to utilise randomised split threshold... | How to perform unsupervised Random Forest classification using R?
Over classification may be caused by prediction bias, which is a problem for the canonical RF method and for which a number of modifications have been researched. Probably the principal approach to mi |
49,518 | How to perform unsupervised Random Forest classification using R? | In the randomforest function, instead of listing a y ~ x model, simply input your predictor matrix.
randomforest thinks you want to run a supervised classification because you are listing the classifying variable factor(category) as the y in your model. | How to perform unsupervised Random Forest classification using R? | In the randomforest function, instead of listing a y ~ x model, simply input your predictor matrix.
randomforest thinks you want to run a supervised classification because you are listing the classify | How to perform unsupervised Random Forest classification using R?
In the randomforest function, instead of listing a y ~ x model, simply input your predictor matrix.
randomforest thinks you want to run a supervised classification because you are listing the classifying variable factor(category) as the y in your model. | How to perform unsupervised Random Forest classification using R?
In the randomforest function, instead of listing a y ~ x model, simply input your predictor matrix.
randomforest thinks you want to run a supervised classification because you are listing the classify |
49,519 | Non-algebric curve-fitting along weighted pointcloud (if possible using python) | (assuming you want to use python)
The easiest (given what's currently available) would be to use a polynomial and robust methods from statsmodels.
something like
endog = y # observed points, one dimensional array
#polynomial array as explanatory variable:
#assuming x contains the vertical points
x = x / float(x.max() ... | Non-algebric curve-fitting along weighted pointcloud (if possible using python) | (assuming you want to use python)
The easiest (given what's currently available) would be to use a polynomial and robust methods from statsmodels.
something like
endog = y # observed points, one dime | Non-algebric curve-fitting along weighted pointcloud (if possible using python)
(assuming you want to use python)
The easiest (given what's currently available) would be to use a polynomial and robust methods from statsmodels.
something like
endog = y # observed points, one dimensional array
#polynomial array as expla... | Non-algebric curve-fitting along weighted pointcloud (if possible using python)
(assuming you want to use python)
The easiest (given what's currently available) would be to use a polynomial and robust methods from statsmodels.
something like
endog = y # observed points, one dime |
49,520 | Non-algebric curve-fitting along weighted pointcloud (if possible using python) | This is an old post but here's a paper worth considering:
"Multidimensional curve fitting to unorganized data points by nonlinear minimization", Lian Fang and David C Gossard
http://www.cs.jhu.edu/~misha/Fall05/Papers/fang95.pdf
And for unordered points this paper is interesting. It describes a method of finding the o... | Non-algebric curve-fitting along weighted pointcloud (if possible using python) | This is an old post but here's a paper worth considering:
"Multidimensional curve fitting to unorganized data points by nonlinear minimization", Lian Fang and David C Gossard
http://www.cs.jhu.edu/~m | Non-algebric curve-fitting along weighted pointcloud (if possible using python)
This is an old post but here's a paper worth considering:
"Multidimensional curve fitting to unorganized data points by nonlinear minimization", Lian Fang and David C Gossard
http://www.cs.jhu.edu/~misha/Fall05/Papers/fang95.pdf
And for un... | Non-algebric curve-fitting along weighted pointcloud (if possible using python)
This is an old post but here's a paper worth considering:
"Multidimensional curve fitting to unorganized data points by nonlinear minimization", Lian Fang and David C Gossard
http://www.cs.jhu.edu/~m |
49,521 | Imputation of missing response variables | As per the first answer, in general there is no reason not to impute all of your variables in one go, generating a single set of imputed datasets. Your two outcomes being strongly correlated should not be too much of an issue - when they serve as independent variables in the imputation model(s) for your missing covaria... | Imputation of missing response variables | As per the first answer, in general there is no reason not to impute all of your variables in one go, generating a single set of imputed datasets. Your two outcomes being strongly correlated should no | Imputation of missing response variables
As per the first answer, in general there is no reason not to impute all of your variables in one go, generating a single set of imputed datasets. Your two outcomes being strongly correlated should not be too much of an issue - when they serve as independent variables in the imp... | Imputation of missing response variables
As per the first answer, in general there is no reason not to impute all of your variables in one go, generating a single set of imputed datasets. Your two outcomes being strongly correlated should no |
49,522 | Imputation of missing response variables | In general, multiple imputation works by using all available information in the model to simulate the missing values: I use the word "simulate" because you're technically doing more than just prediction, which involves more parametric assumptions.
I assume the outcomes are either jointly missing or jointly observed, th... | Imputation of missing response variables | In general, multiple imputation works by using all available information in the model to simulate the missing values: I use the word "simulate" because you're technically doing more than just predicti | Imputation of missing response variables
In general, multiple imputation works by using all available information in the model to simulate the missing values: I use the word "simulate" because you're technically doing more than just prediction, which involves more parametric assumptions.
I assume the outcomes are eithe... | Imputation of missing response variables
In general, multiple imputation works by using all available information in the model to simulate the missing values: I use the word "simulate" because you're technically doing more than just predicti |
49,523 | Should false discovery be controlled at the data acquisition level, or should this be at the data interpretation level? | I would argue strongly that is should apply only at the interpretation level. Multiplicity implicitly involves the definition of an investigation by an investigator(s) (i.e. the study wise error rate to be controlled) and needs to accurately reflect the intentions that drove the process of generating inputs to the infe... | Should false discovery be controlled at the data acquisition level, or should this be at the data in | I would argue strongly that is should apply only at the interpretation level. Multiplicity implicitly involves the definition of an investigation by an investigator(s) (i.e. the study wise error rate | Should false discovery be controlled at the data acquisition level, or should this be at the data interpretation level?
I would argue strongly that is should apply only at the interpretation level. Multiplicity implicitly involves the definition of an investigation by an investigator(s) (i.e. the study wise error rate ... | Should false discovery be controlled at the data acquisition level, or should this be at the data in
I would argue strongly that is should apply only at the interpretation level. Multiplicity implicitly involves the definition of an investigation by an investigator(s) (i.e. the study wise error rate |
49,524 | Should false discovery be controlled at the data acquisition level, or should this be at the data interpretation level? | As @phaneron has stated, there is no need for multiplicity control if you only consider one gene.
I wish to add to that hypothesis testing serves two purposes: (a) convince yourself and (b) convince "the world".
For the purpose of (a), recall that the BH procedure controls the "expected proportion of false discoveries... | Should false discovery be controlled at the data acquisition level, or should this be at the data in | As @phaneron has stated, there is no need for multiplicity control if you only consider one gene.
I wish to add to that hypothesis testing serves two purposes: (a) convince yourself and (b) convince " | Should false discovery be controlled at the data acquisition level, or should this be at the data interpretation level?
As @phaneron has stated, there is no need for multiplicity control if you only consider one gene.
I wish to add to that hypothesis testing serves two purposes: (a) convince yourself and (b) convince "... | Should false discovery be controlled at the data acquisition level, or should this be at the data in
As @phaneron has stated, there is no need for multiplicity control if you only consider one gene.
I wish to add to that hypothesis testing serves two purposes: (a) convince yourself and (b) convince " |
49,525 | Perpendicular offsets in a weighted least squares regression | Completely revised answer, see history.
Take the formula from your link. It contains a lot of sums iterating over your input points. Make sure to multiply the summands in all of these sums with your weights $w$:
\begin{align*}
\sum_{i=1}^n x_i &\to \sum_{i=1}^n w_ix_i \\
\sum_{i=1}^n y_i &\to \sum_{i=1}^n w_iy_i \\
\su... | Perpendicular offsets in a weighted least squares regression | Completely revised answer, see history.
Take the formula from your link. It contains a lot of sums iterating over your input points. Make sure to multiply the summands in all of these sums with your w | Perpendicular offsets in a weighted least squares regression
Completely revised answer, see history.
Take the formula from your link. It contains a lot of sums iterating over your input points. Make sure to multiply the summands in all of these sums with your weights $w$:
\begin{align*}
\sum_{i=1}^n x_i &\to \sum_{i=1}... | Perpendicular offsets in a weighted least squares regression
Completely revised answer, see history.
Take the formula from your link. It contains a lot of sums iterating over your input points. Make sure to multiply the summands in all of these sums with your w |
49,526 | Creating ROC curve for multi-level logistic regression model in R | There's a whole lot of literature about multi-class extensions for ROC.
I have some presentations with illustrations how the calculation works at softclassval's home page (softclassval calculates sensitivities etc. if you have partial class memberships, also for multiple classes - but that is probably an overkill for... | Creating ROC curve for multi-level logistic regression model in R | There's a whole lot of literature about multi-class extensions for ROC.
I have some presentations with illustrations how the calculation works at softclassval's home page (softclassval calculates se | Creating ROC curve for multi-level logistic regression model in R
There's a whole lot of literature about multi-class extensions for ROC.
I have some presentations with illustrations how the calculation works at softclassval's home page (softclassval calculates sensitivities etc. if you have partial class memberships... | Creating ROC curve for multi-level logistic regression model in R
There's a whole lot of literature about multi-class extensions for ROC.
I have some presentations with illustrations how the calculation works at softclassval's home page (softclassval calculates se |
49,527 | Creating ROC curve for multi-level logistic regression model in R | Not possible.
The very idea of ROC requires the concept of sensitivity and specificity, which in turn take only real numbers. To have the idea of ROC working with more than two-valued logic, you would need to accept that sensitivity and specificity are vectors.
You might always convert your dependent variable into set... | Creating ROC curve for multi-level logistic regression model in R | Not possible.
The very idea of ROC requires the concept of sensitivity and specificity, which in turn take only real numbers. To have the idea of ROC working with more than two-valued logic, you would | Creating ROC curve for multi-level logistic regression model in R
Not possible.
The very idea of ROC requires the concept of sensitivity and specificity, which in turn take only real numbers. To have the idea of ROC working with more than two-valued logic, you would need to accept that sensitivity and specificity are v... | Creating ROC curve for multi-level logistic regression model in R
Not possible.
The very idea of ROC requires the concept of sensitivity and specificity, which in turn take only real numbers. To have the idea of ROC working with more than two-valued logic, you would |
49,528 | Predictive model & standardized variables | If one were to fit a model $y= \beta_1 + \beta_2z$ where $z=\frac{x-\bar{x}}{sd(x)}$ and use that model to predict $y$ for some given values of $x$, then use the original $\bar{x}$ and $sd(x)$ to standardize the new $x$ values being used for prediction.
However, if one has many new values of $y$ and $x$ and wants to re... | Predictive model & standardized variables | If one were to fit a model $y= \beta_1 + \beta_2z$ where $z=\frac{x-\bar{x}}{sd(x)}$ and use that model to predict $y$ for some given values of $x$, then use the original $\bar{x}$ and $sd(x)$ to stan | Predictive model & standardized variables
If one were to fit a model $y= \beta_1 + \beta_2z$ where $z=\frac{x-\bar{x}}{sd(x)}$ and use that model to predict $y$ for some given values of $x$, then use the original $\bar{x}$ and $sd(x)$ to standardize the new $x$ values being used for prediction.
However, if one has many... | Predictive model & standardized variables
If one were to fit a model $y= \beta_1 + \beta_2z$ where $z=\frac{x-\bar{x}}{sd(x)}$ and use that model to predict $y$ for some given values of $x$, then use the original $\bar{x}$ and $sd(x)$ to stan |
49,529 | Predictive model & standardized variables | This is one of the major problems with standardizing variables prior to regression. The entire meaning of the output is sample-dependent. I much prefer working with unstandardized variables so that this problem (and similar ones) do not arise. | Predictive model & standardized variables | This is one of the major problems with standardizing variables prior to regression. The entire meaning of the output is sample-dependent. I much prefer working with unstandardized variables so that th | Predictive model & standardized variables
This is one of the major problems with standardizing variables prior to regression. The entire meaning of the output is sample-dependent. I much prefer working with unstandardized variables so that this problem (and similar ones) do not arise. | Predictive model & standardized variables
This is one of the major problems with standardizing variables prior to regression. The entire meaning of the output is sample-dependent. I much prefer working with unstandardized variables so that th |
49,530 | What test should be used for detecting team imbalances in a game? | I think it's a bad idea to ignore the strengths of the players, but it may be hard to completely separate the possible flaws in the rating system from the possible advantages of one option versus another.
You could try the following test for each pair of options A and B. Your null hypothesis is that the rating formula... | What test should be used for detecting team imbalances in a game? | I think it's a bad idea to ignore the strengths of the players, but it may be hard to completely separate the possible flaws in the rating system from the possible advantages of one option versus anot | What test should be used for detecting team imbalances in a game?
I think it's a bad idea to ignore the strengths of the players, but it may be hard to completely separate the possible flaws in the rating system from the possible advantages of one option versus another.
You could try the following test for each pair o... | What test should be used for detecting team imbalances in a game?
I think it's a bad idea to ignore the strengths of the players, but it may be hard to completely separate the possible flaws in the rating system from the possible advantages of one option versus anot |
49,531 | Supervised classifier for events with missing data | As requested, I'll elaborate on my comment, although I don't have experience using it. I work with neural networks for regression problems and often construct new features, but I don't have to deal with missing data so I'm not sure whether this will work.
Let's suppose the features of your data look like
$(0,1)$
$(0... | Supervised classifier for events with missing data | As requested, I'll elaborate on my comment, although I don't have experience using it. I work with neural networks for regression problems and often construct new features, but I don't have to deal wi | Supervised classifier for events with missing data
As requested, I'll elaborate on my comment, although I don't have experience using it. I work with neural networks for regression problems and often construct new features, but I don't have to deal with missing data so I'm not sure whether this will work.
Let's suppo... | Supervised classifier for events with missing data
As requested, I'll elaborate on my comment, although I don't have experience using it. I work with neural networks for regression problems and often construct new features, but I don't have to deal wi |
49,532 | Supervised classifier for events with missing data | Doug Zare's suggestion is a little like a missing data technique called multiple imputation. The data point gets repeated many times with plausible values for the missing variable being input. I think that would allow the classifier to gain the information from the correct coordinate and in a way learn the uncertaint... | Supervised classifier for events with missing data | Doug Zare's suggestion is a little like a missing data technique called multiple imputation. The data point gets repeated many times with plausible values for the missing variable being input. I thi | Supervised classifier for events with missing data
Doug Zare's suggestion is a little like a missing data technique called multiple imputation. The data point gets repeated many times with plausible values for the missing variable being input. I think that would allow the classifier to gain the information from the c... | Supervised classifier for events with missing data
Doug Zare's suggestion is a little like a missing data technique called multiple imputation. The data point gets repeated many times with plausible values for the missing variable being input. I thi |
49,533 | Distribution of atan2 of normal r.v.'s | I don't think there is a simple expression for the pdf. If there were, then there would be a simple expression for the usual $\arctan$, and of the ratio between two (noncentered) normal distributions. The latter is studied in papers like Marsaglia (1965, 2006) and Cedilnik et al (2004). | Distribution of atan2 of normal r.v.'s | I don't think there is a simple expression for the pdf. If there were, then there would be a simple expression for the usual $\arctan$, and of the ratio between two (noncentered) normal distributions. | Distribution of atan2 of normal r.v.'s
I don't think there is a simple expression for the pdf. If there were, then there would be a simple expression for the usual $\arctan$, and of the ratio between two (noncentered) normal distributions. The latter is studied in papers like Marsaglia (1965, 2006) and Cedilnik et al (... | Distribution of atan2 of normal r.v.'s
I don't think there is a simple expression for the pdf. If there were, then there would be a simple expression for the usual $\arctan$, and of the ratio between two (noncentered) normal distributions. |
49,534 | What are Effective Regression Techniques for Linguistic Analysis of Linked Data? | Both questions are hard, I'll give a shot at the first one.
A straightforward approach to classify documents is to compute their tf-idf. In short, you consider the text is a bag of words, i.e. that it has no linear structure, and you compute a score that says how much the word is specific of a document. I explain a lit... | What are Effective Regression Techniques for Linguistic Analysis of Linked Data? | Both questions are hard, I'll give a shot at the first one.
A straightforward approach to classify documents is to compute their tf-idf. In short, you consider the text is a bag of words, i.e. that it | What are Effective Regression Techniques for Linguistic Analysis of Linked Data?
Both questions are hard, I'll give a shot at the first one.
A straightforward approach to classify documents is to compute their tf-idf. In short, you consider the text is a bag of words, i.e. that it has no linear structure, and you compu... | What are Effective Regression Techniques for Linguistic Analysis of Linked Data?
Both questions are hard, I'll give a shot at the first one.
A straightforward approach to classify documents is to compute their tf-idf. In short, you consider the text is a bag of words, i.e. that it |
49,535 | Chi square test on non-normal distributions | Normality is a requirement for the chi square test that a variance equals a specified value but there are many tests that are called chi-square because their asymptotic null distribution is chi-square such as the chi-square test for independence in contingency tables and the chi square goodness of fit test. Neither of... | Chi square test on non-normal distributions | Normality is a requirement for the chi square test that a variance equals a specified value but there are many tests that are called chi-square because their asymptotic null distribution is chi-square | Chi square test on non-normal distributions
Normality is a requirement for the chi square test that a variance equals a specified value but there are many tests that are called chi-square because their asymptotic null distribution is chi-square such as the chi-square test for independence in contingency tables and the ... | Chi square test on non-normal distributions
Normality is a requirement for the chi square test that a variance equals a specified value but there are many tests that are called chi-square because their asymptotic null distribution is chi-square |
49,536 | Chi square test on non-normal distributions | I learned the chi squared distribution as a special case of a gamma density function. What I have read today online on wikipedia and in texts sometimes says "If Z1, ..., Zk are independent, standard normal random variables, then the sum of their squares is distributed according to the chi-squared distribution with k d... | Chi square test on non-normal distributions | I learned the chi squared distribution as a special case of a gamma density function. What I have read today online on wikipedia and in texts sometimes says "If Z1, ..., Zk are independent, standard | Chi square test on non-normal distributions
I learned the chi squared distribution as a special case of a gamma density function. What I have read today online on wikipedia and in texts sometimes says "If Z1, ..., Zk are independent, standard normal random variables, then the sum of their squares is distributed accord... | Chi square test on non-normal distributions
I learned the chi squared distribution as a special case of a gamma density function. What I have read today online on wikipedia and in texts sometimes says "If Z1, ..., Zk are independent, standard |
49,537 | To aggregate and lose resolution OR not to aggregate and suffer with correlated binary data? | You're right that averaging over the responses and performing a repeated measures ANOVA is not the ideal thing to do. Your intuitions are good; there should be a difference between a global accuracy that's based on 48 responses and one based on 400. First, you should be using logistic regression. If you're not very ... | To aggregate and lose resolution OR not to aggregate and suffer with correlated binary data? | You're right that averaging over the responses and performing a repeated measures ANOVA is not the ideal thing to do. Your intuitions are good; there should be a difference between a global accuracy | To aggregate and lose resolution OR not to aggregate and suffer with correlated binary data?
You're right that averaging over the responses and performing a repeated measures ANOVA is not the ideal thing to do. Your intuitions are good; there should be a difference between a global accuracy that's based on 48 response... | To aggregate and lose resolution OR not to aggregate and suffer with correlated binary data?
You're right that averaging over the responses and performing a repeated measures ANOVA is not the ideal thing to do. Your intuitions are good; there should be a difference between a global accuracy |
49,538 | How to know the stochastic gradient descent is converging when the objective function is expensive to compute | Yes, if your cost function is convex, stochastic gradient descent (SGD) should converge.
If computing the cost value takes too much time, then you can estimate it by computing the cost over a randomly sampled subset of your dataset. You can naturally do this in the mini-batch setting. | How to know the stochastic gradient descent is converging when the objective function is expensive t | Yes, if your cost function is convex, stochastic gradient descent (SGD) should converge.
If computing the cost value takes too much time, then you can estimate it by computing the cost over a randoml | How to know the stochastic gradient descent is converging when the objective function is expensive to compute
Yes, if your cost function is convex, stochastic gradient descent (SGD) should converge.
If computing the cost value takes too much time, then you can estimate it by computing the cost over a randomly sampled ... | How to know the stochastic gradient descent is converging when the objective function is expensive t
Yes, if your cost function is convex, stochastic gradient descent (SGD) should converge.
If computing the cost value takes too much time, then you can estimate it by computing the cost over a randoml |
49,539 | How to know the stochastic gradient descent is converging when the objective function is expensive to compute | One approach is to use "progressive validation error" for SGD diagnostics as per "Beating the Hold-Out: Bounds for K-fold and Progressive Cross-Validation"
Basically, every new case is first plugged into your loss function, and only then is passed to SGD, and the resulting loss function values are averaged across "rec... | How to know the stochastic gradient descent is converging when the objective function is expensive t | One approach is to use "progressive validation error" for SGD diagnostics as per "Beating the Hold-Out: Bounds for K-fold and Progressive Cross-Validation"
Basically, every new case is first plugged | How to know the stochastic gradient descent is converging when the objective function is expensive to compute
One approach is to use "progressive validation error" for SGD diagnostics as per "Beating the Hold-Out: Bounds for K-fold and Progressive Cross-Validation"
Basically, every new case is first plugged into your ... | How to know the stochastic gradient descent is converging when the objective function is expensive t
One approach is to use "progressive validation error" for SGD diagnostics as per "Beating the Hold-Out: Bounds for K-fold and Progressive Cross-Validation"
Basically, every new case is first plugged |
49,540 | How do you identify the variables that separate several groups? | The first question is whether you already know which frog belongs to which morphotype If you do know, and your goal is to use these frogs to better analyze how the morphotypes vary on these variables, then you want discriminant analysis. This might enable later investigators to accurately place frogs into morphotypes b... | How do you identify the variables that separate several groups? | The first question is whether you already know which frog belongs to which morphotype If you do know, and your goal is to use these frogs to better analyze how the morphotypes vary on these variables, | How do you identify the variables that separate several groups?
The first question is whether you already know which frog belongs to which morphotype If you do know, and your goal is to use these frogs to better analyze how the morphotypes vary on these variables, then you want discriminant analysis. This might enable ... | How do you identify the variables that separate several groups?
The first question is whether you already know which frog belongs to which morphotype If you do know, and your goal is to use these frogs to better analyze how the morphotypes vary on these variables, |
49,541 | How do you identify the variables that separate several groups? | I think that you know the group membership so as @PeterFlom said discriminant analysis is a good altternative. A similar method would be to estimate a Multinomial (logit or probit) model. In this model, you estimate the probability of clasyfing a frog into a given $k$ group depending on its characteristics $x$.
$P[G=k]... | How do you identify the variables that separate several groups? | I think that you know the group membership so as @PeterFlom said discriminant analysis is a good altternative. A similar method would be to estimate a Multinomial (logit or probit) model. In this mode | How do you identify the variables that separate several groups?
I think that you know the group membership so as @PeterFlom said discriminant analysis is a good altternative. A similar method would be to estimate a Multinomial (logit or probit) model. In this model, you estimate the probability of clasyfing a frog into... | How do you identify the variables that separate several groups?
I think that you know the group membership so as @PeterFlom said discriminant analysis is a good altternative. A similar method would be to estimate a Multinomial (logit or probit) model. In this mode |
49,542 | Are sample means for quantiles of sorted data unbiased estimators of the true means? | For some distributions there is a positive bias due to measurement errors. If you assume the noise has mean $0$, then if you sample people from the top decile, their average measured income will be the average income of the top decile. However, the top decile of your sample will include some people who have displaced p... | Are sample means for quantiles of sorted data unbiased estimators of the true means? | For some distributions there is a positive bias due to measurement errors. If you assume the noise has mean $0$, then if you sample people from the top decile, their average measured income will be th | Are sample means for quantiles of sorted data unbiased estimators of the true means?
For some distributions there is a positive bias due to measurement errors. If you assume the noise has mean $0$, then if you sample people from the top decile, their average measured income will be the average income of the top decile.... | Are sample means for quantiles of sorted data unbiased estimators of the true means?
For some distributions there is a positive bias due to measurement errors. If you assume the noise has mean $0$, then if you sample people from the top decile, their average measured income will be th |
49,543 | Posterior distribution for multinomial parameter | Unfortunately, the data is a bit difficult to deal with, since it
consists of mostly "soft evidence", so the parameter estimation
doesn't seem to have an easy analytic solution such as a direct update
of Dirichlet counts.
— why does that follow? Why not just scale the counts based on the amount of evidence supp... | Posterior distribution for multinomial parameter | Unfortunately, the data is a bit difficult to deal with, since it
consists of mostly "soft evidence", so the parameter estimation
doesn't seem to have an easy analytic solution such as a direct up | Posterior distribution for multinomial parameter
Unfortunately, the data is a bit difficult to deal with, since it
consists of mostly "soft evidence", so the parameter estimation
doesn't seem to have an easy analytic solution such as a direct update
of Dirichlet counts.
— why does that follow? Why not just scal... | Posterior distribution for multinomial parameter
Unfortunately, the data is a bit difficult to deal with, since it
consists of mostly "soft evidence", so the parameter estimation
doesn't seem to have an easy analytic solution such as a direct up |
49,544 | Calculating entropy of a binary matrix | The results you are referring to can be replicated using the following code:
https://github.com/cosmoharrigan/matrix-entropy
This code generates the visualizations and includes the calculation of the "profile" (a list of the entropies) of the set of scaled filtered matrices. Note that the specific entropy values have b... | Calculating entropy of a binary matrix | The results you are referring to can be replicated using the following code:
https://github.com/cosmoharrigan/matrix-entropy
This code generates the visualizations and includes the calculation of the | Calculating entropy of a binary matrix
The results you are referring to can be replicated using the following code:
https://github.com/cosmoharrigan/matrix-entropy
This code generates the visualizations and includes the calculation of the "profile" (a list of the entropies) of the set of scaled filtered matrices. Note ... | Calculating entropy of a binary matrix
The results you are referring to can be replicated using the following code:
https://github.com/cosmoharrigan/matrix-entropy
This code generates the visualizations and includes the calculation of the |
49,545 | Wilcoxon test in boot() function | This is not boot that is calling the Wilcoxon test, but verification::roc.area which can be checked by looking at the on-line help:
P-value produced is related to the Mann-Whitney U statistics. The
p-value is calculated using the wilcox.test function which
automatically handles ties and makes approximations for l... | Wilcoxon test in boot() function | This is not boot that is calling the Wilcoxon test, but verification::roc.area which can be checked by looking at the on-line help:
P-value produced is related to the Mann-Whitney U statistics. The
| Wilcoxon test in boot() function
This is not boot that is calling the Wilcoxon test, but verification::roc.area which can be checked by looking at the on-line help:
P-value produced is related to the Mann-Whitney U statistics. The
p-value is calculated using the wilcox.test function which
automatically handles ti... | Wilcoxon test in boot() function
This is not boot that is calling the Wilcoxon test, but verification::roc.area which can be checked by looking at the on-line help:
P-value produced is related to the Mann-Whitney U statistics. The
|
49,546 | Are randomForest variable importance values comparable across same variables on different dates? | Ad 1. IncMSE is an actual result of cross-bag test, so in theory it is better than IncNodePurity which is a training by-product.
Ad 3. & 4. To be honest, those values have a little sense of their own -- they depend on how good RF is on a current test, and this is terribly variable. If you want to compare anything, comp... | Are randomForest variable importance values comparable across same variables on different dates? | Ad 1. IncMSE is an actual result of cross-bag test, so in theory it is better than IncNodePurity which is a training by-product.
Ad 3. & 4. To be honest, those values have a little sense of their own | Are randomForest variable importance values comparable across same variables on different dates?
Ad 1. IncMSE is an actual result of cross-bag test, so in theory it is better than IncNodePurity which is a training by-product.
Ad 3. & 4. To be honest, those values have a little sense of their own -- they depend on how g... | Are randomForest variable importance values comparable across same variables on different dates?
Ad 1. IncMSE is an actual result of cross-bag test, so in theory it is better than IncNodePurity which is a training by-product.
Ad 3. & 4. To be honest, those values have a little sense of their own |
49,547 | Mixture distributions moments if one distribution has undefined/infinite moments | Yes, you are correct. If $X_1 \sim f_1$, $X_2 \sim f_2$, and $X_3 \sim f_3$, then your equation shows that $$E(X_3) = p \cdot E(X_1) + (1-p) \cdot E(X_2)$$ Therefore if either one of $E(X_1)$ or $E(X_2)$ in non-finite/non-existent then $E(X_3)$ will be non-finite/non-existent also if $p \in (0,1)$ - this is true even i... | Mixture distributions moments if one distribution has undefined/infinite moments | Yes, you are correct. If $X_1 \sim f_1$, $X_2 \sim f_2$, and $X_3 \sim f_3$, then your equation shows that $$E(X_3) = p \cdot E(X_1) + (1-p) \cdot E(X_2)$$ Therefore if either one of $E(X_1)$ or $E(X_ | Mixture distributions moments if one distribution has undefined/infinite moments
Yes, you are correct. If $X_1 \sim f_1$, $X_2 \sim f_2$, and $X_3 \sim f_3$, then your equation shows that $$E(X_3) = p \cdot E(X_1) + (1-p) \cdot E(X_2)$$ Therefore if either one of $E(X_1)$ or $E(X_2)$ in non-finite/non-existent then $E(... | Mixture distributions moments if one distribution has undefined/infinite moments
Yes, you are correct. If $X_1 \sim f_1$, $X_2 \sim f_2$, and $X_3 \sim f_3$, then your equation shows that $$E(X_3) = p \cdot E(X_1) + (1-p) \cdot E(X_2)$$ Therefore if either one of $E(X_1)$ or $E(X_ |
49,548 | Normalize sample data for clustering | Clustering in general requires a similarity metric to compute a partitioning of your data. Do you know how to compute the similarity of $\vec{a}$ to $\vec{b}$? Whether you need normalization or not will mainly depend on this question. If you don't have such a metric/measure, and you want to go with the regular Euclidea... | Normalize sample data for clustering | Clustering in general requires a similarity metric to compute a partitioning of your data. Do you know how to compute the similarity of $\vec{a}$ to $\vec{b}$? Whether you need normalization or not wi | Normalize sample data for clustering
Clustering in general requires a similarity metric to compute a partitioning of your data. Do you know how to compute the similarity of $\vec{a}$ to $\vec{b}$? Whether you need normalization or not will mainly depend on this question. If you don't have such a metric/measure, and you... | Normalize sample data for clustering
Clustering in general requires a similarity metric to compute a partitioning of your data. Do you know how to compute the similarity of $\vec{a}$ to $\vec{b}$? Whether you need normalization or not wi |
49,549 | Normalize sample data for clustering | To perform z-score normalisation on x, you don't have to test whether x is of normal distribution or not.
For whatever distribution, z will be in a distribution of zero mean, one standard deviation.
Type of distribution matters when you use any test on the data, based on that particular distribution.
Convenience of nor... | Normalize sample data for clustering | To perform z-score normalisation on x, you don't have to test whether x is of normal distribution or not.
For whatever distribution, z will be in a distribution of zero mean, one standard deviation.
T | Normalize sample data for clustering
To perform z-score normalisation on x, you don't have to test whether x is of normal distribution or not.
For whatever distribution, z will be in a distribution of zero mean, one standard deviation.
Type of distribution matters when you use any test on the data, based on that partic... | Normalize sample data for clustering
To perform z-score normalisation on x, you don't have to test whether x is of normal distribution or not.
For whatever distribution, z will be in a distribution of zero mean, one standard deviation.
T |
49,550 | How to conduct a factor analysis on questionnaire data based on 30 items in three blocks? | I think that what you need is Multiple Correspondence Analysis (MCA). You can lookup the basics on Wikipedia.
MCA is part of the R-core, in the package MASS. So I suggest you start with
library(MASS)
?mca
Here is the help page for the function mca.
The output of MCA is a set of ordered factors capturing the relationsh... | How to conduct a factor analysis on questionnaire data based on 30 items in three blocks? | I think that what you need is Multiple Correspondence Analysis (MCA). You can lookup the basics on Wikipedia.
MCA is part of the R-core, in the package MASS. So I suggest you start with
library(MASS)
| How to conduct a factor analysis on questionnaire data based on 30 items in three blocks?
I think that what you need is Multiple Correspondence Analysis (MCA). You can lookup the basics on Wikipedia.
MCA is part of the R-core, in the package MASS. So I suggest you start with
library(MASS)
?mca
Here is the help page fo... | How to conduct a factor analysis on questionnaire data based on 30 items in three blocks?
I think that what you need is Multiple Correspondence Analysis (MCA). You can lookup the basics on Wikipedia.
MCA is part of the R-core, in the package MASS. So I suggest you start with
library(MASS)
|
49,551 | How to conduct a factor analysis on questionnaire data based on 30 items in three blocks? | One approach would be to calculate first principal component in each of the three blocks, and then perform a regression with your final score as the response variable and those three block scores as the explanatory variables. This seems to me one way to answer your question of how much each block contributes to varian... | How to conduct a factor analysis on questionnaire data based on 30 items in three blocks? | One approach would be to calculate first principal component in each of the three blocks, and then perform a regression with your final score as the response variable and those three block scores as t | How to conduct a factor analysis on questionnaire data based on 30 items in three blocks?
One approach would be to calculate first principal component in each of the three blocks, and then perform a regression with your final score as the response variable and those three block scores as the explanatory variables. Thi... | How to conduct a factor analysis on questionnaire data based on 30 items in three blocks?
One approach would be to calculate first principal component in each of the three blocks, and then perform a regression with your final score as the response variable and those three block scores as t |
49,552 | Odds of X occurrences in a row given Y trials (A coin flip problem) | I believe this is only a partial solution for the case when $N<2X$.
Define $A_i$ to be the set of all sequences of $Y$ events with $N$ successes such that at least $X$ successes occur consecutively beginning at position $i$ in the sequence, and no string of $X$ successes is to begin before position $i$. For example, if... | Odds of X occurrences in a row given Y trials (A coin flip problem) | I believe this is only a partial solution for the case when $N<2X$.
Define $A_i$ to be the set of all sequences of $Y$ events with $N$ successes such that at least $X$ successes occur consecutively be | Odds of X occurrences in a row given Y trials (A coin flip problem)
I believe this is only a partial solution for the case when $N<2X$.
Define $A_i$ to be the set of all sequences of $Y$ events with $N$ successes such that at least $X$ successes occur consecutively beginning at position $i$ in the sequence, and no stri... | Odds of X occurrences in a row given Y trials (A coin flip problem)
I believe this is only a partial solution for the case when $N<2X$.
Define $A_i$ to be the set of all sequences of $Y$ events with $N$ successes such that at least $X$ successes occur consecutively be |
49,553 | Odds of X occurrences in a row given Y trials (A coin flip problem) | This is a difficult problem. Let's start with the N condition. As often a possible way to simplify the problem is to instead calculate the chance of never X occurences in a row given Y trials.
Note that for $Y < X$ you will never have X occurences, much less in a row, so the probability here is 1. Let us denote the pr... | Odds of X occurrences in a row given Y trials (A coin flip problem) | This is a difficult problem. Let's start with the N condition. As often a possible way to simplify the problem is to instead calculate the chance of never X occurences in a row given Y trials.
Note t | Odds of X occurrences in a row given Y trials (A coin flip problem)
This is a difficult problem. Let's start with the N condition. As often a possible way to simplify the problem is to instead calculate the chance of never X occurences in a row given Y trials.
Note that for $Y < X$ you will never have X occurences, mu... | Odds of X occurrences in a row given Y trials (A coin flip problem)
This is a difficult problem. Let's start with the N condition. As often a possible way to simplify the problem is to instead calculate the chance of never X occurences in a row given Y trials.
Note t |
49,554 | Odds of X occurrences in a row given Y trials (A coin flip problem) | This solution works for all values of $n$.
You can define a recursive formula for the probability of $x$ consecutive successes, $y$ trials, and $n$ successes:
\begin{align}
f(x,y,n) &= g(x, x, y, n)
\end{align}
where
\begin{align}
g(x,x',y,n) &=
\begin{cases}
1 & \text{if }x = 0 \\
\frac{n}{y}g(x-1,x',y-1,n-1)+\frac{y-... | Odds of X occurrences in a row given Y trials (A coin flip problem) | This solution works for all values of $n$.
You can define a recursive formula for the probability of $x$ consecutive successes, $y$ trials, and $n$ successes:
\begin{align}
f(x,y,n) &= g(x, x, y, n)
\ | Odds of X occurrences in a row given Y trials (A coin flip problem)
This solution works for all values of $n$.
You can define a recursive formula for the probability of $x$ consecutive successes, $y$ trials, and $n$ successes:
\begin{align}
f(x,y,n) &= g(x, x, y, n)
\end{align}
where
\begin{align}
g(x,x',y,n) &=
\begin... | Odds of X occurrences in a row given Y trials (A coin flip problem)
This solution works for all values of $n$.
You can define a recursive formula for the probability of $x$ consecutive successes, $y$ trials, and $n$ successes:
\begin{align}
f(x,y,n) &= g(x, x, y, n)
\ |
49,555 | Odds of X occurrences in a row given Y trials (A coin flip problem) | If p is the probability of success the probability of X successes in a row is p^X. For your problem these X successes can occur in many different slots in the sequence. So you have to multiply by the number of ways you can pick X consecutive slots out of the total of Y available slots with the additional requirement t... | Odds of X occurrences in a row given Y trials (A coin flip problem) | If p is the probability of success the probability of X successes in a row is p^X. For your problem these X successes can occur in many different slots in the sequence. So you have to multiply by the | Odds of X occurrences in a row given Y trials (A coin flip problem)
If p is the probability of success the probability of X successes in a row is p^X. For your problem these X successes can occur in many different slots in the sequence. So you have to multiply by the number of ways you can pick X consecutive slots out... | Odds of X occurrences in a row given Y trials (A coin flip problem)
If p is the probability of success the probability of X successes in a row is p^X. For your problem these X successes can occur in many different slots in the sequence. So you have to multiply by the |
49,556 | PDFs and probability in naive Bayes classification | You're right that the statement is wrong. It should be a likelihood:
$$L(c \mid x=v)=\frac{1}{\sqrt{2\pi\sigma_c^2}}e^{-\frac{(v-\mu_c)^2}{2\sigma_c^2}}$$
A likelihood applies here because we are interested in the relative likelihood that a point belongs to each class:
$$P(c=c' \mid x=v) = \frac{L(c=c' \mid x=v)}{\sum... | PDFs and probability in naive Bayes classification | You're right that the statement is wrong. It should be a likelihood:
$$L(c \mid x=v)=\frac{1}{\sqrt{2\pi\sigma_c^2}}e^{-\frac{(v-\mu_c)^2}{2\sigma_c^2}}$$
A likelihood applies here because we are int | PDFs and probability in naive Bayes classification
You're right that the statement is wrong. It should be a likelihood:
$$L(c \mid x=v)=\frac{1}{\sqrt{2\pi\sigma_c^2}}e^{-\frac{(v-\mu_c)^2}{2\sigma_c^2}}$$
A likelihood applies here because we are interested in the relative likelihood that a point belongs to each class... | PDFs and probability in naive Bayes classification
You're right that the statement is wrong. It should be a likelihood:
$$L(c \mid x=v)=\frac{1}{\sqrt{2\pi\sigma_c^2}}e^{-\frac{(v-\mu_c)^2}{2\sigma_c^2}}$$
A likelihood applies here because we are int |
49,557 | PDFs and probability in naive Bayes classification | If you're interested in a lengthy and rigorous explanation check this out. To summarize, it all comes down to integral approximations. To get the probability of a specific variable value from the variable's continuous probability density function (PDF), you integrate the PDF around the value in question over an interva... | PDFs and probability in naive Bayes classification | If you're interested in a lengthy and rigorous explanation check this out. To summarize, it all comes down to integral approximations. To get the probability of a specific variable value from the vari | PDFs and probability in naive Bayes classification
If you're interested in a lengthy and rigorous explanation check this out. To summarize, it all comes down to integral approximations. To get the probability of a specific variable value from the variable's continuous probability density function (PDF), you integrate t... | PDFs and probability in naive Bayes classification
If you're interested in a lengthy and rigorous explanation check this out. To summarize, it all comes down to integral approximations. To get the probability of a specific variable value from the vari |
49,558 | Markov chain convergence, total variation and KL divergence | It is important to state the theorem correctly with all conditions. Theorem 4 in the paper by Roberts and Rosenthal states that the $n$-step transition probabilities $P^n(x, \cdot)$ converge in total variation to a probability measure $\pi$ for $\pi$-almost all $x$ if the chain is $\phi$-irreducible, aperiodic and has ... | Markov chain convergence, total variation and KL divergence | It is important to state the theorem correctly with all conditions. Theorem 4 in the paper by Roberts and Rosenthal states that the $n$-step transition probabilities $P^n(x, \cdot)$ converge in total | Markov chain convergence, total variation and KL divergence
It is important to state the theorem correctly with all conditions. Theorem 4 in the paper by Roberts and Rosenthal states that the $n$-step transition probabilities $P^n(x, \cdot)$ converge in total variation to a probability measure $\pi$ for $\pi$-almost al... | Markov chain convergence, total variation and KL divergence
It is important to state the theorem correctly with all conditions. Theorem 4 in the paper by Roberts and Rosenthal states that the $n$-step transition probabilities $P^n(x, \cdot)$ converge in total |
49,559 | Interpreting positive and negative signs of the elements of PCA eigenvectors | I think you have it backwards. If the value is positive, then a higher score on that variable is associated with a higher score on the component, if the value is negative, then a higher score implies a lower score on the component.
In addition, people sometimes use PCA to determine whether to keep or combine certain... | Interpreting positive and negative signs of the elements of PCA eigenvectors | I think you have it backwards. If the value is positive, then a higher score on that variable is associated with a higher score on the component, if the value is negative, then a higher score implies | Interpreting positive and negative signs of the elements of PCA eigenvectors
I think you have it backwards. If the value is positive, then a higher score on that variable is associated with a higher score on the component, if the value is negative, then a higher score implies a lower score on the component.
In addit... | Interpreting positive and negative signs of the elements of PCA eigenvectors
I think you have it backwards. If the value is positive, then a higher score on that variable is associated with a higher score on the component, if the value is negative, then a higher score implies |
49,560 | Interpreting positive and negative signs of the elements of PCA eigenvectors | centering your variables shouldn't change the PCA results, as PCA first determines a correlation matrix and goes on from there. The correlations between your variables should be the same regardless, so the PCA results should not be affected by any mean centering you perform. | Interpreting positive and negative signs of the elements of PCA eigenvectors | centering your variables shouldn't change the PCA results, as PCA first determines a correlation matrix and goes on from there. The correlations between your variables should be the same regardless, s | Interpreting positive and negative signs of the elements of PCA eigenvectors
centering your variables shouldn't change the PCA results, as PCA first determines a correlation matrix and goes on from there. The correlations between your variables should be the same regardless, so the PCA results should not be affected by... | Interpreting positive and negative signs of the elements of PCA eigenvectors
centering your variables shouldn't change the PCA results, as PCA first determines a correlation matrix and goes on from there. The correlations between your variables should be the same regardless, s |
49,561 | Interpreting positive and negative signs of the elements of PCA eigenvectors | When we say correlation that means can be two directional i.e. positive and negative. Interpretation of the principal components is based on finding which variables are most strongly correlated with each component, i.e., which of these numbers are large in magnitude, the farthest from zero in either positive or negativ... | Interpreting positive and negative signs of the elements of PCA eigenvectors | When we say correlation that means can be two directional i.e. positive and negative. Interpretation of the principal components is based on finding which variables are most strongly correlated with e | Interpreting positive and negative signs of the elements of PCA eigenvectors
When we say correlation that means can be two directional i.e. positive and negative. Interpretation of the principal components is based on finding which variables are most strongly correlated with each component, i.e., which of these numbers... | Interpreting positive and negative signs of the elements of PCA eigenvectors
When we say correlation that means can be two directional i.e. positive and negative. Interpretation of the principal components is based on finding which variables are most strongly correlated with e |
49,562 | What sort of problems is backpropagation best suited to solving, and what are the best alternatives to backprop for solving those problems? | In general, feed-forward networks utilizing backpropagation are great for classification tasks in which you have a number of probabilistic cues which need to be integrated. They're obviously used for a great many other things, but this is an example of one driving many people to use them -- it's difficult to capture th... | What sort of problems is backpropagation best suited to solving, and what are the best alternatives | In general, feed-forward networks utilizing backpropagation are great for classification tasks in which you have a number of probabilistic cues which need to be integrated. They're obviously used for | What sort of problems is backpropagation best suited to solving, and what are the best alternatives to backprop for solving those problems?
In general, feed-forward networks utilizing backpropagation are great for classification tasks in which you have a number of probabilistic cues which need to be integrated. They're... | What sort of problems is backpropagation best suited to solving, and what are the best alternatives
In general, feed-forward networks utilizing backpropagation are great for classification tasks in which you have a number of probabilistic cues which need to be integrated. They're obviously used for |
49,563 | What sort of problems is backpropagation best suited to solving, and what are the best alternatives to backprop for solving those problems? | Edit
Originally this answer discussed alternate learning algorithms and topologies for Neural Nets. After the edit, the answer is divided into three parts:
Uses and problems with Backpropogation;
Alternate Neural Network Training Schemes; and
Alternates to Neural Networks (newly added).
Part 1
Backpropogation algor... | What sort of problems is backpropagation best suited to solving, and what are the best alternatives | Edit
Originally this answer discussed alternate learning algorithms and topologies for Neural Nets. After the edit, the answer is divided into three parts:
Uses and problems with Backpropogation;
Al | What sort of problems is backpropagation best suited to solving, and what are the best alternatives to backprop for solving those problems?
Edit
Originally this answer discussed alternate learning algorithms and topologies for Neural Nets. After the edit, the answer is divided into three parts:
Uses and problems with... | What sort of problems is backpropagation best suited to solving, and what are the best alternatives
Edit
Originally this answer discussed alternate learning algorithms and topologies for Neural Nets. After the edit, the answer is divided into three parts:
Uses and problems with Backpropogation;
Al |
49,564 | Comparing two discrete distributions (with small cell counts) | There are two technical issues to deal with: (1) measuring the discrepancy between observed and expected and (2) computing the p-value.
We can retain the chi-squared measure of discrepancy (thereby finessing issue 1) and compute an exact p-value. The simple way is to simulate sampling from the expected distribution. ... | Comparing two discrete distributions (with small cell counts) | There are two technical issues to deal with: (1) measuring the discrepancy between observed and expected and (2) computing the p-value.
We can retain the chi-squared measure of discrepancy (thereby fi | Comparing two discrete distributions (with small cell counts)
There are two technical issues to deal with: (1) measuring the discrepancy between observed and expected and (2) computing the p-value.
We can retain the chi-squared measure of discrepancy (thereby finessing issue 1) and compute an exact p-value. The simple... | Comparing two discrete distributions (with small cell counts)
There are two technical issues to deal with: (1) measuring the discrepancy between observed and expected and (2) computing the p-value.
We can retain the chi-squared measure of discrepancy (thereby fi |
49,565 | Training models on data that may be incorrectly classified? | Yes, there is a bias. For example, assume your classificator agrees with the expert 80% of the time. Now, there are several options, here are the two extremes: your model is better because the 20% where it does not agree is where the experts are wrong -> your performance is underestimated OR the 20% where you disagree ... | Training models on data that may be incorrectly classified? | Yes, there is a bias. For example, assume your classificator agrees with the expert 80% of the time. Now, there are several options, here are the two extremes: your model is better because the 20% whe | Training models on data that may be incorrectly classified?
Yes, there is a bias. For example, assume your classificator agrees with the expert 80% of the time. Now, there are several options, here are the two extremes: your model is better because the 20% where it does not agree is where the experts are wrong -> your ... | Training models on data that may be incorrectly classified?
Yes, there is a bias. For example, assume your classificator agrees with the expert 80% of the time. Now, there are several options, here are the two extremes: your model is better because the 20% whe |
49,566 | Training models on data that may be incorrectly classified? | We have done some work on this for the case of random label flipping noise. Papers:
J. Bootkrajang and A. Kaban. Label-noise Robust Logistic Regression and its Applications. Proc. ECML-PKDD(1) 2012, pp. 143-158.
J. Bootkrajang and A. Kaban. Classification of Mislabelled Microarrays using Robust Sparse Logistic Regressi... | Training models on data that may be incorrectly classified? | We have done some work on this for the case of random label flipping noise. Papers:
J. Bootkrajang and A. Kaban. Label-noise Robust Logistic Regression and its Applications. Proc. ECML-PKDD(1) 2012, p | Training models on data that may be incorrectly classified?
We have done some work on this for the case of random label flipping noise. Papers:
J. Bootkrajang and A. Kaban. Label-noise Robust Logistic Regression and its Applications. Proc. ECML-PKDD(1) 2012, pp. 143-158.
J. Bootkrajang and A. Kaban. Classification of M... | Training models on data that may be incorrectly classified?
We have done some work on this for the case of random label flipping noise. Papers:
J. Bootkrajang and A. Kaban. Label-noise Robust Logistic Regression and its Applications. Proc. ECML-PKDD(1) 2012, p |
49,567 | Analyzing Logistic Regression when not using a dichotomous dependent variable | In your case the response variable actually is binary, it has just been summarised into a ratio. Each individual either gets out of the building (1) or doesn't (0). So logistic regression is quite appropriate, you just need to put your data into an appropriate form (which will depend on your software).
In R you do th... | Analyzing Logistic Regression when not using a dichotomous dependent variable | In your case the response variable actually is binary, it has just been summarised into a ratio. Each individual either gets out of the building (1) or doesn't (0). So logistic regression is quite a | Analyzing Logistic Regression when not using a dichotomous dependent variable
In your case the response variable actually is binary, it has just been summarised into a ratio. Each individual either gets out of the building (1) or doesn't (0). So logistic regression is quite appropriate, you just need to put your data... | Analyzing Logistic Regression when not using a dichotomous dependent variable
In your case the response variable actually is binary, it has just been summarised into a ratio. Each individual either gets out of the building (1) or doesn't (0). So logistic regression is quite a |
49,568 | Analyzing Logistic Regression when not using a dichotomous dependent variable | I don't mean to complain, but you have two questions that appear to be closely related where neither of them is clear enough / has enough information to get you a really good answer. You may want to see if you can edit them. @PeterEllis has provided a good answer to the question about why p-values can be high. I don... | Analyzing Logistic Regression when not using a dichotomous dependent variable | I don't mean to complain, but you have two questions that appear to be closely related where neither of them is clear enough / has enough information to get you a really good answer. You may want to | Analyzing Logistic Regression when not using a dichotomous dependent variable
I don't mean to complain, but you have two questions that appear to be closely related where neither of them is clear enough / has enough information to get you a really good answer. You may want to see if you can edit them. @PeterEllis has... | Analyzing Logistic Regression when not using a dichotomous dependent variable
I don't mean to complain, but you have two questions that appear to be closely related where neither of them is clear enough / has enough information to get you a really good answer. You may want to |
49,569 | Decision trees and backward pruning | Oh well, gotta answer my own question. Quotting "Data Mining: Practical Machine Learning Tools and Techniques",
..postpruning does seem to offer some advantages. For example, situations occur in which two attributes individually seem to have nothing to contribute but are powerful predictors when
combined—a sort of c... | Decision trees and backward pruning | Oh well, gotta answer my own question. Quotting "Data Mining: Practical Machine Learning Tools and Techniques",
..postpruning does seem to offer some advantages. For example, situations occur in whic | Decision trees and backward pruning
Oh well, gotta answer my own question. Quotting "Data Mining: Practical Machine Learning Tools and Techniques",
..postpruning does seem to offer some advantages. For example, situations occur in which two attributes individually seem to have nothing to contribute but are powerful pr... | Decision trees and backward pruning
Oh well, gotta answer my own question. Quotting "Data Mining: Practical Machine Learning Tools and Techniques",
..postpruning does seem to offer some advantages. For example, situations occur in whic |
49,570 | Kernel matrix normalisation | As long as you understand what you're doing you'll be fine :-)
You're actually normalizing your data to have unit length in feature space. It is equivalent to use this kernel: $K(x,y)/\sqrt{K(x,x)K(y,y)}$. Your data will now fall on a hypersphere of radius 1 in feature space. When you add kernel matrices you're actuall... | Kernel matrix normalisation | As long as you understand what you're doing you'll be fine :-)
You're actually normalizing your data to have unit length in feature space. It is equivalent to use this kernel: $K(x,y)/\sqrt{K(x,x)K(y, | Kernel matrix normalisation
As long as you understand what you're doing you'll be fine :-)
You're actually normalizing your data to have unit length in feature space. It is equivalent to use this kernel: $K(x,y)/\sqrt{K(x,x)K(y,y)}$. Your data will now fall on a hypersphere of radius 1 in feature space. When you add ke... | Kernel matrix normalisation
As long as you understand what you're doing you'll be fine :-)
You're actually normalizing your data to have unit length in feature space. It is equivalent to use this kernel: $K(x,y)/\sqrt{K(x,x)K(y, |
49,571 | Probabilistic outputs from SVMs | I don't know whether there are recent approaches to the problem, but I think I know why John Platt solved the problem in this kind of unsatisfactory way. Many machine learning algorithms can be written as regularizer plus loss function. For example, ridge regression would be $\lambda ||w||^2 + \sum_i (y_i - w^\top x_i)... | Probabilistic outputs from SVMs | I don't know whether there are recent approaches to the problem, but I think I know why John Platt solved the problem in this kind of unsatisfactory way. Many machine learning algorithms can be writte | Probabilistic outputs from SVMs
I don't know whether there are recent approaches to the problem, but I think I know why John Platt solved the problem in this kind of unsatisfactory way. Many machine learning algorithms can be written as regularizer plus loss function. For example, ridge regression would be $\lambda ||w... | Probabilistic outputs from SVMs
I don't know whether there are recent approaches to the problem, but I think I know why John Platt solved the problem in this kind of unsatisfactory way. Many machine learning algorithms can be writte |
49,572 | How to deal with RAM limitations when working with big datasets in R? | I rely on having a 64-bit operating system and running 64-bit R and even then I still crash.
Depending on what you want to do, have a look at this CRAN site. Unfortunately because my large data frame was using mixed methods, biglm wasn't any good for me. I read up on ff and it didn't suit my needs either, because the m... | How to deal with RAM limitations when working with big datasets in R? | I rely on having a 64-bit operating system and running 64-bit R and even then I still crash.
Depending on what you want to do, have a look at this CRAN site. Unfortunately because my large data frame | How to deal with RAM limitations when working with big datasets in R?
I rely on having a 64-bit operating system and running 64-bit R and even then I still crash.
Depending on what you want to do, have a look at this CRAN site. Unfortunately because my large data frame was using mixed methods, biglm wasn't any good for... | How to deal with RAM limitations when working with big datasets in R?
I rely on having a 64-bit operating system and running 64-bit R and even then I still crash.
Depending on what you want to do, have a look at this CRAN site. Unfortunately because my large data frame |
49,573 | How to use weights for imbalanced data in R's randomForest? | Ok, so I found part of my answer but not the good part. It turns out the randomForest package can do stratified sampling but only for classification. Here is a link to the package author's explanation.
I'm still looking for ideas on how to do stratified sampling for regression rf's. | How to use weights for imbalanced data in R's randomForest? | Ok, so I found part of my answer but not the good part. It turns out the randomForest package can do stratified sampling but only for classification. Here is a link to the package author's explanati | How to use weights for imbalanced data in R's randomForest?
Ok, so I found part of my answer but not the good part. It turns out the randomForest package can do stratified sampling but only for classification. Here is a link to the package author's explanation.
I'm still looking for ideas on how to do stratified sa... | How to use weights for imbalanced data in R's randomForest?
Ok, so I found part of my answer but not the good part. It turns out the randomForest package can do stratified sampling but only for classification. Here is a link to the package author's explanati |
49,574 | Probability density function (pdf) of normal sample variance ($S^2$) | Given $\frac{(n-1)S^2}{\sigma^2} \sim \chi^2_{n-1} \>,$
and the fact that a chi-squared($\nu$) is a Gamma($\frac{\nu}{2},2$), (under the scale parameterization) then
$S^2 = \frac{(n-1)S^2}{\sigma^2}\cdot \frac{\sigma^2}{(n-1)}\sim \text{Gamma}(\frac{(n-1)}{2},\frac{2\sigma^2}{(n-1)})$
If you need a proof, it should suf... | Probability density function (pdf) of normal sample variance ($S^2$) | Given $\frac{(n-1)S^2}{\sigma^2} \sim \chi^2_{n-1} \>,$
and the fact that a chi-squared($\nu$) is a Gamma($\frac{\nu}{2},2$), (under the scale parameterization) then
$S^2 = \frac{(n-1)S^2}{\sigma^2}\c | Probability density function (pdf) of normal sample variance ($S^2$)
Given $\frac{(n-1)S^2}{\sigma^2} \sim \chi^2_{n-1} \>,$
and the fact that a chi-squared($\nu$) is a Gamma($\frac{\nu}{2},2$), (under the scale parameterization) then
$S^2 = \frac{(n-1)S^2}{\sigma^2}\cdot \frac{\sigma^2}{(n-1)}\sim \text{Gamma}(\frac{(... | Probability density function (pdf) of normal sample variance ($S^2$)
Given $\frac{(n-1)S^2}{\sigma^2} \sim \chi^2_{n-1} \>,$
and the fact that a chi-squared($\nu$) is a Gamma($\frac{\nu}{2},2$), (under the scale parameterization) then
$S^2 = \frac{(n-1)S^2}{\sigma^2}\c |
49,575 | Probability density function (pdf) of normal sample variance ($S^2$) | The pdf is as follows:
\begin{equation}
f(x) = \frac{\left(\frac{\nu}{2\, \sigma^{2}}\right)^{\frac{\nu}{2}}}{\Gamma\left(\frac{\nu}{2}\right)}\, x^{\frac{\nu}{2}-1}\, \exp\left\{-x\, \frac{\nu}{2\, \sigma^{2}}\right\}
\end{equation}
$\nu \equiv \text{degrees of freedom}= N-1$, where $N$ is the sample size.
$\sigma \eq... | Probability density function (pdf) of normal sample variance ($S^2$) | The pdf is as follows:
\begin{equation}
f(x) = \frac{\left(\frac{\nu}{2\, \sigma^{2}}\right)^{\frac{\nu}{2}}}{\Gamma\left(\frac{\nu}{2}\right)}\, x^{\frac{\nu}{2}-1}\, \exp\left\{-x\, \frac{\nu}{2\, \ | Probability density function (pdf) of normal sample variance ($S^2$)
The pdf is as follows:
\begin{equation}
f(x) = \frac{\left(\frac{\nu}{2\, \sigma^{2}}\right)^{\frac{\nu}{2}}}{\Gamma\left(\frac{\nu}{2}\right)}\, x^{\frac{\nu}{2}-1}\, \exp\left\{-x\, \frac{\nu}{2\, \sigma^{2}}\right\}
\end{equation}
$\nu \equiv \text... | Probability density function (pdf) of normal sample variance ($S^2$)
The pdf is as follows:
\begin{equation}
f(x) = \frac{\left(\frac{\nu}{2\, \sigma^{2}}\right)^{\frac{\nu}{2}}}{\Gamma\left(\frac{\nu}{2}\right)}\, x^{\frac{\nu}{2}-1}\, \exp\left\{-x\, \frac{\nu}{2\, \ |
49,576 | Ways to determine if experience or recent practice time is more significant in ranking? | thanks for updating your question with the scatterplot, it does give us some information we didn't have before. Eyeballing the scatterplot, it looks like 1v1 performance and 3v3 (adjusted) performance aren't related. What this tells us is that there is no simple relationship between 1v1 and 3v3 performance.
That sounds... | Ways to determine if experience or recent practice time is more significant in ranking? | thanks for updating your question with the scatterplot, it does give us some information we didn't have before. Eyeballing the scatterplot, it looks like 1v1 performance and 3v3 (adjusted) performance | Ways to determine if experience or recent practice time is more significant in ranking?
thanks for updating your question with the scatterplot, it does give us some information we didn't have before. Eyeballing the scatterplot, it looks like 1v1 performance and 3v3 (adjusted) performance aren't related. What this tells... | Ways to determine if experience or recent practice time is more significant in ranking?
thanks for updating your question with the scatterplot, it does give us some information we didn't have before. Eyeballing the scatterplot, it looks like 1v1 performance and 3v3 (adjusted) performance |
49,577 | TF-IDF cutoff percentage for tweets | Probably the most effective (but also timeconsuming) approach will be to hand pick a set of examples that you know are postive, negative, and neutral. You can then train a classifier (Naive Bayes, SVM, Fisher Discriminant or whatever) on these examples (since you are using 3 classes, you will need to do multi-class cla... | TF-IDF cutoff percentage for tweets | Probably the most effective (but also timeconsuming) approach will be to hand pick a set of examples that you know are postive, negative, and neutral. You can then train a classifier (Naive Bayes, SVM | TF-IDF cutoff percentage for tweets
Probably the most effective (but also timeconsuming) approach will be to hand pick a set of examples that you know are postive, negative, and neutral. You can then train a classifier (Naive Bayes, SVM, Fisher Discriminant or whatever) on these examples (since you are using 3 classes,... | TF-IDF cutoff percentage for tweets
Probably the most effective (but also timeconsuming) approach will be to hand pick a set of examples that you know are postive, negative, and neutral. You can then train a classifier (Naive Bayes, SVM |
49,578 | TF-IDF cutoff percentage for tweets | For training, if possible, look for users who tweets mostly positive(like celebrities, politicians etc) and some others who mostly tweets negative(no example right now) and use their tweets accordingly. there will be some miscalculation in training data but you can get a lot of data using this technique. | TF-IDF cutoff percentage for tweets | For training, if possible, look for users who tweets mostly positive(like celebrities, politicians etc) and some others who mostly tweets negative(no example right now) and use their tweets accordingl | TF-IDF cutoff percentage for tweets
For training, if possible, look for users who tweets mostly positive(like celebrities, politicians etc) and some others who mostly tweets negative(no example right now) and use their tweets accordingly. there will be some miscalculation in training data but you can get a lot of data ... | TF-IDF cutoff percentage for tweets
For training, if possible, look for users who tweets mostly positive(like celebrities, politicians etc) and some others who mostly tweets negative(no example right now) and use their tweets accordingl |
49,579 | Whether to leave the data unaltered in the face of outliers and non-normality when performing structural equation modelling? | A lot depends on where exactly the outliers occur within the model -- in the indicators? in the latent variables and their measurement errors? in the exogenous variables, at the top of the causal chain? In the former case, you cannot do much, as you really have a high leverage influential cases rather than outliers. To... | Whether to leave the data unaltered in the face of outliers and non-normality when performing struct | A lot depends on where exactly the outliers occur within the model -- in the indicators? in the latent variables and their measurement errors? in the exogenous variables, at the top of the causal chai | Whether to leave the data unaltered in the face of outliers and non-normality when performing structural equation modelling?
A lot depends on where exactly the outliers occur within the model -- in the indicators? in the latent variables and their measurement errors? in the exogenous variables, at the top of the causal... | Whether to leave the data unaltered in the face of outliers and non-normality when performing struct
A lot depends on where exactly the outliers occur within the model -- in the indicators? in the latent variables and their measurement errors? in the exogenous variables, at the top of the causal chai |
49,580 | Whether to leave the data unaltered in the face of outliers and non-normality when performing structural equation modelling? | General References
Hair et al has a fairly extensive non-mathematical discussion of issues of multivariate data cleaning and assumption testing that you might find accessible.
First step: Understand your data
Why are the distributions as they are?
What is causing the outliers?
You might want to think about whethe... | Whether to leave the data unaltered in the face of outliers and non-normality when performing struct | General References
Hair et al has a fairly extensive non-mathematical discussion of issues of multivariate data cleaning and assumption testing that you might find accessible.
First step: Understan | Whether to leave the data unaltered in the face of outliers and non-normality when performing structural equation modelling?
General References
Hair et al has a fairly extensive non-mathematical discussion of issues of multivariate data cleaning and assumption testing that you might find accessible.
First step: Unde... | Whether to leave the data unaltered in the face of outliers and non-normality when performing struct
General References
Hair et al has a fairly extensive non-mathematical discussion of issues of multivariate data cleaning and assumption testing that you might find accessible.
First step: Understan |
49,581 | Data mining classification competition | An easy way to build an ensemble is by using a random forest. I'm fairly sure weka has a random forest algorithm, and if other tree-based models are performing well it's worth trying out.
You could also build your own ensemble by training multiple (say 50 or 100) J48 decision trees and using them to "vote" on the clas... | Data mining classification competition | An easy way to build an ensemble is by using a random forest. I'm fairly sure weka has a random forest algorithm, and if other tree-based models are performing well it's worth trying out.
You could a | Data mining classification competition
An easy way to build an ensemble is by using a random forest. I'm fairly sure weka has a random forest algorithm, and if other tree-based models are performing well it's worth trying out.
You could also build your own ensemble by training multiple (say 50 or 100) J48 decision tre... | Data mining classification competition
An easy way to build an ensemble is by using a random forest. I'm fairly sure weka has a random forest algorithm, and if other tree-based models are performing well it's worth trying out.
You could a |
49,582 | Data mining classification competition | A model ensemble is simply a collection of models whose output is combined (hopefully generating superior performance in the process). Obviously, to be of any interest, the base models must vary somehow, and there are several ways to do this: vary the model type (tree induction, neural network, discriminant function, ... | Data mining classification competition | A model ensemble is simply a collection of models whose output is combined (hopefully generating superior performance in the process). Obviously, to be of any interest, the base models must vary some | Data mining classification competition
A model ensemble is simply a collection of models whose output is combined (hopefully generating superior performance in the process). Obviously, to be of any interest, the base models must vary somehow, and there are several ways to do this: vary the model type (tree induction, ... | Data mining classification competition
A model ensemble is simply a collection of models whose output is combined (hopefully generating superior performance in the process). Obviously, to be of any interest, the base models must vary some |
49,583 | Data mining classification competition | You could try the new machine learning library called ML-Flex (http://mlflex.sourceforge.net). It is designed to execute a variety of ensemble methods and can also provide side-by-side comparisons when different algorithm parameters are used (though perhaps not exactly as you desire). If you're interested, give it a tr... | Data mining classification competition | You could try the new machine learning library called ML-Flex (http://mlflex.sourceforge.net). It is designed to execute a variety of ensemble methods and can also provide side-by-side comparisons whe | Data mining classification competition
You could try the new machine learning library called ML-Flex (http://mlflex.sourceforge.net). It is designed to execute a variety of ensemble methods and can also provide side-by-side comparisons when different algorithm parameters are used (though perhaps not exactly as you desi... | Data mining classification competition
You could try the new machine learning library called ML-Flex (http://mlflex.sourceforge.net). It is designed to execute a variety of ensemble methods and can also provide side-by-side comparisons whe |
49,584 | Are survivor functions meaningful with proportional hazards models? | It has always been my understanding that the appeal of the Cox proportional hazards model is that there's no estimation of the underlying hazard function, and as such it is unbound from some of the assumptions about the shape of that hazard.
From that, I've asserted that that means you can't use the Cox model to genera... | Are survivor functions meaningful with proportional hazards models? | It has always been my understanding that the appeal of the Cox proportional hazards model is that there's no estimation of the underlying hazard function, and as such it is unbound from some of the as | Are survivor functions meaningful with proportional hazards models?
It has always been my understanding that the appeal of the Cox proportional hazards model is that there's no estimation of the underlying hazard function, and as such it is unbound from some of the assumptions about the shape of that hazard.
From that,... | Are survivor functions meaningful with proportional hazards models?
It has always been my understanding that the appeal of the Cox proportional hazards model is that there's no estimation of the underlying hazard function, and as such it is unbound from some of the as |
49,585 | Finding a minimum variance unbiased (linear) estimator | Your setup is analogous to sampling from a finite population (the $c_i$) without replacement, with a fixed probability $p_i$ of selecting each member of the population for the sample. Successfully opening the $i^{th}$ box corresponds to selecting the corresponding $c_i$ for inclusion in the sample.
The estimator you d... | Finding a minimum variance unbiased (linear) estimator | Your setup is analogous to sampling from a finite population (the $c_i$) without replacement, with a fixed probability $p_i$ of selecting each member of the population for the sample. Successfully op | Finding a minimum variance unbiased (linear) estimator
Your setup is analogous to sampling from a finite population (the $c_i$) without replacement, with a fixed probability $p_i$ of selecting each member of the population for the sample. Successfully opening the $i^{th}$ box corresponds to selecting the corresponding... | Finding a minimum variance unbiased (linear) estimator
Your setup is analogous to sampling from a finite population (the $c_i$) without replacement, with a fixed probability $p_i$ of selecting each member of the population for the sample. Successfully op |
49,586 | How to apply unsupervised classification to spatial data | This sounds to me like an image processing question, unless you are looking for a very complex structure.
You may want to use a gaussian filter on the image, and then apply a threshold.
Also, you can ask in https://dsp.stackexchange.com/ . | How to apply unsupervised classification to spatial data | This sounds to me like an image processing question, unless you are looking for a very complex structure.
You may want to use a gaussian filter on the image, and then apply a threshold.
Also, you can | How to apply unsupervised classification to spatial data
This sounds to me like an image processing question, unless you are looking for a very complex structure.
You may want to use a gaussian filter on the image, and then apply a threshold.
Also, you can ask in https://dsp.stackexchange.com/ . | How to apply unsupervised classification to spatial data
This sounds to me like an image processing question, unless you are looking for a very complex structure.
You may want to use a gaussian filter on the image, and then apply a threshold.
Also, you can |
49,587 | How to apply unsupervised classification to spatial data | This software (it won the best demonstration award at SSTD 2011) Link should be able to do spatial clustering, too. | How to apply unsupervised classification to spatial data | This software (it won the best demonstration award at SSTD 2011) Link should be able to do spatial clustering, too. | How to apply unsupervised classification to spatial data
This software (it won the best demonstration award at SSTD 2011) Link should be able to do spatial clustering, too. | How to apply unsupervised classification to spatial data
This software (it won the best demonstration award at SSTD 2011) Link should be able to do spatial clustering, too. |
49,588 | Neural network model to predict treatment outcome | It's often a good idea to do PCA before fitting a neural network, so your instinct could be right there. The only way you are going to determine which model is better for a given problem is to cross-validate both and compare out-of-sample error.
The caret package in R is a good way to compare models using this techniq... | Neural network model to predict treatment outcome | It's often a good idea to do PCA before fitting a neural network, so your instinct could be right there. The only way you are going to determine which model is better for a given problem is to cross- | Neural network model to predict treatment outcome
It's often a good idea to do PCA before fitting a neural network, so your instinct could be right there. The only way you are going to determine which model is better for a given problem is to cross-validate both and compare out-of-sample error.
The caret package in ... | Neural network model to predict treatment outcome
It's often a good idea to do PCA before fitting a neural network, so your instinct could be right there. The only way you are going to determine which model is better for a given problem is to cross- |
49,589 | Neural network model to predict treatment outcome | General rules for when to use a neural network:
1) you can tell, relatively easily, what the right answer is, but not describe how you know that's the right answer; if you know what steps to take to get the right answer, then code it rather than training a NN, and if you can't tell what the right answer is likely to be... | Neural network model to predict treatment outcome | General rules for when to use a neural network:
1) you can tell, relatively easily, what the right answer is, but not describe how you know that's the right answer; if you know what steps to take to g | Neural network model to predict treatment outcome
General rules for when to use a neural network:
1) you can tell, relatively easily, what the right answer is, but not describe how you know that's the right answer; if you know what steps to take to get the right answer, then code it rather than training a NN, and if ... | Neural network model to predict treatment outcome
General rules for when to use a neural network:
1) you can tell, relatively easily, what the right answer is, but not describe how you know that's the right answer; if you know what steps to take to g |
49,590 | Function to convert arithmetic to log-based covariance matrix? | If I have understood the code correctly (ignoring the "$-1$" in the computation of $m$), its input is an $n$-vector $\mu = (\mu_1, \ldots, \mu_n)$ and a symmetric $n$ by $n$ matrix $\Sigma = (\sigma_{ij})$. The output is an $n$-vector $m$ with
$$m_i = \exp(\mu_i + \sigma_{ii}/2)$$
and an $n$ by $n$ matrix $S$ with
$$S... | Function to convert arithmetic to log-based covariance matrix? | If I have understood the code correctly (ignoring the "$-1$" in the computation of $m$), its input is an $n$-vector $\mu = (\mu_1, \ldots, \mu_n)$ and a symmetric $n$ by $n$ matrix $\Sigma = (\sigma_{ | Function to convert arithmetic to log-based covariance matrix?
If I have understood the code correctly (ignoring the "$-1$" in the computation of $m$), its input is an $n$-vector $\mu = (\mu_1, \ldots, \mu_n)$ and a symmetric $n$ by $n$ matrix $\Sigma = (\sigma_{ij})$. The output is an $n$-vector $m$ with
$$m_i = \exp... | Function to convert arithmetic to log-based covariance matrix?
If I have understood the code correctly (ignoring the "$-1$" in the computation of $m$), its input is an $n$-vector $\mu = (\mu_1, \ldots, \mu_n)$ and a symmetric $n$ by $n$ matrix $\Sigma = (\sigma_{ |
49,591 | Odd error with caret function rfe | You have to specify the sizes argument ($\leq 2$ in your example). The default value in rfe is sizes=2^(2:4), but you only have two features.
?rfe
Arguments
...
sizes
a numeric vector of integers corresponding to the number of
features that should be retained | Odd error with caret function rfe | You have to specify the sizes argument ($\leq 2$ in your example). The default value in rfe is sizes=2^(2:4), but you only have two features.
?rfe
Arguments
...
sizes
a numeric vector of integers | Odd error with caret function rfe
You have to specify the sizes argument ($\leq 2$ in your example). The default value in rfe is sizes=2^(2:4), but you only have two features.
?rfe
Arguments
...
sizes
a numeric vector of integers corresponding to the number of
features that should be retained | Odd error with caret function rfe
You have to specify the sizes argument ($\leq 2$ in your example). The default value in rfe is sizes=2^(2:4), but you only have two features.
?rfe
Arguments
...
sizes
a numeric vector of integers |
49,592 | How to compare Harrell C-index from different models in survival analysis? | Harrell would advise that you NOT do so:
How to do ROC-analysis in R with a Cox model
Doing model comparison with LR statistics is more powerful than using methods that depend on an asymptotic distribution of the C-index. | How to compare Harrell C-index from different models in survival analysis? | Harrell would advise that you NOT do so:
How to do ROC-analysis in R with a Cox model
Doing model comparison with LR statistics is more powerful than using methods that depend on an asymptotic distrib | How to compare Harrell C-index from different models in survival analysis?
Harrell would advise that you NOT do so:
How to do ROC-analysis in R with a Cox model
Doing model comparison with LR statistics is more powerful than using methods that depend on an asymptotic distribution of the C-index. | How to compare Harrell C-index from different models in survival analysis?
Harrell would advise that you NOT do so:
How to do ROC-analysis in R with a Cox model
Doing model comparison with LR statistics is more powerful than using methods that depend on an asymptotic distrib |
49,593 | How to compare Harrell C-index from different models in survival analysis? | Want to improve this post? Provide detailed answers to this question, including citations and an explanation of why your answer is correct. Answers without enough detail may be edited or deleted.
LR statistics are well suited for hierarchical models.... | How to compare Harrell C-index from different models in survival analysis? | Want to improve this post? Provide detailed answers to this question, including citations and an explanation of why your answer is correct. Answers without enough detail may be edited or deleted.
| How to compare Harrell C-index from different models in survival analysis?
Want to improve this post? Provide detailed answers to this question, including citations and an explanation of why your answer is correct. Answers without enough detail may be edited or deleted.
... | How to compare Harrell C-index from different models in survival analysis?
Want to improve this post? Provide detailed answers to this question, including citations and an explanation of why your answer is correct. Answers without enough detail may be edited or deleted.
|
49,594 | Is sequential Bayesian updating an option when using MCMC? | In this setting, MCMC is less appropriate than particle systems or sequential Monte Carlo, because you can use the previous particle system as an approximation to your prior (posterior for the earlier datapoints) and only use one observation at a time. Appropriate references for this are, e.g., Del Moral, Doucet, and J... | Is sequential Bayesian updating an option when using MCMC? | In this setting, MCMC is less appropriate than particle systems or sequential Monte Carlo, because you can use the previous particle system as an approximation to your prior (posterior for the earlier | Is sequential Bayesian updating an option when using MCMC?
In this setting, MCMC is less appropriate than particle systems or sequential Monte Carlo, because you can use the previous particle system as an approximation to your prior (posterior for the earlier datapoints) and only use one observation at a time. Appropri... | Is sequential Bayesian updating an option when using MCMC?
In this setting, MCMC is less appropriate than particle systems or sequential Monte Carlo, because you can use the previous particle system as an approximation to your prior (posterior for the earlier |
49,595 | Is sequential Bayesian updating an option when using MCMC? | Are you underflowing because you are not anywhere near reasonable parameter values? Perhaps you just need to find a good starting location. I otherwise don't see how you could underflow short of having 1e20 data points or parameters. You could use a small (but randomly sampled) portion of your data and to ML estimation... | Is sequential Bayesian updating an option when using MCMC? | Are you underflowing because you are not anywhere near reasonable parameter values? Perhaps you just need to find a good starting location. I otherwise don't see how you could underflow short of havin | Is sequential Bayesian updating an option when using MCMC?
Are you underflowing because you are not anywhere near reasonable parameter values? Perhaps you just need to find a good starting location. I otherwise don't see how you could underflow short of having 1e20 data points or parameters. You could use a small (but ... | Is sequential Bayesian updating an option when using MCMC?
Are you underflowing because you are not anywhere near reasonable parameter values? Perhaps you just need to find a good starting location. I otherwise don't see how you could underflow short of havin |
49,596 | How to calculate mean and standard deviation of a count variable when the raw data is based on frequency categories? | You need to be creative, because these data are consistent with any mean exceeding $0\times .05 + 1\times .07 + \cdots + 5\times .18$ = $2.89$ and any standard deviation exceeding $1.38$ (which are attained by assuming nobody visited any more than five times per month).
For reporting purposes, simply tabulate or graph ... | How to calculate mean and standard deviation of a count variable when the raw data is based on frequ | You need to be creative, because these data are consistent with any mean exceeding $0\times .05 + 1\times .07 + \cdots + 5\times .18$ = $2.89$ and any standard deviation exceeding $1.38$ (which are at | How to calculate mean and standard deviation of a count variable when the raw data is based on frequency categories?
You need to be creative, because these data are consistent with any mean exceeding $0\times .05 + 1\times .07 + \cdots + 5\times .18$ = $2.89$ and any standard deviation exceeding $1.38$ (which are attai... | How to calculate mean and standard deviation of a count variable when the raw data is based on frequ
You need to be creative, because these data are consistent with any mean exceeding $0\times .05 + 1\times .07 + \cdots + 5\times .18$ = $2.89$ and any standard deviation exceeding $1.38$ (which are at |
49,597 | How to calculate mean and standard deviation of a count variable when the raw data is based on frequency categories? | You definitely have to associate a numerical value to the class "visited five and more times a month".
By the way, I would calculate the mean and the standard deviation in the usual way. In fact, $x_i$ are your values and $p_i$ are their empirical frequency estimated on the sample. In your case
$$x_0=0 \ x_1=1 \ x_2=2 ... | How to calculate mean and standard deviation of a count variable when the raw data is based on frequ | You definitely have to associate a numerical value to the class "visited five and more times a month".
By the way, I would calculate the mean and the standard deviation in the usual way. In fact, $x_i | How to calculate mean and standard deviation of a count variable when the raw data is based on frequency categories?
You definitely have to associate a numerical value to the class "visited five and more times a month".
By the way, I would calculate the mean and the standard deviation in the usual way. In fact, $x_i$ a... | How to calculate mean and standard deviation of a count variable when the raw data is based on frequ
You definitely have to associate a numerical value to the class "visited five and more times a month".
By the way, I would calculate the mean and the standard deviation in the usual way. In fact, $x_i |
49,598 | Estimating a p-value when you can't compute it for the whole set | It's not correct to randomly sample both lists a large number of times and average the p-values; the result would understate the evidence against the null hypothesis if it's false, as you then expect the p-value to get smaller as the sample size gets larger, but with this procedure it would stay the same on average.
In... | Estimating a p-value when you can't compute it for the whole set | It's not correct to randomly sample both lists a large number of times and average the p-values; the result would understate the evidence against the null hypothesis if it's false, as you then expect | Estimating a p-value when you can't compute it for the whole set
It's not correct to randomly sample both lists a large number of times and average the p-values; the result would understate the evidence against the null hypothesis if it's false, as you then expect the p-value to get smaller as the sample size gets larg... | Estimating a p-value when you can't compute it for the whole set
It's not correct to randomly sample both lists a large number of times and average the p-values; the result would understate the evidence against the null hypothesis if it's false, as you then expect |
49,599 | Putting a confidence interval on the mean of a very rare event | The normal approximation for the confidence interval of binomial proportions breaks down very badly for rare events and the rules of thumb about sample sizes are inconsistent and unreliable. Better methods are just as easy to calculate (i.e. you click the button!) and so there is no reason for anyone to use the normal ... | Putting a confidence interval on the mean of a very rare event | The normal approximation for the confidence interval of binomial proportions breaks down very badly for rare events and the rules of thumb about sample sizes are inconsistent and unreliable. Better me | Putting a confidence interval on the mean of a very rare event
The normal approximation for the confidence interval of binomial proportions breaks down very badly for rare events and the rules of thumb about sample sizes are inconsistent and unreliable. Better methods are just as easy to calculate (i.e. you click the b... | Putting a confidence interval on the mean of a very rare event
The normal approximation for the confidence interval of binomial proportions breaks down very badly for rare events and the rules of thumb about sample sizes are inconsistent and unreliable. Better me |
49,600 | Putting a confidence interval on the mean of a very rare event | Now that it is clear that you have a weighting function, I suggest that you use Bayesian intervals (often called credible intervals) with the weighting function being the prior. Multiply that by the likelihood function provided by your results to get the posterior. Any interval containing 95% of the area under that pos... | Putting a confidence interval on the mean of a very rare event | Now that it is clear that you have a weighting function, I suggest that you use Bayesian intervals (often called credible intervals) with the weighting function being the prior. Multiply that by the l | Putting a confidence interval on the mean of a very rare event
Now that it is clear that you have a weighting function, I suggest that you use Bayesian intervals (often called credible intervals) with the weighting function being the prior. Multiply that by the likelihood function provided by your results to get the po... | Putting a confidence interval on the mean of a very rare event
Now that it is clear that you have a weighting function, I suggest that you use Bayesian intervals (often called credible intervals) with the weighting function being the prior. Multiply that by the l |
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