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 |
|---|---|---|---|---|---|---|
54,601 | Will the silhouette formula change depending on the distance metric? | Silhouette statistic works on distances, not similarities. One should revert similarities into distances. The general pass to do it: 1) set diagonal as 0, 2) revert sign of elements, 3) find the smallest element and substract it from each element, 4) set diagonal as 0.
For cosine or correlation there is also a geometri... | Will the silhouette formula change depending on the distance metric? | Silhouette statistic works on distances, not similarities. One should revert similarities into distances. The general pass to do it: 1) set diagonal as 0, 2) revert sign of elements, 3) find the small | Will the silhouette formula change depending on the distance metric?
Silhouette statistic works on distances, not similarities. One should revert similarities into distances. The general pass to do it: 1) set diagonal as 0, 2) revert sign of elements, 3) find the smallest element and substract it from each element, 4) ... | Will the silhouette formula change depending on the distance metric?
Silhouette statistic works on distances, not similarities. One should revert similarities into distances. The general pass to do it: 1) set diagonal as 0, 2) revert sign of elements, 3) find the small |
54,602 | Will the silhouette formula change depending on the distance metric? | You can calculate the silhouette for similarity matrix. The seminal paper, by P.J Rousseeuw about silhouette, explains about how to calculate silhouette from similarity matrix:
calculation for Cohesion remains same.
For computing Separation, take maximum instead of minimum.
for calculating silhouete, the numerator c... | Will the silhouette formula change depending on the distance metric? | You can calculate the silhouette for similarity matrix. The seminal paper, by P.J Rousseeuw about silhouette, explains about how to calculate silhouette from similarity matrix:
calculation for Cohesi | Will the silhouette formula change depending on the distance metric?
You can calculate the silhouette for similarity matrix. The seminal paper, by P.J Rousseeuw about silhouette, explains about how to calculate silhouette from similarity matrix:
calculation for Cohesion remains same.
For computing Separation, take ma... | Will the silhouette formula change depending on the distance metric?
You can calculate the silhouette for similarity matrix. The seminal paper, by P.J Rousseeuw about silhouette, explains about how to calculate silhouette from similarity matrix:
calculation for Cohesi |
54,603 | What is the best way to determine if pageviews are trending upward or downward? | General thoughts about pageviews
I think there is a fair amount of domain specific knowledge that can be brought to bear on page views.
From examining my Google Analytics statistics from particular blog posts, I observe the following characteristics:
Large initial spike in pageviews when an article is first posted rel... | What is the best way to determine if pageviews are trending upward or downward? | General thoughts about pageviews
I think there is a fair amount of domain specific knowledge that can be brought to bear on page views.
From examining my Google Analytics statistics from particular bl | What is the best way to determine if pageviews are trending upward or downward?
General thoughts about pageviews
I think there is a fair amount of domain specific knowledge that can be brought to bear on page views.
From examining my Google Analytics statistics from particular blog posts, I observe the following charac... | What is the best way to determine if pageviews are trending upward or downward?
General thoughts about pageviews
I think there is a fair amount of domain specific knowledge that can be brought to bear on page views.
From examining my Google Analytics statistics from particular bl |
54,604 | What is the best way to determine if pageviews are trending upward or downward? | Simply build an ARIMA MODEL that separate signal from noise incorporating any identifiable deterministic structure such as changes in levels/trends/seaonal pulses/parameter or variance change over time. Develop a prediction for the next 5 days and use the uncertainty in that sum to create possible bounds. Compare the a... | What is the best way to determine if pageviews are trending upward or downward? | Simply build an ARIMA MODEL that separate signal from noise incorporating any identifiable deterministic structure such as changes in levels/trends/seaonal pulses/parameter or variance change over tim | What is the best way to determine if pageviews are trending upward or downward?
Simply build an ARIMA MODEL that separate signal from noise incorporating any identifiable deterministic structure such as changes in levels/trends/seaonal pulses/parameter or variance change over time. Develop a prediction for the next 5 d... | What is the best way to determine if pageviews are trending upward or downward?
Simply build an ARIMA MODEL that separate signal from noise incorporating any identifiable deterministic structure such as changes in levels/trends/seaonal pulses/parameter or variance change over tim |
54,605 | What is the best way to determine if pageviews are trending upward or downward? | Jeromy Anglim and IrishStat both give great answers, but they sound maybe a little more complex than what you're looking for.
A simpler method could could be to perform a linear regression on your data, to get PageViews = a * Date + b for some constants a and b; the constant a is then a measure of the linear "slope" o... | What is the best way to determine if pageviews are trending upward or downward? | Jeromy Anglim and IrishStat both give great answers, but they sound maybe a little more complex than what you're looking for.
A simpler method could could be to perform a linear regression on your da | What is the best way to determine if pageviews are trending upward or downward?
Jeromy Anglim and IrishStat both give great answers, but they sound maybe a little more complex than what you're looking for.
A simpler method could could be to perform a linear regression on your data, to get PageViews = a * Date + b for ... | What is the best way to determine if pageviews are trending upward or downward?
Jeromy Anglim and IrishStat both give great answers, but they sound maybe a little more complex than what you're looking for.
A simpler method could could be to perform a linear regression on your da |
54,606 | How to extract data from published articles (RCTs) to do a meta-analysis? | Your question indicates, to me, you're not yet ready to embark on the data abstraction portion of your meta-analysis. Your question needs refining, and you need to decide exactly what you're interested in asking. In your examples above, you appear to be interested in the main reported effects of the RCTs, which are fou... | How to extract data from published articles (RCTs) to do a meta-analysis? | Your question indicates, to me, you're not yet ready to embark on the data abstraction portion of your meta-analysis. Your question needs refining, and you need to decide exactly what you're intereste | How to extract data from published articles (RCTs) to do a meta-analysis?
Your question indicates, to me, you're not yet ready to embark on the data abstraction portion of your meta-analysis. Your question needs refining, and you need to decide exactly what you're interested in asking. In your examples above, you appea... | How to extract data from published articles (RCTs) to do a meta-analysis?
Your question indicates, to me, you're not yet ready to embark on the data abstraction portion of your meta-analysis. Your question needs refining, and you need to decide exactly what you're intereste |
54,607 | Uniform random variable distribution | $[t]$ is the floor function, and $t$ just represents a generic argument. So for example $[0.5]=0$, $[0.9]=0$, $[1.01]=1$, $[1]=1$, $[23.567]=23$, and so on. You simply ignore whats written after the decimal point (note: this is not the same thing as rounding, for $[0.9]=0$ whereas rounding would give $1$.)
With non-s... | Uniform random variable distribution | $[t]$ is the floor function, and $t$ just represents a generic argument. So for example $[0.5]=0$, $[0.9]=0$, $[1.01]=1$, $[1]=1$, $[23.567]=23$, and so on. You simply ignore whats written after the | Uniform random variable distribution
$[t]$ is the floor function, and $t$ just represents a generic argument. So for example $[0.5]=0$, $[0.9]=0$, $[1.01]=1$, $[1]=1$, $[23.567]=23$, and so on. You simply ignore whats written after the decimal point (note: this is not the same thing as rounding, for $[0.9]=0$ whereas... | Uniform random variable distribution
$[t]$ is the floor function, and $t$ just represents a generic argument. So for example $[0.5]=0$, $[0.9]=0$, $[1.01]=1$, $[1]=1$, $[23.567]=23$, and so on. You simply ignore whats written after the |
54,608 | Uniform random variable distribution | $t$ is just a placeholder name for a variable, the actual focus in that explanation is on the square brackets which refer to the floor function.
I would start by plotting the function that maps from $U$ to $X$, that is $X(u)=[nu]$ in the range of all the values $U$ can assume. What does the set of possible function val... | Uniform random variable distribution | $t$ is just a placeholder name for a variable, the actual focus in that explanation is on the square brackets which refer to the floor function.
I would start by plotting the function that maps from $ | Uniform random variable distribution
$t$ is just a placeholder name for a variable, the actual focus in that explanation is on the square brackets which refer to the floor function.
I would start by plotting the function that maps from $U$ to $X$, that is $X(u)=[nu]$ in the range of all the values $U$ can assume. What ... | Uniform random variable distribution
$t$ is just a placeholder name for a variable, the actual focus in that explanation is on the square brackets which refer to the floor function.
I would start by plotting the function that maps from $ |
54,609 | Sample size required for mixed design ANOVA to achieve adequate statistical power | You need to decide what is acceptable statistical power for a given significance test. The rule of thumb of 80% power being reasonable is often bandied about.
However, I think it is more sensible to see sample size selection as an optimisation problem, where statistical power is but one consideration, and the cost of c... | Sample size required for mixed design ANOVA to achieve adequate statistical power | You need to decide what is acceptable statistical power for a given significance test. The rule of thumb of 80% power being reasonable is often bandied about.
However, I think it is more sensible to s | Sample size required for mixed design ANOVA to achieve adequate statistical power
You need to decide what is acceptable statistical power for a given significance test. The rule of thumb of 80% power being reasonable is often bandied about.
However, I think it is more sensible to see sample size selection as an optimis... | Sample size required for mixed design ANOVA to achieve adequate statistical power
You need to decide what is acceptable statistical power for a given significance test. The rule of thumb of 80% power being reasonable is often bandied about.
However, I think it is more sensible to s |
54,610 | How to perform diallel analysis in R? | There is beta package plantbreeding, which can do diallel analysis.
https://r-forge.r-project.org/projects/plantbreeding/
They has a blog:
http://rplantbreeding.blogspot.com/
The following is example from this package:
require(plantbreeding)
data(fulldial)
out <-diallele1(dataframe = fulldial, male = "MALE", fema... | How to perform diallel analysis in R? | There is beta package plantbreeding, which can do diallel analysis.
https://r-forge.r-project.org/projects/plantbreeding/
They has a blog:
http://rplantbreeding.blogspot.com/
The following is examp | How to perform diallel analysis in R?
There is beta package plantbreeding, which can do diallel analysis.
https://r-forge.r-project.org/projects/plantbreeding/
They has a blog:
http://rplantbreeding.blogspot.com/
The following is example from this package:
require(plantbreeding)
data(fulldial)
out <-diallele1(dat... | How to perform diallel analysis in R?
There is beta package plantbreeding, which can do diallel analysis.
https://r-forge.r-project.org/projects/plantbreeding/
They has a blog:
http://rplantbreeding.blogspot.com/
The following is examp |
54,611 | How to perform diallel analysis in R? | I think it's unlikely that you'll find worked examples in R for the analysis of diallels.
I did find some references for diallel analysis in SAS (e.g., here, and there's a chapter on DIALLEL-SAS in the book Handbook of formulas and software for plant geneticists and breeders). | How to perform diallel analysis in R? | I think it's unlikely that you'll find worked examples in R for the analysis of diallels.
I did find some references for diallel analysis in SAS (e.g., here, and there's a chapter on DIALLEL-SAS in th | How to perform diallel analysis in R?
I think it's unlikely that you'll find worked examples in R for the analysis of diallels.
I did find some references for diallel analysis in SAS (e.g., here, and there's a chapter on DIALLEL-SAS in the book Handbook of formulas and software for plant geneticists and breeders). | How to perform diallel analysis in R?
I think it's unlikely that you'll find worked examples in R for the analysis of diallels.
I did find some references for diallel analysis in SAS (e.g., here, and there's a chapter on DIALLEL-SAS in th |
54,612 | How to perform diallel analysis in R? | There's a nice worked example in the book Statistical and Biometrical Techniques in Plant Breeding by Jawahar R. Sharma on about page 184. Visible in Google books. | How to perform diallel analysis in R? | There's a nice worked example in the book Statistical and Biometrical Techniques in Plant Breeding by Jawahar R. Sharma on about page 184. Visible in Google books. | How to perform diallel analysis in R?
There's a nice worked example in the book Statistical and Biometrical Techniques in Plant Breeding by Jawahar R. Sharma on about page 184. Visible in Google books. | How to perform diallel analysis in R?
There's a nice worked example in the book Statistical and Biometrical Techniques in Plant Breeding by Jawahar R. Sharma on about page 184. Visible in Google books. |
54,613 | How do I use the GPML package for multi dimensional input? | Here is a more minimal example of a 2-d regression problem (I haven't got octave, only matlab, but hopefully the difference won't matter). meanfunc and covfunc should be happy with any number of inputs, provided that the covariance function doesn't have a hyper-parameter per inpit feature (as e.g. covSEiso does). Hop... | How do I use the GPML package for multi dimensional input? | Here is a more minimal example of a 2-d regression problem (I haven't got octave, only matlab, but hopefully the difference won't matter). meanfunc and covfunc should be happy with any number of inpu | How do I use the GPML package for multi dimensional input?
Here is a more minimal example of a 2-d regression problem (I haven't got octave, only matlab, but hopefully the difference won't matter). meanfunc and covfunc should be happy with any number of inputs, provided that the covariance function doesn't have a hype... | How do I use the GPML package for multi dimensional input?
Here is a more minimal example of a 2-d regression problem (I haven't got octave, only matlab, but hopefully the difference won't matter). meanfunc and covfunc should be happy with any number of inpu |
54,614 | What is a good way of estimating the dependence of an output variable on the input parameters? | EDIT: After some reflection, I modified my answer substantially.
The best thing to do would be to try to find a reasonable model for your data (for example, by using multiple linear regression). If you cannot get enough data to do this, I would try the following "non-parametric" approach. Suppose that in your data se... | What is a good way of estimating the dependence of an output variable on the input parameters? | EDIT: After some reflection, I modified my answer substantially.
The best thing to do would be to try to find a reasonable model for your data (for example, by using multiple linear regression). If y | What is a good way of estimating the dependence of an output variable on the input parameters?
EDIT: After some reflection, I modified my answer substantially.
The best thing to do would be to try to find a reasonable model for your data (for example, by using multiple linear regression). If you cannot get enough data... | What is a good way of estimating the dependence of an output variable on the input parameters?
EDIT: After some reflection, I modified my answer substantially.
The best thing to do would be to try to find a reasonable model for your data (for example, by using multiple linear regression). If y |
54,615 | What is a good way of estimating the dependence of an output variable on the input parameters? | A few comments:
Why did you go with your particular experimental design set-up? For example, fix A+B and vary C. What would you fix A + B at? If you are interesting in determining the effect of A and B, it seems a bit strange that you can fix them at "optimal values". There are standard statistical techniques for samp... | What is a good way of estimating the dependence of an output variable on the input parameters? | A few comments:
Why did you go with your particular experimental design set-up? For example, fix A+B and vary C. What would you fix A + B at? If you are interesting in determining the effect of A and | What is a good way of estimating the dependence of an output variable on the input parameters?
A few comments:
Why did you go with your particular experimental design set-up? For example, fix A+B and vary C. What would you fix A + B at? If you are interesting in determining the effect of A and B, it seems a bit strang... | What is a good way of estimating the dependence of an output variable on the input parameters?
A few comments:
Why did you go with your particular experimental design set-up? For example, fix A+B and vary C. What would you fix A + B at? If you are interesting in determining the effect of A and |
54,616 | Effect size of Spearman's rank test | I see no obvious reason not to do so. As far as I know, we usually make a distinction between two kind of effect size (ES) measures for qualifying the strength of an observed association: ES based on $d$ (difference of means) and ES based on $r$ (correlation). The latter includes Pearson's $r$, but also Spearman's $\rh... | Effect size of Spearman's rank test | I see no obvious reason not to do so. As far as I know, we usually make a distinction between two kind of effect size (ES) measures for qualifying the strength of an observed association: ES based on | Effect size of Spearman's rank test
I see no obvious reason not to do so. As far as I know, we usually make a distinction between two kind of effect size (ES) measures for qualifying the strength of an observed association: ES based on $d$ (difference of means) and ES based on $r$ (correlation). The latter includes Pea... | Effect size of Spearman's rank test
I see no obvious reason not to do so. As far as I know, we usually make a distinction between two kind of effect size (ES) measures for qualifying the strength of an observed association: ES based on |
54,617 | Effect size of Spearman's rank test | With increasing sample size $n$, $r_{z} = \sqrt{n-1} r_{S}$ is asymptotically $N(0, 1)$ distributed (standard normal distribution). In R
rSz <- sqrt(n-1) * rS
(pVal <- 1-pnorm(rSz)) # one-sided p-value, test for positive rank correlation | Effect size of Spearman's rank test | With increasing sample size $n$, $r_{z} = \sqrt{n-1} r_{S}$ is asymptotically $N(0, 1)$ distributed (standard normal distribution). In R
rSz <- sqrt(n-1) * rS
(pVal <- 1-pnorm(rSz)) # one-sided p- | Effect size of Spearman's rank test
With increasing sample size $n$, $r_{z} = \sqrt{n-1} r_{S}$ is asymptotically $N(0, 1)$ distributed (standard normal distribution). In R
rSz <- sqrt(n-1) * rS
(pVal <- 1-pnorm(rSz)) # one-sided p-value, test for positive rank correlation | Effect size of Spearman's rank test
With increasing sample size $n$, $r_{z} = \sqrt{n-1} r_{S}$ is asymptotically $N(0, 1)$ distributed (standard normal distribution). In R
rSz <- sqrt(n-1) * rS
(pVal <- 1-pnorm(rSz)) # one-sided p- |
54,618 | How to view GBM package trees? [closed] | This is not a bug. The model is stored using a 0-based index. So SplitVar=0 is X1, SplitVar=1 is X2, and SplitVar=2 is X3. So this split corresponds to a split on X3. Since X3 is an ordinal factor and the split is at 1.5, this corresponds to splitting levels 0&1 from 2&3.
> sum(data$X3<="c")
[1] 522
> sum(data$X3>="b")... | How to view GBM package trees? [closed] | This is not a bug. The model is stored using a 0-based index. So SplitVar=0 is X1, SplitVar=1 is X2, and SplitVar=2 is X3. So this split corresponds to a split on X3. Since X3 is an ordinal factor and | How to view GBM package trees? [closed]
This is not a bug. The model is stored using a 0-based index. So SplitVar=0 is X1, SplitVar=1 is X2, and SplitVar=2 is X3. So this split corresponds to a split on X3. Since X3 is an ordinal factor and the split is at 1.5, this corresponds to splitting levels 0&1 from 2&3.
> sum(d... | How to view GBM package trees? [closed]
This is not a bug. The model is stored using a 0-based index. So SplitVar=0 is X1, SplitVar=1 is X2, and SplitVar=2 is X3. So this split corresponds to a split on X3. Since X3 is an ordinal factor and |
54,619 | Expectation of $\left(X-M\right)^T\left(X-M\right)\left(X-M\right)^T\left(X-M\right)$ | Because $\left(X-M\right)^T\left(X-M\right) = \sum_i{(X_i - m_i)^2}$,
$$\left(X-M\right)^T\left(X-M\right)\left(X-M\right)^T\left(X-M\right) = \sum_{i,j}{(X_i - m_i)^2(X_j - m_j)^2} \text{.}$$
There are two kinds of expectations to obtain here. Assuming the $X_i$ are independent and $i \ne j$,
$$\eqalign{
E \left[ ... | Expectation of $\left(X-M\right)^T\left(X-M\right)\left(X-M\right)^T\left(X-M\right)$ | Because $\left(X-M\right)^T\left(X-M\right) = \sum_i{(X_i - m_i)^2}$,
$$\left(X-M\right)^T\left(X-M\right)\left(X-M\right)^T\left(X-M\right) = \sum_{i,j}{(X_i - m_i)^2(X_j - m_j)^2} \text{.}$$
There | Expectation of $\left(X-M\right)^T\left(X-M\right)\left(X-M\right)^T\left(X-M\right)$
Because $\left(X-M\right)^T\left(X-M\right) = \sum_i{(X_i - m_i)^2}$,
$$\left(X-M\right)^T\left(X-M\right)\left(X-M\right)^T\left(X-M\right) = \sum_{i,j}{(X_i - m_i)^2(X_j - m_j)^2} \text{.}$$
There are two kinds of expectations to o... | Expectation of $\left(X-M\right)^T\left(X-M\right)\left(X-M\right)^T\left(X-M\right)$
Because $\left(X-M\right)^T\left(X-M\right) = \sum_i{(X_i - m_i)^2}$,
$$\left(X-M\right)^T\left(X-M\right)\left(X-M\right)^T\left(X-M\right) = \sum_{i,j}{(X_i - m_i)^2(X_j - m_j)^2} \text{.}$$
There |
54,620 | Expectation of $\left(X-M\right)^T\left(X-M\right)\left(X-M\right)^T\left(X-M\right)$ | I believe this depends on the kurtosis of $X$. If I am reading this correctly, and assuming the $X_i$ are independent, you are trying to find the expectation of $\sum_i (X_i - m_i)^4$. Because $X_i^4$ appears, you cannot find this expectation in terms of $M$ and $\Sigma$ without making further assumptions. (Even withou... | Expectation of $\left(X-M\right)^T\left(X-M\right)\left(X-M\right)^T\left(X-M\right)$ | I believe this depends on the kurtosis of $X$. If I am reading this correctly, and assuming the $X_i$ are independent, you are trying to find the expectation of $\sum_i (X_i - m_i)^4$. Because $X_i^4$ | Expectation of $\left(X-M\right)^T\left(X-M\right)\left(X-M\right)^T\left(X-M\right)$
I believe this depends on the kurtosis of $X$. If I am reading this correctly, and assuming the $X_i$ are independent, you are trying to find the expectation of $\sum_i (X_i - m_i)^4$. Because $X_i^4$ appears, you cannot find this exp... | Expectation of $\left(X-M\right)^T\left(X-M\right)\left(X-M\right)^T\left(X-M\right)$
I believe this depends on the kurtosis of $X$. If I am reading this correctly, and assuming the $X_i$ are independent, you are trying to find the expectation of $\sum_i (X_i - m_i)^4$. Because $X_i^4$ |
54,621 | Expectation of $\left(X-M\right)^T\left(X-M\right)\left(X-M\right)^T\left(X-M\right)$ | If you lose iid and normality assumptions things can get ugly. In Anderson book you can find explicit formulas for expectations of type
$\sum_{s,r,t,u}E(X_s-m)(X_r-m)(X_t-m)(X_u-m)$
when $X=(x_1,...,x_n)$ is a sample from stationary process, with mean $m$. In general it is not possible to express such types of moments... | Expectation of $\left(X-M\right)^T\left(X-M\right)\left(X-M\right)^T\left(X-M\right)$ | If you lose iid and normality assumptions things can get ugly. In Anderson book you can find explicit formulas for expectations of type
$\sum_{s,r,t,u}E(X_s-m)(X_r-m)(X_t-m)(X_u-m)$
when $X=(x_1,..., | Expectation of $\left(X-M\right)^T\left(X-M\right)\left(X-M\right)^T\left(X-M\right)$
If you lose iid and normality assumptions things can get ugly. In Anderson book you can find explicit formulas for expectations of type
$\sum_{s,r,t,u}E(X_s-m)(X_r-m)(X_t-m)(X_u-m)$
when $X=(x_1,...,x_n)$ is a sample from stationary ... | Expectation of $\left(X-M\right)^T\left(X-M\right)\left(X-M\right)^T\left(X-M\right)$
If you lose iid and normality assumptions things can get ugly. In Anderson book you can find explicit formulas for expectations of type
$\sum_{s,r,t,u}E(X_s-m)(X_r-m)(X_t-m)(X_u-m)$
when $X=(x_1,..., |
54,622 | Developing a statistical test to ascertain better "fit" | Smoothing, rolling averages, running means... are all nice ways (perhaps) to display data. But using the results of smoothed data as an input to any statistical analysis is likely to give misleading results, especially when done by novices. William Briggs emphasizes this point in his excellent blog in this article and ... | Developing a statistical test to ascertain better "fit" | Smoothing, rolling averages, running means... are all nice ways (perhaps) to display data. But using the results of smoothed data as an input to any statistical analysis is likely to give misleading r | Developing a statistical test to ascertain better "fit"
Smoothing, rolling averages, running means... are all nice ways (perhaps) to display data. But using the results of smoothed data as an input to any statistical analysis is likely to give misleading results, especially when done by novices. William Briggs emphasiz... | Developing a statistical test to ascertain better "fit"
Smoothing, rolling averages, running means... are all nice ways (perhaps) to display data. But using the results of smoothed data as an input to any statistical analysis is likely to give misleading r |
54,623 | Developing a statistical test to ascertain better "fit" | Based on the information given, I think that you could consider AIC, a measure of likelihood that is penalized by degrees of freedom. | Developing a statistical test to ascertain better "fit" | Based on the information given, I think that you could consider AIC, a measure of likelihood that is penalized by degrees of freedom. | Developing a statistical test to ascertain better "fit"
Based on the information given, I think that you could consider AIC, a measure of likelihood that is penalized by degrees of freedom. | Developing a statistical test to ascertain better "fit"
Based on the information given, I think that you could consider AIC, a measure of likelihood that is penalized by degrees of freedom. |
54,624 | Specifying conditional probabilities in hybrid Bayesian networks | First of all, your usage of the term "prior probability" seems to be wrong. For any node N with discrete values $n_i$ the probability that a certain value of N occurs a priori is $p(N=n_i)$. If a node has no parents, one is interested in calculate this prob. But if a node has parents P, one is interested in calculating... | Specifying conditional probabilities in hybrid Bayesian networks | First of all, your usage of the term "prior probability" seems to be wrong. For any node N with discrete values $n_i$ the probability that a certain value of N occurs a priori is $p(N=n_i)$. If a node | Specifying conditional probabilities in hybrid Bayesian networks
First of all, your usage of the term "prior probability" seems to be wrong. For any node N with discrete values $n_i$ the probability that a certain value of N occurs a priori is $p(N=n_i)$. If a node has no parents, one is interested in calculate this pr... | Specifying conditional probabilities in hybrid Bayesian networks
First of all, your usage of the term "prior probability" seems to be wrong. For any node N with discrete values $n_i$ the probability that a certain value of N occurs a priori is $p(N=n_i)$. If a node |
54,625 | Specifying conditional probabilities in hybrid Bayesian networks | Consider two simple cases,
1) a real valued variable X is the parent of another real valued variable Y
2) a real valued variable X is the parent of a discrete valued variable Y
Assume that the Bayes net is a directed graph X -> Y. The Bayes net is fully specified, in both cases, when P(X) and P(Y | X) are specified. ... | Specifying conditional probabilities in hybrid Bayesian networks | Consider two simple cases,
1) a real valued variable X is the parent of another real valued variable Y
2) a real valued variable X is the parent of a discrete valued variable Y
Assume that the Bayes | Specifying conditional probabilities in hybrid Bayesian networks
Consider two simple cases,
1) a real valued variable X is the parent of another real valued variable Y
2) a real valued variable X is the parent of a discrete valued variable Y
Assume that the Bayes net is a directed graph X -> Y. The Bayes net is fully... | Specifying conditional probabilities in hybrid Bayesian networks
Consider two simple cases,
1) a real valued variable X is the parent of another real valued variable Y
2) a real valued variable X is the parent of a discrete valued variable Y
Assume that the Bayes |
54,626 | Sampling with non-uniform costs | Methods to find a solution are well known, but this is a messy problem. A tiny example reveals much, so consider the case $n = 2$. Let the cost of sampling bit 1 be $c_1 = 1$ and the cost of sampling bit 2 be $c_2 = c$. Without any loss of generality assume this is the expensive bit: $c \ge 1$.
Either we sample both... | Sampling with non-uniform costs | Methods to find a solution are well known, but this is a messy problem. A tiny example reveals much, so consider the case $n = 2$. Let the cost of sampling bit 1 be $c_1 = 1$ and the cost of samplin | Sampling with non-uniform costs
Methods to find a solution are well known, but this is a messy problem. A tiny example reveals much, so consider the case $n = 2$. Let the cost of sampling bit 1 be $c_1 = 1$ and the cost of sampling bit 2 be $c_2 = c$. Without any loss of generality assume this is the expensive bit: ... | Sampling with non-uniform costs
Methods to find a solution are well known, but this is a messy problem. A tiny example reveals much, so consider the case $n = 2$. Let the cost of sampling bit 1 be $c_1 = 1$ and the cost of samplin |
54,627 | Sampling with non-uniform costs | Despite promising not to, I have thought about this problem further. This approach differs enough from the previous one I outlined that it seems worthwhile posting it as a separate reply.
Both @Aniko and @shabbychef are right: you need to "almost exhaust the population" with "greedy sampling." But there's a twist--o... | Sampling with non-uniform costs | Despite promising not to, I have thought about this problem further. This approach differs enough from the previous one I outlined that it seems worthwhile posting it as a separate reply.
Both @Anik | Sampling with non-uniform costs
Despite promising not to, I have thought about this problem further. This approach differs enough from the previous one I outlined that it seems worthwhile posting it as a separate reply.
Both @Aniko and @shabbychef are right: you need to "almost exhaust the population" with "greedy sa... | Sampling with non-uniform costs
Despite promising not to, I have thought about this problem further. This approach differs enough from the previous one I outlined that it seems worthwhile posting it as a separate reply.
Both @Anik |
54,628 | Sampling with non-uniform costs | If the costs $c_i$ are known a priori, it seems like a greedy sampling would give you some guarantees. That is, sample the $n-2k$ bits in order of increasing cost. This gives a $k$-error guarantee on $B$ with probability $1$ in the obvious way. I am curious if this strategy is the limit strategy of some sane sequence o... | Sampling with non-uniform costs | If the costs $c_i$ are known a priori, it seems like a greedy sampling would give you some guarantees. That is, sample the $n-2k$ bits in order of increasing cost. This gives a $k$-error guarantee on | Sampling with non-uniform costs
If the costs $c_i$ are known a priori, it seems like a greedy sampling would give you some guarantees. That is, sample the $n-2k$ bits in order of increasing cost. This gives a $k$-error guarantee on $B$ with probability $1$ in the obvious way. I am curious if this strategy is the limit ... | Sampling with non-uniform costs
If the costs $c_i$ are known a priori, it seems like a greedy sampling would give you some guarantees. That is, sample the $n-2k$ bits in order of increasing cost. This gives a $k$-error guarantee on |
54,629 | Statistical test to compare two ratios from two independent models | In response to an old question, and given that a good response has been provided already elsewhere by jbowman and StasK to a very similar (but better defined) problem. I refer anyone who stumbles on this to the following question (and answers):
Test for significant difference in ratios of normally distributed random va... | Statistical test to compare two ratios from two independent models | In response to an old question, and given that a good response has been provided already elsewhere by jbowman and StasK to a very similar (but better defined) problem. I refer anyone who stumbles on t | Statistical test to compare two ratios from two independent models
In response to an old question, and given that a good response has been provided already elsewhere by jbowman and StasK to a very similar (but better defined) problem. I refer anyone who stumbles on this to the following question (and answers):
Test for... | Statistical test to compare two ratios from two independent models
In response to an old question, and given that a good response has been provided already elsewhere by jbowman and StasK to a very similar (but better defined) problem. I refer anyone who stumbles on t |
54,630 | Statistical test to compare two ratios from two independent models | Any test for independence of a 2x2 contingency table will do! A chi-square or t-test are the textbook simple solutions. The "best" test in this situation is called Barnard's test for superiority -- the StatXact software will happily calculate this for you. | Statistical test to compare two ratios from two independent models | Any test for independence of a 2x2 contingency table will do! A chi-square or t-test are the textbook simple solutions. The "best" test in this situation is called Barnard's test for superiority -- th | Statistical test to compare two ratios from two independent models
Any test for independence of a 2x2 contingency table will do! A chi-square or t-test are the textbook simple solutions. The "best" test in this situation is called Barnard's test for superiority -- the StatXact software will happily calculate this for y... | Statistical test to compare two ratios from two independent models
Any test for independence of a 2x2 contingency table will do! A chi-square or t-test are the textbook simple solutions. The "best" test in this situation is called Barnard's test for superiority -- th |
54,631 | Statistical test to compare two ratios from two independent models | I assume you are trying to test the difference of two proportions here. For example, a click-through rate of a website before and after a button change, which is defined by
no of visitors who visit the page/no of visitors who click the button and navigate to another page
If that's the case, you can use Z-test if you... | Statistical test to compare two ratios from two independent models | I assume you are trying to test the difference of two proportions here. For example, a click-through rate of a website before and after a button change, which is defined by
no of visitors who visit | Statistical test to compare two ratios from two independent models
I assume you are trying to test the difference of two proportions here. For example, a click-through rate of a website before and after a button change, which is defined by
no of visitors who visit the page/no of visitors who click the button and navi... | Statistical test to compare two ratios from two independent models
I assume you are trying to test the difference of two proportions here. For example, a click-through rate of a website before and after a button change, which is defined by
no of visitors who visit |
54,632 | "Multiple response" analysis of arrest records | I can't particularly comment on how to handle multiple response categories, but you need to further refine your question for people on this forum to be able to give useful advice.
You mention various interests, such as some sort of drug policy intervention, and differential charges according to race, arrest location, a... | "Multiple response" analysis of arrest records | I can't particularly comment on how to handle multiple response categories, but you need to further refine your question for people on this forum to be able to give useful advice.
You mention various | "Multiple response" analysis of arrest records
I can't particularly comment on how to handle multiple response categories, but you need to further refine your question for people on this forum to be able to give useful advice.
You mention various interests, such as some sort of drug policy intervention, and differentia... | "Multiple response" analysis of arrest records
I can't particularly comment on how to handle multiple response categories, but you need to further refine your question for people on this forum to be able to give useful advice.
You mention various |
54,633 | "Multiple response" analysis of arrest records | It is not clear what you questions you are trying to answer but here are are several ways to deal with the multiple-response data:
Arresting Officer
Convert the two columns into a single count variable (1 or 2) which indicates the no of arresting officers. You will lose the arresting officer's identities but perhaps t... | "Multiple response" analysis of arrest records | It is not clear what you questions you are trying to answer but here are are several ways to deal with the multiple-response data:
Arresting Officer
Convert the two columns into a single count variab | "Multiple response" analysis of arrest records
It is not clear what you questions you are trying to answer but here are are several ways to deal with the multiple-response data:
Arresting Officer
Convert the two columns into a single count variable (1 or 2) which indicates the no of arresting officers. You will lose t... | "Multiple response" analysis of arrest records
It is not clear what you questions you are trying to answer but here are are several ways to deal with the multiple-response data:
Arresting Officer
Convert the two columns into a single count variab |
54,634 | "Multiple response" analysis of arrest records | I've examined associations between multiple response categorical variables in the past basically following the log-linear approach for marginal data outlined in the following:
Strategies for Modeling Two Categorical Variables with Multiple Category Choices (Bilder, Loughlin, 2003)
Your case may be more complicated si... | "Multiple response" analysis of arrest records | I've examined associations between multiple response categorical variables in the past basically following the log-linear approach for marginal data outlined in the following:
Strategies for Modeling | "Multiple response" analysis of arrest records
I've examined associations between multiple response categorical variables in the past basically following the log-linear approach for marginal data outlined in the following:
Strategies for Modeling Two Categorical Variables with Multiple Category Choices (Bilder, Loughl... | "Multiple response" analysis of arrest records
I've examined associations between multiple response categorical variables in the past basically following the log-linear approach for marginal data outlined in the following:
Strategies for Modeling |
54,635 | Where can I find a good resources for making publication quality line plots | See this related question. All the same advice applies in your case. Just to highlight a few points:
Using R is a good way to go, especially with the ggplot2 package. This is both flexible and produces very high quality output. There are plenty of examples on the ggplot2 website and across the web (including on th... | Where can I find a good resources for making publication quality line plots | See this related question. All the same advice applies in your case. Just to highlight a few points:
Using R is a good way to go, especially with the ggplot2 package. This is both flexible and pro | Where can I find a good resources for making publication quality line plots
See this related question. All the same advice applies in your case. Just to highlight a few points:
Using R is a good way to go, especially with the ggplot2 package. This is both flexible and produces very high quality output. There are p... | Where can I find a good resources for making publication quality line plots
See this related question. All the same advice applies in your case. Just to highlight a few points:
Using R is a good way to go, especially with the ggplot2 package. This is both flexible and pro |
54,636 | Where can I find a good resources for making publication quality line plots | You are probably aware of TeXexample.net. The TeX package pgfplots might also be of interest to you: it provides a pretty complete manual and allows to directly invoke gnuplot.
Personally, I use Sweave to embed R code, plots and table (see package xtable) into Latex documents. It is very handy especially if you need to... | Where can I find a good resources for making publication quality line plots | You are probably aware of TeXexample.net. The TeX package pgfplots might also be of interest to you: it provides a pretty complete manual and allows to directly invoke gnuplot.
Personally, I use Sweav | Where can I find a good resources for making publication quality line plots
You are probably aware of TeXexample.net. The TeX package pgfplots might also be of interest to you: it provides a pretty complete manual and allows to directly invoke gnuplot.
Personally, I use Sweave to embed R code, plots and table (see pack... | Where can I find a good resources for making publication quality line plots
You are probably aware of TeXexample.net. The TeX package pgfplots might also be of interest to you: it provides a pretty complete manual and allows to directly invoke gnuplot.
Personally, I use Sweav |
54,637 | PCA on out-of-sample data | Following the comments exchange with Ebony (see Whuber's answer). I gather that in Ebony's application, $p$ is much larger than $n$ which is itself very large. In this case the complexity of computing the eigen decomposition is in the order of $O(n^3)$. Two solutions spring to mind:
partial decomposition: assuming $p$... | PCA on out-of-sample data | Following the comments exchange with Ebony (see Whuber's answer). I gather that in Ebony's application, $p$ is much larger than $n$ which is itself very large. In this case the complexity of computing | PCA on out-of-sample data
Following the comments exchange with Ebony (see Whuber's answer). I gather that in Ebony's application, $p$ is much larger than $n$ which is itself very large. In this case the complexity of computing the eigen decomposition is in the order of $O(n^3)$. Two solutions spring to mind:
partial d... | PCA on out-of-sample data
Following the comments exchange with Ebony (see Whuber's answer). I gather that in Ebony's application, $p$ is much larger than $n$ which is itself very large. In this case the complexity of computing |
54,638 | PCA on out-of-sample data | What computational savings? The PCA computation is based on the covariance (or correlation) matrix, whose size depends on the number of variables, not the number of data points. The calculation of a covariance matrix is fast. Even if you were doing PCA repeatedly (as part of a simulation, for instance), reducing fro... | PCA on out-of-sample data | What computational savings? The PCA computation is based on the covariance (or correlation) matrix, whose size depends on the number of variables, not the number of data points. The calculation of a | PCA on out-of-sample data
What computational savings? The PCA computation is based on the covariance (or correlation) matrix, whose size depends on the number of variables, not the number of data points. The calculation of a covariance matrix is fast. Even if you were doing PCA repeatedly (as part of a simulation, f... | PCA on out-of-sample data
What computational savings? The PCA computation is based on the covariance (or correlation) matrix, whose size depends on the number of variables, not the number of data points. The calculation of a |
54,639 | PCA on out-of-sample data | This isn't unlike a model selection problem where the goal is to arrive at something close to the "true dimensionality" of the data. You could try a cross validation approach, say 5-fold CV with your 500 data points. This will give you a reasonable metric of generalization error for out-of-sample data. The following... | PCA on out-of-sample data | This isn't unlike a model selection problem where the goal is to arrive at something close to the "true dimensionality" of the data. You could try a cross validation approach, say 5-fold CV with your | PCA on out-of-sample data
This isn't unlike a model selection problem where the goal is to arrive at something close to the "true dimensionality" of the data. You could try a cross validation approach, say 5-fold CV with your 500 data points. This will give you a reasonable metric of generalization error for out-of-s... | PCA on out-of-sample data
This isn't unlike a model selection problem where the goal is to arrive at something close to the "true dimensionality" of the data. You could try a cross validation approach, say 5-fold CV with your |
54,640 | PCA on out-of-sample data | I have never done this but my intuition suggests that the answer would depend to the extent to which the covariance matrix for the 500 data points is 'different' from the out-of-sample data. If the out-of-sample covariance matrix is very different then clearly the projection matrix of those points would be different th... | PCA on out-of-sample data | I have never done this but my intuition suggests that the answer would depend to the extent to which the covariance matrix for the 500 data points is 'different' from the out-of-sample data. If the ou | PCA on out-of-sample data
I have never done this but my intuition suggests that the answer would depend to the extent to which the covariance matrix for the 500 data points is 'different' from the out-of-sample data. If the out-of-sample covariance matrix is very different then clearly the projection matrix of those po... | PCA on out-of-sample data
I have never done this but my intuition suggests that the answer would depend to the extent to which the covariance matrix for the 500 data points is 'different' from the out-of-sample data. If the ou |
54,641 | Parametric techniques for n-related samples | Multilevel/hierarchical linear models can be used for this. Essentially, each repetition of the measure is clustered within the individual; individuals can then be clustered within other hierarchies. For me, at least, it's more intuitive than repeated-measures ANOVA.
The canonical text is Raudenbush and Bryk; I'm als... | Parametric techniques for n-related samples | Multilevel/hierarchical linear models can be used for this. Essentially, each repetition of the measure is clustered within the individual; individuals can then be clustered within other hierarchies. | Parametric techniques for n-related samples
Multilevel/hierarchical linear models can be used for this. Essentially, each repetition of the measure is clustered within the individual; individuals can then be clustered within other hierarchies. For me, at least, it's more intuitive than repeated-measures ANOVA.
The ca... | Parametric techniques for n-related samples
Multilevel/hierarchical linear models can be used for this. Essentially, each repetition of the measure is clustered within the individual; individuals can then be clustered within other hierarchies. |
54,642 | Use of Bayesian Search Theory in geological interpretation | Though it is not generally labeled as Bayesian search theory, such methods are pretty widely used in oil exploration. There are, however, important differences in the standard examples that drive different features of their respective modeling problems.
In the case of lost vessel exploration (in Bayesian search theo... | Use of Bayesian Search Theory in geological interpretation | Though it is not generally labeled as Bayesian search theory, such methods are pretty widely used in oil exploration. There are, however, important differences in the standard examples that drive dif | Use of Bayesian Search Theory in geological interpretation
Though it is not generally labeled as Bayesian search theory, such methods are pretty widely used in oil exploration. There are, however, important differences in the standard examples that drive different features of their respective modeling problems.
In t... | Use of Bayesian Search Theory in geological interpretation
Though it is not generally labeled as Bayesian search theory, such methods are pretty widely used in oil exploration. There are, however, important differences in the standard examples that drive dif |
54,643 | Use of Bayesian Search Theory in geological interpretation | There is a free book on Geostatistical Mapping with R here it might help your problem. | Use of Bayesian Search Theory in geological interpretation | There is a free book on Geostatistical Mapping with R here it might help your problem. | Use of Bayesian Search Theory in geological interpretation
There is a free book on Geostatistical Mapping with R here it might help your problem. | Use of Bayesian Search Theory in geological interpretation
There is a free book on Geostatistical Mapping with R here it might help your problem. |
54,644 | Measuring the effectiveness of a pattern recognition software | Yes, there are many methods. You would need to specify which model you're using, because it can vary.
For instance, Some models will be compared based on the AIC or BIC criteria. In other cases, one would look at the MSE from cross validation (as, for instance, with a support vector machine).
I recommend reading P... | Measuring the effectiveness of a pattern recognition software | Yes, there are many methods. You would need to specify which model you're using, because it can vary.
For instance, Some models will be compared based on the AIC or BIC criteria. In other cases, o | Measuring the effectiveness of a pattern recognition software
Yes, there are many methods. You would need to specify which model you're using, because it can vary.
For instance, Some models will be compared based on the AIC or BIC criteria. In other cases, one would look at the MSE from cross validation (as, for in... | Measuring the effectiveness of a pattern recognition software
Yes, there are many methods. You would need to specify which model you're using, because it can vary.
For instance, Some models will be compared based on the AIC or BIC criteria. In other cases, o |
54,645 | dispersion parameter in Poisson models | That's correct!
You've found out why glm doesn't use deviance/df as an estimate of dispersion: it's not a very good one. It uses the better estimate based on the variance of the Pearson residuals (though for family=poisson it doesn't need to estimate).
The estimate is bad because the deviance residuals aren't actually... | dispersion parameter in Poisson models | That's correct!
You've found out why glm doesn't use deviance/df as an estimate of dispersion: it's not a very good one. It uses the better estimate based on the variance of the Pearson residuals (th | dispersion parameter in Poisson models
That's correct!
You've found out why glm doesn't use deviance/df as an estimate of dispersion: it's not a very good one. It uses the better estimate based on the variance of the Pearson residuals (though for family=poisson it doesn't need to estimate).
The estimate is bad because... | dispersion parameter in Poisson models
That's correct!
You've found out why glm doesn't use deviance/df as an estimate of dispersion: it's not a very good one. It uses the better estimate based on the variance of the Pearson residuals (th |
54,646 | Combining Bayesian and Frequentist Estimation into a Single Model? | You can look at the a priori inferential properties of estimators (which treats both the data and parameters as random), but this is weaker than standard analysis
If you look at a statistical problem from a perspective where both the data and the model parameters are treated as random, you are essentially looking at th... | Combining Bayesian and Frequentist Estimation into a Single Model? | You can look at the a priori inferential properties of estimators (which treats both the data and parameters as random), but this is weaker than standard analysis
If you look at a statistical problem | Combining Bayesian and Frequentist Estimation into a Single Model?
You can look at the a priori inferential properties of estimators (which treats both the data and parameters as random), but this is weaker than standard analysis
If you look at a statistical problem from a perspective where both the data and the model ... | Combining Bayesian and Frequentist Estimation into a Single Model?
You can look at the a priori inferential properties of estimators (which treats both the data and parameters as random), but this is weaker than standard analysis
If you look at a statistical problem |
54,647 | Combining Bayesian and Frequentist Estimation into a Single Model? | As J. Delaney's comment says, the Bayesian approach already allows both the data and the parameters to be random.
I think the confusion arises because "the parameters are fixed and the data is random" is not true under the frequentist approach, and "the parameters are random and the data is fixed" is not true under the... | Combining Bayesian and Frequentist Estimation into a Single Model? | As J. Delaney's comment says, the Bayesian approach already allows both the data and the parameters to be random.
I think the confusion arises because "the parameters are fixed and the data is random" | Combining Bayesian and Frequentist Estimation into a Single Model?
As J. Delaney's comment says, the Bayesian approach already allows both the data and the parameters to be random.
I think the confusion arises because "the parameters are fixed and the data is random" is not true under the frequentist approach, and "the... | Combining Bayesian and Frequentist Estimation into a Single Model?
As J. Delaney's comment says, the Bayesian approach already allows both the data and the parameters to be random.
I think the confusion arises because "the parameters are fixed and the data is random" |
54,648 | What is non-parametric regression? | In general, this is an interesting question that comes up a lot.
I'll be the first to say "non-parametric" regression is not well-defined. You might be referred to Wasserman's text "All of Non-Parametric Statistics" which was the first seminal reference of its kind, attempting to broach the concept. The text wasn't wit... | What is non-parametric regression? | In general, this is an interesting question that comes up a lot.
I'll be the first to say "non-parametric" regression is not well-defined. You might be referred to Wasserman's text "All of Non-Paramet | What is non-parametric regression?
In general, this is an interesting question that comes up a lot.
I'll be the first to say "non-parametric" regression is not well-defined. You might be referred to Wasserman's text "All of Non-Parametric Statistics" which was the first seminal reference of its kind, attempting to broa... | What is non-parametric regression?
In general, this is an interesting question that comes up a lot.
I'll be the first to say "non-parametric" regression is not well-defined. You might be referred to Wasserman's text "All of Non-Paramet |
54,649 | Who first suggested weak stationarity and strict stationarity? | It was developed by Khintchine in Korrelationstheorie der stationare stochastischen Processe, Math. Ann. 109, 604-615.
As $\rm [I]$ notes:
The second line of development began with a series of papers in 1932-1934 by the Russian mathematician Khintchine who introduced both stationary and weakly stationary stochastic p... | Who first suggested weak stationarity and strict stationarity? | It was developed by Khintchine in Korrelationstheorie der stationare stochastischen Processe, Math. Ann. 109, 604-615.
As $\rm [I]$ notes:
The second line of development began with a series of papers | Who first suggested weak stationarity and strict stationarity?
It was developed by Khintchine in Korrelationstheorie der stationare stochastischen Processe, Math. Ann. 109, 604-615.
As $\rm [I]$ notes:
The second line of development began with a series of papers in 1932-1934 by the Russian mathematician Khintchine wh... | Who first suggested weak stationarity and strict stationarity?
It was developed by Khintchine in Korrelationstheorie der stationare stochastischen Processe, Math. Ann. 109, 604-615.
As $\rm [I]$ notes:
The second line of development began with a series of papers |
54,650 | Rigorous but elementary statistics for self study | Statistical Inference by Casella and Berger is the standard textbook for this. If you’re good at some elementary real analysis (say calculus at the level of Spivak, not necessarily Rudin), you have the mathematical background to handle most of it. Some multivariable calculus might be helpful to know, but the basics of ... | Rigorous but elementary statistics for self study | Statistical Inference by Casella and Berger is the standard textbook for this. If you’re good at some elementary real analysis (say calculus at the level of Spivak, not necessarily Rudin), you have th | Rigorous but elementary statistics for self study
Statistical Inference by Casella and Berger is the standard textbook for this. If you’re good at some elementary real analysis (say calculus at the level of Spivak, not necessarily Rudin), you have the mathematical background to handle most of it. Some multivariable cal... | Rigorous but elementary statistics for self study
Statistical Inference by Casella and Berger is the standard textbook for this. If you’re good at some elementary real analysis (say calculus at the level of Spivak, not necessarily Rudin), you have th |
54,651 | Why are superlearners used in TMLE? | Asymptotic inference (i.e., the variance of the estimator) for TMLE using influence functions requires the nuisance models--the models for the expected potential outcomes $E[Y|A,X]$ and propensity scores $E[A|X]$--to converge to the truth (i.e., for the predicted values to converge to the true values) at a certain rate... | Why are superlearners used in TMLE? | Asymptotic inference (i.e., the variance of the estimator) for TMLE using influence functions requires the nuisance models--the models for the expected potential outcomes $E[Y|A,X]$ and propensity sco | Why are superlearners used in TMLE?
Asymptotic inference (i.e., the variance of the estimator) for TMLE using influence functions requires the nuisance models--the models for the expected potential outcomes $E[Y|A,X]$ and propensity scores $E[A|X]$--to converge to the truth (i.e., for the predicted values to converge t... | Why are superlearners used in TMLE?
Asymptotic inference (i.e., the variance of the estimator) for TMLE using influence functions requires the nuisance models--the models for the expected potential outcomes $E[Y|A,X]$ and propensity sco |
54,652 | Why are superlearners used in TMLE? | Minimizing the prediction error of nuisance parameters is (generally) the correct goal when developing efficient estimators using e.g. estimating equations or one-step estimators. To suggest this, let's rigorously focus on a case study: estimating $\mu:=E\{AY/\pi(W)\}$ in a nonparametric model, for $A$ binary and $\pi(... | Why are superlearners used in TMLE? | Minimizing the prediction error of nuisance parameters is (generally) the correct goal when developing efficient estimators using e.g. estimating equations or one-step estimators. To suggest this, let | Why are superlearners used in TMLE?
Minimizing the prediction error of nuisance parameters is (generally) the correct goal when developing efficient estimators using e.g. estimating equations or one-step estimators. To suggest this, let's rigorously focus on a case study: estimating $\mu:=E\{AY/\pi(W)\}$ in a nonparame... | Why are superlearners used in TMLE?
Minimizing the prediction error of nuisance parameters is (generally) the correct goal when developing efficient estimators using e.g. estimating equations or one-step estimators. To suggest this, let |
54,653 | How to implement Adaptive Lasso penalty for a Logistic regression in Python? | Adaptive LASSO is a two-step estimator; check out section 3.1 of Zou "The Adaptive Lasso and Its Oracle Properties" (2006). (This is the original paper that proposed adaptive LASSO.) You can implement the steps separately. Let $p$ be the number of regressors in your model.
You start with a $\sqrt{n}$-consistent estima... | How to implement Adaptive Lasso penalty for a Logistic regression in Python? | Adaptive LASSO is a two-step estimator; check out section 3.1 of Zou "The Adaptive Lasso and Its Oracle Properties" (2006). (This is the original paper that proposed adaptive LASSO.) You can implement | How to implement Adaptive Lasso penalty for a Logistic regression in Python?
Adaptive LASSO is a two-step estimator; check out section 3.1 of Zou "The Adaptive Lasso and Its Oracle Properties" (2006). (This is the original paper that proposed adaptive LASSO.) You can implement the steps separately. Let $p$ be the numbe... | How to implement Adaptive Lasso penalty for a Logistic regression in Python?
Adaptive LASSO is a two-step estimator; check out section 3.1 of Zou "The Adaptive Lasso and Its Oracle Properties" (2006). (This is the original paper that proposed adaptive LASSO.) You can implement |
54,654 | How to check the data is generated by machine or human? | Without any further information on the stipulated sampling method for the survey or the meaning of the three outcomes, any possible response could have some from humans or a machine, and there is no statistical test to check the difference.
It is only possible to test for a difference between human and machine-generate... | How to check the data is generated by machine or human? | Without any further information on the stipulated sampling method for the survey or the meaning of the three outcomes, any possible response could have some from humans or a machine, and there is no s | How to check the data is generated by machine or human?
Without any further information on the stipulated sampling method for the survey or the meaning of the three outcomes, any possible response could have some from humans or a machine, and there is no statistical test to check the difference.
It is only possible to ... | How to check the data is generated by machine or human?
Without any further information on the stipulated sampling method for the survey or the meaning of the three outcomes, any possible response could have some from humans or a machine, and there is no s |
54,655 | How to check the data is generated by machine or human? | There are many ways in which this could go wrong in real life, but given that it sounds like a test question for students, conceptually simplifying it is a reasonable thing to do. If the survey questions had been randomized (such that the answers (1,2, or 3) were equally likely, this would be a situation where run leng... | How to check the data is generated by machine or human? | There are many ways in which this could go wrong in real life, but given that it sounds like a test question for students, conceptually simplifying it is a reasonable thing to do. If the survey questi | How to check the data is generated by machine or human?
There are many ways in which this could go wrong in real life, but given that it sounds like a test question for students, conceptually simplifying it is a reasonable thing to do. If the survey questions had been randomized (such that the answers (1,2, or 3) were ... | How to check the data is generated by machine or human?
There are many ways in which this could go wrong in real life, but given that it sounds like a test question for students, conceptually simplifying it is a reasonable thing to do. If the survey questi |
54,656 | How to check the data is generated by machine or human? | If you have labelled instances (i.e. you know if a sample is generated by machine or by human) you can train a machine learning classifier to find the pattern which separates the two classes.
Not sure if you would count a ML method as "statistical method". | How to check the data is generated by machine or human? | If you have labelled instances (i.e. you know if a sample is generated by machine or by human) you can train a machine learning classifier to find the pattern which separates the two classes.
Not sure | How to check the data is generated by machine or human?
If you have labelled instances (i.e. you know if a sample is generated by machine or by human) you can train a machine learning classifier to find the pattern which separates the two classes.
Not sure if you would count a ML method as "statistical method". | How to check the data is generated by machine or human?
If you have labelled instances (i.e. you know if a sample is generated by machine or by human) you can train a machine learning classifier to find the pattern which separates the two classes.
Not sure |
54,657 | Is there a name for a logical fallacy that uses irrelevant or unfamiliar statistics to make a point? | I think you could reasonably call this an instance of context-dropping --- in the present case the conclusion is a fallacious inference from the evidence, since the inference relies on a lack of context around what is a "normal" or "big" value of radiation dosage. | Is there a name for a logical fallacy that uses irrelevant or unfamiliar statistics to make a point? | I think you could reasonably call this an instance of context-dropping --- in the present case the conclusion is a fallacious inference from the evidence, since the inference relies on a lack of conte | Is there a name for a logical fallacy that uses irrelevant or unfamiliar statistics to make a point?
I think you could reasonably call this an instance of context-dropping --- in the present case the conclusion is a fallacious inference from the evidence, since the inference relies on a lack of context around what is a... | Is there a name for a logical fallacy that uses irrelevant or unfamiliar statistics to make a point?
I think you could reasonably call this an instance of context-dropping --- in the present case the conclusion is a fallacious inference from the evidence, since the inference relies on a lack of conte |
54,658 | Is there a name for a logical fallacy that uses irrelevant or unfamiliar statistics to make a point? | One is unreasonable averaging. And I have a great real-world example. This paper Staff Memo 4/2021 from the Norwegian Central bank. (link at the bottom).
To explain unreasonable averaging, here is a thought experiment. Suppose you have two kids, one 15 and one 19 years old. You decide to stimulate your kids finances by... | Is there a name for a logical fallacy that uses irrelevant or unfamiliar statistics to make a point? | One is unreasonable averaging. And I have a great real-world example. This paper Staff Memo 4/2021 from the Norwegian Central bank. (link at the bottom).
To explain unreasonable averaging, here is a t | Is there a name for a logical fallacy that uses irrelevant or unfamiliar statistics to make a point?
One is unreasonable averaging. And I have a great real-world example. This paper Staff Memo 4/2021 from the Norwegian Central bank. (link at the bottom).
To explain unreasonable averaging, here is a thought experiment. ... | Is there a name for a logical fallacy that uses irrelevant or unfamiliar statistics to make a point?
One is unreasonable averaging. And I have a great real-world example. This paper Staff Memo 4/2021 from the Norwegian Central bank. (link at the bottom).
To explain unreasonable averaging, here is a t |
54,659 | Where does the Logistic Distribution get its name? | The cumulative distribution function of the logistic distribution is the logistic function
$$
F(x) = \frac{1}{1+e^{-(x-\mu)/s}}
$$
For an explanation of where the logistic function got its name, check the What does the name "Logistic Regression" mean? thread. | Where does the Logistic Distribution get its name? | The cumulative distribution function of the logistic distribution is the logistic function
$$
F(x) = \frac{1}{1+e^{-(x-\mu)/s}}
$$
For an explanation of where the logistic function got its name, check | Where does the Logistic Distribution get its name?
The cumulative distribution function of the logistic distribution is the logistic function
$$
F(x) = \frac{1}{1+e^{-(x-\mu)/s}}
$$
For an explanation of where the logistic function got its name, check the What does the name "Logistic Regression" mean? thread. | Where does the Logistic Distribution get its name?
The cumulative distribution function of the logistic distribution is the logistic function
$$
F(x) = \frac{1}{1+e^{-(x-\mu)/s}}
$$
For an explanation of where the logistic function got its name, check |
54,660 | Basic understanding of control variables in observational studies | Factors, whose only connection with the considered variables is that they influence only the dependent variable, in particular, have no connection with the independent variable, will not cause bias to your results so they don't have to be controlled. However, they could improve the precision. This paper is a good intro... | Basic understanding of control variables in observational studies | Factors, whose only connection with the considered variables is that they influence only the dependent variable, in particular, have no connection with the independent variable, will not cause bias to | Basic understanding of control variables in observational studies
Factors, whose only connection with the considered variables is that they influence only the dependent variable, in particular, have no connection with the independent variable, will not cause bias to your results so they don't have to be controlled. How... | Basic understanding of control variables in observational studies
Factors, whose only connection with the considered variables is that they influence only the dependent variable, in particular, have no connection with the independent variable, will not cause bias to |
54,661 | Basic understanding of control variables in observational studies | Yes, both are right. Basically, the idea is that if you omit an important variable in your analysis, then you are going to miss some predictive power. In addition, if the variable you omitted is correlated to some of your independent variables, then your estimates for the coefficients of these variables are going to be... | Basic understanding of control variables in observational studies | Yes, both are right. Basically, the idea is that if you omit an important variable in your analysis, then you are going to miss some predictive power. In addition, if the variable you omitted is corre | Basic understanding of control variables in observational studies
Yes, both are right. Basically, the idea is that if you omit an important variable in your analysis, then you are going to miss some predictive power. In addition, if the variable you omitted is correlated to some of your independent variables, then your... | Basic understanding of control variables in observational studies
Yes, both are right. Basically, the idea is that if you omit an important variable in your analysis, then you are going to miss some predictive power. In addition, if the variable you omitted is corre |
54,662 | Solving Poisson probability problem using only other known probabilities | Since $X_t\sim\text{Pois}(\lambda t)$, $$\mathbb{P}(X_t=k)=e^{-\lambda t}\frac{\left(\lambda t\right)^k}{k!}$$
As a consequence, you can develop expressions of your values $\mathbb{P}(X_1=1)$ and $\mathbb{P}(X_2=3)$ as functions of $\lambda$. Then, you can find a couple of ways to use these 2 formulas and the numerical... | Solving Poisson probability problem using only other known probabilities | Since $X_t\sim\text{Pois}(\lambda t)$, $$\mathbb{P}(X_t=k)=e^{-\lambda t}\frac{\left(\lambda t\right)^k}{k!}$$
As a consequence, you can develop expressions of your values $\mathbb{P}(X_1=1)$ and $\ma | Solving Poisson probability problem using only other known probabilities
Since $X_t\sim\text{Pois}(\lambda t)$, $$\mathbb{P}(X_t=k)=e^{-\lambda t}\frac{\left(\lambda t\right)^k}{k!}$$
As a consequence, you can develop expressions of your values $\mathbb{P}(X_1=1)$ and $\mathbb{P}(X_2=3)$ as functions of $\lambda$. Then... | Solving Poisson probability problem using only other known probabilities
Since $X_t\sim\text{Pois}(\lambda t)$, $$\mathbb{P}(X_t=k)=e^{-\lambda t}\frac{\left(\lambda t\right)^k}{k!}$$
As a consequence, you can develop expressions of your values $\mathbb{P}(X_1=1)$ and $\ma |
54,663 | How to prove statistically that mean jumps when a parameter crosses an unknown threshold value? | You could consider "post-selection inference" methods. This is a collection of approaches to getting p-values (or confidence intervals) for a selected model's parameters, designed to be valid given that you ran model-selection first instead of using a model chosen a priori. In your case, the "model selection" consists ... | How to prove statistically that mean jumps when a parameter crosses an unknown threshold value? | You could consider "post-selection inference" methods. This is a collection of approaches to getting p-values (or confidence intervals) for a selected model's parameters, designed to be valid given th | How to prove statistically that mean jumps when a parameter crosses an unknown threshold value?
You could consider "post-selection inference" methods. This is a collection of approaches to getting p-values (or confidence intervals) for a selected model's parameters, designed to be valid given that you ran model-selecti... | How to prove statistically that mean jumps when a parameter crosses an unknown threshold value?
You could consider "post-selection inference" methods. This is a collection of approaches to getting p-values (or confidence intervals) for a selected model's parameters, designed to be valid given th |
54,664 | How to prove statistically that mean jumps when a parameter crosses an unknown threshold value? | Just in case a Bayesian approach is of interest, there are some potential tools readily available in R or Python for use. The one probably most appropriate for your case is the mcp package--regression with multiple changepoints. Another popular one is bcp. But here I will choose a package Rbeast (https://github.com/zha... | How to prove statistically that mean jumps when a parameter crosses an unknown threshold value? | Just in case a Bayesian approach is of interest, there are some potential tools readily available in R or Python for use. The one probably most appropriate for your case is the mcp package--regression | How to prove statistically that mean jumps when a parameter crosses an unknown threshold value?
Just in case a Bayesian approach is of interest, there are some potential tools readily available in R or Python for use. The one probably most appropriate for your case is the mcp package--regression with multiple changepoi... | How to prove statistically that mean jumps when a parameter crosses an unknown threshold value?
Just in case a Bayesian approach is of interest, there are some potential tools readily available in R or Python for use. The one probably most appropriate for your case is the mcp package--regression |
54,665 | How to prove statistically that mean jumps when a parameter crosses an unknown threshold value? | Use the temperatures to sort your data (from low to high temperatures). Then, run a test for structural breaks (e.g. cusum, or Bai-Perron) on the random numbers (as if they were a time series).
If the software you use to run the structural break tests asks you to frame your model as a regression model, then make it a r... | How to prove statistically that mean jumps when a parameter crosses an unknown threshold value? | Use the temperatures to sort your data (from low to high temperatures). Then, run a test for structural breaks (e.g. cusum, or Bai-Perron) on the random numbers (as if they were a time series).
If the | How to prove statistically that mean jumps when a parameter crosses an unknown threshold value?
Use the temperatures to sort your data (from low to high temperatures). Then, run a test for structural breaks (e.g. cusum, or Bai-Perron) on the random numbers (as if they were a time series).
If the software you use to run... | How to prove statistically that mean jumps when a parameter crosses an unknown threshold value?
Use the temperatures to sort your data (from low to high temperatures). Then, run a test for structural breaks (e.g. cusum, or Bai-Perron) on the random numbers (as if they were a time series).
If the |
54,666 | How to prove statistically that mean jumps when a parameter crosses an unknown threshold value? | Your question involves two tasks, estimation and significance testing.
In both cases you have uncertainties about the model (like no specification for the distribution of the "random number generator").
A way to resolve this is to use general methods. These methods work for different types of distributions, but they ma... | How to prove statistically that mean jumps when a parameter crosses an unknown threshold value? | Your question involves two tasks, estimation and significance testing.
In both cases you have uncertainties about the model (like no specification for the distribution of the "random number generator" | How to prove statistically that mean jumps when a parameter crosses an unknown threshold value?
Your question involves two tasks, estimation and significance testing.
In both cases you have uncertainties about the model (like no specification for the distribution of the "random number generator").
A way to resolve this... | How to prove statistically that mean jumps when a parameter crosses an unknown threshold value?
Your question involves two tasks, estimation and significance testing.
In both cases you have uncertainties about the model (like no specification for the distribution of the "random number generator" |
54,667 | What is the meaning of the variance in a prior that represents L2 regularization? | The basic idea of the prior is, that it describes your knowledge about the weights before you get to know the observations (the data). Thus, a prior with a mean equal to zero and a small prior variance keeps the parameters near zero, i.e. it is used as regularization. Alternatively, a large prior variance means that yo... | What is the meaning of the variance in a prior that represents L2 regularization? | The basic idea of the prior is, that it describes your knowledge about the weights before you get to know the observations (the data). Thus, a prior with a mean equal to zero and a small prior varianc | What is the meaning of the variance in a prior that represents L2 regularization?
The basic idea of the prior is, that it describes your knowledge about the weights before you get to know the observations (the data). Thus, a prior with a mean equal to zero and a small prior variance keeps the parameters near zero, i.e.... | What is the meaning of the variance in a prior that represents L2 regularization?
The basic idea of the prior is, that it describes your knowledge about the weights before you get to know the observations (the data). Thus, a prior with a mean equal to zero and a small prior varianc |
54,668 | What is the meaning of the variance in a prior that represents L2 regularization? | In case the prior is a single Gaussian, its variance means how confident you are regarding your prior beliefs. That is, the smaller the variance you put into your prior Gaussian, the more confident you are in your prior belief that the data has to be around the mean of the prior. Calling it "noise", like you say, might... | What is the meaning of the variance in a prior that represents L2 regularization? | In case the prior is a single Gaussian, its variance means how confident you are regarding your prior beliefs. That is, the smaller the variance you put into your prior Gaussian, the more confident yo | What is the meaning of the variance in a prior that represents L2 regularization?
In case the prior is a single Gaussian, its variance means how confident you are regarding your prior beliefs. That is, the smaller the variance you put into your prior Gaussian, the more confident you are in your prior belief that the da... | What is the meaning of the variance in a prior that represents L2 regularization?
In case the prior is a single Gaussian, its variance means how confident you are regarding your prior beliefs. That is, the smaller the variance you put into your prior Gaussian, the more confident yo |
54,669 | Random variate of a singular Wishart distribution with non-integral degrees of freedom | The Wishart Distribution is defined on the manifold $\mathcal{M}(p)$ of all positive-definite symmetric (psd) $p\times p$ matrices. In the coordinate system $(x_{ij}, 1\le j \le i \le p)$ (which identifies this space of matrices with a subset of $\mathbb{R}^{p(p+1)/2}$) the density of the "standard" Wishart distribut... | Random variate of a singular Wishart distribution with non-integral degrees of freedom | The Wishart Distribution is defined on the manifold $\mathcal{M}(p)$ of all positive-definite symmetric (psd) $p\times p$ matrices. In the coordinate system $(x_{ij}, 1\le j \le i \le p)$ (which ide | Random variate of a singular Wishart distribution with non-integral degrees of freedom
The Wishart Distribution is defined on the manifold $\mathcal{M}(p)$ of all positive-definite symmetric (psd) $p\times p$ matrices. In the coordinate system $(x_{ij}, 1\le j \le i \le p)$ (which identifies this space of matrices wi... | Random variate of a singular Wishart distribution with non-integral degrees of freedom
The Wishart Distribution is defined on the manifold $\mathcal{M}(p)$ of all positive-definite symmetric (psd) $p\times p$ matrices. In the coordinate system $(x_{ij}, 1\le j \le i \le p)$ (which ide |
54,670 | Random variate of a singular Wishart distribution with non-integral degrees of freedom | The answer to this question is negative, we must have an integral number of degrees of freedom $\nu$ if $\nu\le p-1$. To prove it, we can look at the singular Wishart, defined as:
$$W_p(\nu,\Sigma)=\sum_{i=1}^nY_iY_i'$$
with $Y_i\sim\mathcal N(0,\Sigma)$, and $\Sigma$ a positive definite matrix.
The rank of the random ... | Random variate of a singular Wishart distribution with non-integral degrees of freedom | The answer to this question is negative, we must have an integral number of degrees of freedom $\nu$ if $\nu\le p-1$. To prove it, we can look at the singular Wishart, defined as:
$$W_p(\nu,\Sigma)=\s | Random variate of a singular Wishart distribution with non-integral degrees of freedom
The answer to this question is negative, we must have an integral number of degrees of freedom $\nu$ if $\nu\le p-1$. To prove it, we can look at the singular Wishart, defined as:
$$W_p(\nu,\Sigma)=\sum_{i=1}^nY_iY_i'$$
with $Y_i\sim... | Random variate of a singular Wishart distribution with non-integral degrees of freedom
The answer to this question is negative, we must have an integral number of degrees of freedom $\nu$ if $\nu\le p-1$. To prove it, we can look at the singular Wishart, defined as:
$$W_p(\nu,\Sigma)=\s |
54,671 | Post-hoc power analysis for null results: how to use 95% confidence interval instead? | If your CIs are narrow, then you have an idea of how large the effect is, and you can say with some confidence that the effect is small, and that's why you didn't detect it.
If the CIs are wide, then you don't know how big the effect is. Maybe it's big and you didn't detect it because you didn't have enough power. Mayb... | Post-hoc power analysis for null results: how to use 95% confidence interval instead? | If your CIs are narrow, then you have an idea of how large the effect is, and you can say with some confidence that the effect is small, and that's why you didn't detect it.
If the CIs are wide, then | Post-hoc power analysis for null results: how to use 95% confidence interval instead?
If your CIs are narrow, then you have an idea of how large the effect is, and you can say with some confidence that the effect is small, and that's why you didn't detect it.
If the CIs are wide, then you don't know how big the effect ... | Post-hoc power analysis for null results: how to use 95% confidence interval instead?
If your CIs are narrow, then you have an idea of how large the effect is, and you can say with some confidence that the effect is small, and that's why you didn't detect it.
If the CIs are wide, then |
54,672 | Units for likelihoods and probabilities | Probabilities (also called "probability masses") are unitless, but probability densities have units of 1/(units of the variable).
Let's say we have a probability density $p\left(x\right)$ of some variable $x$. If we integrate this density over some range in $x$, we obtain the probability that $x$ falls in this range:
$... | Units for likelihoods and probabilities | Probabilities (also called "probability masses") are unitless, but probability densities have units of 1/(units of the variable).
Let's say we have a probability density $p\left(x\right)$ of some vari | Units for likelihoods and probabilities
Probabilities (also called "probability masses") are unitless, but probability densities have units of 1/(units of the variable).
Let's say we have a probability density $p\left(x\right)$ of some variable $x$. If we integrate this density over some range in $x$, we obtain the pro... | Units for likelihoods and probabilities
Probabilities (also called "probability masses") are unitless, but probability densities have units of 1/(units of the variable).
Let's say we have a probability density $p\left(x\right)$ of some vari |
54,673 | Interpreting standard error for dummy variables in linear regression models | The underlying math is that the intercept ($\beta_0$) indicates the average salary of men, in \$1000; the parameter $\beta_1$ indicates the difference between the average woman's and average man's salary. So we could say something like "on average, women make \$530 less than men (with a standard error of \$1,776)". Th... | Interpreting standard error for dummy variables in linear regression models | The underlying math is that the intercept ($\beta_0$) indicates the average salary of men, in \$1000; the parameter $\beta_1$ indicates the difference between the average woman's and average man's sal | Interpreting standard error for dummy variables in linear regression models
The underlying math is that the intercept ($\beta_0$) indicates the average salary of men, in \$1000; the parameter $\beta_1$ indicates the difference between the average woman's and average man's salary. So we could say something like "on ave... | Interpreting standard error for dummy variables in linear regression models
The underlying math is that the intercept ($\beta_0$) indicates the average salary of men, in \$1000; the parameter $\beta_1$ indicates the difference between the average woman's and average man's sal |
54,674 | Neural network gives very different accuracies if repeated on same data, why? | It means that the neural network has a high variance. It is prone to overfitting, it sometimes picks the right patterns, sometimes the noise. It can be due to using different training data, random initialization, or both. That is why procedures, as employed by yourself, are useful, if you trained and validated it only ... | Neural network gives very different accuracies if repeated on same data, why? | It means that the neural network has a high variance. It is prone to overfitting, it sometimes picks the right patterns, sometimes the noise. It can be due to using different training data, random ini | Neural network gives very different accuracies if repeated on same data, why?
It means that the neural network has a high variance. It is prone to overfitting, it sometimes picks the right patterns, sometimes the noise. It can be due to using different training data, random initialization, or both. That is why procedur... | Neural network gives very different accuracies if repeated on same data, why?
It means that the neural network has a high variance. It is prone to overfitting, it sometimes picks the right patterns, sometimes the noise. It can be due to using different training data, random ini |
54,675 | How do I best select data for a linear regression? | The question calls for choosing an experimental design and selecting a sample size sufficiently large to estimate the slope $\beta_1$ to within a desired level of precision.
Let $n$ be the number of observations needed and suppose an optimal solution calls for setting the explanatory variable (hydration) to values $x_1... | How do I best select data for a linear regression? | The question calls for choosing an experimental design and selecting a sample size sufficiently large to estimate the slope $\beta_1$ to within a desired level of precision.
Let $n$ be the number of o | How do I best select data for a linear regression?
The question calls for choosing an experimental design and selecting a sample size sufficiently large to estimate the slope $\beta_1$ to within a desired level of precision.
Let $n$ be the number of observations needed and suppose an optimal solution calls for setting ... | How do I best select data for a linear regression?
The question calls for choosing an experimental design and selecting a sample size sufficiently large to estimate the slope $\beta_1$ to within a desired level of precision.
Let $n$ be the number of o |
54,676 | Can I interpret coefficients for "Year" as differences between years that are not explained by my predictors? | Well done. I think your interpretation is OK. Running anova() will give you a more general test for a time trend than how you described it---a test of whether the time trend is flat, i.e., where there is a difference between any pair of years. It would also be useful to examine the difference in $R^2$ due to yearf w... | Can I interpret coefficients for "Year" as differences between years that are not explained by my pr | Well done. I think your interpretation is OK. Running anova() will give you a more general test for a time trend than how you described it---a test of whether the time trend is flat, i.e., where the | Can I interpret coefficients for "Year" as differences between years that are not explained by my predictors?
Well done. I think your interpretation is OK. Running anova() will give you a more general test for a time trend than how you described it---a test of whether the time trend is flat, i.e., where there is a di... | Can I interpret coefficients for "Year" as differences between years that are not explained by my pr
Well done. I think your interpretation is OK. Running anova() will give you a more general test for a time trend than how you described it---a test of whether the time trend is flat, i.e., where the |
54,677 | What are the first four moments of a linear function of IID random variables? | To facilitate this analysis, define the sums $S_{n,r} \equiv \sum_{i=1}^n c_i^r$. Using these quantities the mean, variance, skewness and kurtosis of the quantity $H_n$ can be written as shown in the box below. These formulae are valid for any case where the underlying values are IID with finite kurtosis.
$$\begin{al... | What are the first four moments of a linear function of IID random variables? | To facilitate this analysis, define the sums $S_{n,r} \equiv \sum_{i=1}^n c_i^r$. Using these quantities the mean, variance, skewness and kurtosis of the quantity $H_n$ can be written as shown in the | What are the first four moments of a linear function of IID random variables?
To facilitate this analysis, define the sums $S_{n,r} \equiv \sum_{i=1}^n c_i^r$. Using these quantities the mean, variance, skewness and kurtosis of the quantity $H_n$ can be written as shown in the box below. These formulae are valid for ... | What are the first four moments of a linear function of IID random variables?
To facilitate this analysis, define the sums $S_{n,r} \equiv \sum_{i=1}^n c_i^r$. Using these quantities the mean, variance, skewness and kurtosis of the quantity $H_n$ can be written as shown in the |
54,678 | Linear assumption for logistic regression | One way to write the data generating mechanism for logistic regression is as follows
$$ \mbox{logit}(p) = X\beta $$
$$ y \sim \mbox{Binomial}(n , p) $$
From this formulation, we find that the linearity assumption is made on the log odds scale. So were we to plot the log odds of the outcome versus the predictor, we wou... | Linear assumption for logistic regression | One way to write the data generating mechanism for logistic regression is as follows
$$ \mbox{logit}(p) = X\beta $$
$$ y \sim \mbox{Binomial}(n , p) $$
From this formulation, we find that the linearit | Linear assumption for logistic regression
One way to write the data generating mechanism for logistic regression is as follows
$$ \mbox{logit}(p) = X\beta $$
$$ y \sim \mbox{Binomial}(n , p) $$
From this formulation, we find that the linearity assumption is made on the log odds scale. So were we to plot the log odds o... | Linear assumption for logistic regression
One way to write the data generating mechanism for logistic regression is as follows
$$ \mbox{logit}(p) = X\beta $$
$$ y \sim \mbox{Binomial}(n , p) $$
From this formulation, we find that the linearit |
54,679 | Pair-matched count regression in R with offset? | You should be able to do this with a mixed model with a count response (e.g. Poisson or negative binomial): you want the "standard" count-GLM-with-offset model with random variation in the intercept across IDs:
$$
\begin{split}
\eta_{ij} & = \beta_0 + b_i + \beta_1 E_{ij} + \log(A_{ij}) \\
b_i & \sim N(0, \sigma^2_b) ... | Pair-matched count regression in R with offset? | You should be able to do this with a mixed model with a count response (e.g. Poisson or negative binomial): you want the "standard" count-GLM-with-offset model with random variation in the intercept a | Pair-matched count regression in R with offset?
You should be able to do this with a mixed model with a count response (e.g. Poisson or negative binomial): you want the "standard" count-GLM-with-offset model with random variation in the intercept across IDs:
$$
\begin{split}
\eta_{ij} & = \beta_0 + b_i + \beta_1 E_{ij... | Pair-matched count regression in R with offset?
You should be able to do this with a mixed model with a count response (e.g. Poisson or negative binomial): you want the "standard" count-GLM-with-offset model with random variation in the intercept a |
54,680 | Convergence of sum of normal random variables with variance $\frac{1}{\sqrt{i}}$ | First of all, since the distribution of $X_i$ depends on $i$, the sequence of variables is not IID. Rather, you have independent but not identically distributed random variables. In any case, to look at convergence, let's examine the partial sums:
$$S_n \equiv \sum_{i=1}^n X_i.$$
Since the underlying variables are in... | Convergence of sum of normal random variables with variance $\frac{1}{\sqrt{i}}$ | First of all, since the distribution of $X_i$ depends on $i$, the sequence of variables is not IID. Rather, you have independent but not identically distributed random variables. In any case, to loo | Convergence of sum of normal random variables with variance $\frac{1}{\sqrt{i}}$
First of all, since the distribution of $X_i$ depends on $i$, the sequence of variables is not IID. Rather, you have independent but not identically distributed random variables. In any case, to look at convergence, let's examine the par... | Convergence of sum of normal random variables with variance $\frac{1}{\sqrt{i}}$
First of all, since the distribution of $X_i$ depends on $i$, the sequence of variables is not IID. Rather, you have independent but not identically distributed random variables. In any case, to loo |
54,681 | Which link function in binomial regression is better? | I think it should be a matter of interpretation of model results. The logit link has you modeling the log odds, or equivalently the multiplicative effect in the odds for a one-unit increase in a covariate. The probit link has you modeling the standard normal percentile, or equivalently, the additive effect in the sta... | Which link function in binomial regression is better? | I think it should be a matter of interpretation of model results. The logit link has you modeling the log odds, or equivalently the multiplicative effect in the odds for a one-unit increase in a cova | Which link function in binomial regression is better?
I think it should be a matter of interpretation of model results. The logit link has you modeling the log odds, or equivalently the multiplicative effect in the odds for a one-unit increase in a covariate. The probit link has you modeling the standard normal perce... | Which link function in binomial regression is better?
I think it should be a matter of interpretation of model results. The logit link has you modeling the log odds, or equivalently the multiplicative effect in the odds for a one-unit increase in a cova |
54,682 | Resampling small datasets - Issue of overcounting? | When bootstrapping, we are assuming that the sample is representative of the population.
The whole purpose of bootstrapping is to estimate a sampling distribution and infer the likely standard errors and confidence intervals for the population as a whole.
However, the issue with small sample sizes is that bias is more ... | Resampling small datasets - Issue of overcounting? | When bootstrapping, we are assuming that the sample is representative of the population.
The whole purpose of bootstrapping is to estimate a sampling distribution and infer the likely standard errors | Resampling small datasets - Issue of overcounting?
When bootstrapping, we are assuming that the sample is representative of the population.
The whole purpose of bootstrapping is to estimate a sampling distribution and infer the likely standard errors and confidence intervals for the population as a whole.
However, the ... | Resampling small datasets - Issue of overcounting?
When bootstrapping, we are assuming that the sample is representative of the population.
The whole purpose of bootstrapping is to estimate a sampling distribution and infer the likely standard errors |
54,683 | Resampling small datasets - Issue of overcounting? | The issue with small sample sizes is not that you will repeat bootstrap samples but that the original small sample might not be so representative of the population.
Let’s obtain a sample of coin flips from a fair coin, so the true population is $Binom(1, 0.5)$, and let’s use your small sample size of $n=5$. In R…
set.s... | Resampling small datasets - Issue of overcounting? | The issue with small sample sizes is not that you will repeat bootstrap samples but that the original small sample might not be so representative of the population.
Let’s obtain a sample of coin flips | Resampling small datasets - Issue of overcounting?
The issue with small sample sizes is not that you will repeat bootstrap samples but that the original small sample might not be so representative of the population.
Let’s obtain a sample of coin flips from a fair coin, so the true population is $Binom(1, 0.5)$, and let... | Resampling small datasets - Issue of overcounting?
The issue with small sample sizes is not that you will repeat bootstrap samples but that the original small sample might not be so representative of the population.
Let’s obtain a sample of coin flips |
54,684 | Resampling small datasets - Issue of overcounting? | Many bootstrap replications are drawn in order to approximate (in a standard situation) the distribution of i.i.d. samples from the empirical distribution. Now if you can get this distribution explicitly, which is possible with a small sample as you can list all possible samples and their probabilities, it isn't necess... | Resampling small datasets - Issue of overcounting? | Many bootstrap replications are drawn in order to approximate (in a standard situation) the distribution of i.i.d. samples from the empirical distribution. Now if you can get this distribution explici | Resampling small datasets - Issue of overcounting?
Many bootstrap replications are drawn in order to approximate (in a standard situation) the distribution of i.i.d. samples from the empirical distribution. Now if you can get this distribution explicitly, which is possible with a small sample as you can list all possib... | Resampling small datasets - Issue of overcounting?
Many bootstrap replications are drawn in order to approximate (in a standard situation) the distribution of i.i.d. samples from the empirical distribution. Now if you can get this distribution explici |
54,685 | Is my understanding of the Metropolis sampling algorithm correct? | This is a correct description of the (symmetric) Metropolis-[Rosenbluth²]-Hastings algorithm, but the motivation is not:
(i) ignoring the normalising constant $Z_p$ is common to a lot of simulation techniques, like accept-reject methods. The normalising constant is useful when computing the cdf and using the inverse cd... | Is my understanding of the Metropolis sampling algorithm correct? | This is a correct description of the (symmetric) Metropolis-[Rosenbluth²]-Hastings algorithm, but the motivation is not:
(i) ignoring the normalising constant $Z_p$ is common to a lot of simulation te | Is my understanding of the Metropolis sampling algorithm correct?
This is a correct description of the (symmetric) Metropolis-[Rosenbluth²]-Hastings algorithm, but the motivation is not:
(i) ignoring the normalising constant $Z_p$ is common to a lot of simulation techniques, like accept-reject methods. The normalising ... | Is my understanding of the Metropolis sampling algorithm correct?
This is a correct description of the (symmetric) Metropolis-[Rosenbluth²]-Hastings algorithm, but the motivation is not:
(i) ignoring the normalising constant $Z_p$ is common to a lot of simulation te |
54,686 | Finding a Common Thread in Disparate Indicators | Have you considered the bifactor measurement model? From what I can glean from your question, it looks as though you are interested in a single social norms dimension with an item bank that could reasonably be used to measure very different dimensions (e.g., alcohol abuse). If I am correct, the bifactor model may be th... | Finding a Common Thread in Disparate Indicators | Have you considered the bifactor measurement model? From what I can glean from your question, it looks as though you are interested in a single social norms dimension with an item bank that could reas | Finding a Common Thread in Disparate Indicators
Have you considered the bifactor measurement model? From what I can glean from your question, it looks as though you are interested in a single social norms dimension with an item bank that could reasonably be used to measure very different dimensions (e.g., alcohol abuse... | Finding a Common Thread in Disparate Indicators
Have you considered the bifactor measurement model? From what I can glean from your question, it looks as though you are interested in a single social norms dimension with an item bank that could reas |
54,687 | Finding a Common Thread in Disparate Indicators | This adds a bit more to Preston's answer. I approve of the Reise citation.
However, I'd urge you to consider how closely related the traits you're trying to measure are.
He has a whole range of disparate measures of acting-under-social-norms (from alcohol abuse, to registering with a doctor, etc). We don't want to spl... | Finding a Common Thread in Disparate Indicators | This adds a bit more to Preston's answer. I approve of the Reise citation.
However, I'd urge you to consider how closely related the traits you're trying to measure are.
He has a whole range of dispa | Finding a Common Thread in Disparate Indicators
This adds a bit more to Preston's answer. I approve of the Reise citation.
However, I'd urge you to consider how closely related the traits you're trying to measure are.
He has a whole range of disparate measures of acting-under-social-norms (from alcohol abuse, to regis... | Finding a Common Thread in Disparate Indicators
This adds a bit more to Preston's answer. I approve of the Reise citation.
However, I'd urge you to consider how closely related the traits you're trying to measure are.
He has a whole range of dispa |
54,688 | Why do you need non-linear regression if you can use a linear one to fit any kind of curvature to your data? | Model Parsimony
If you have a sine curve, you can approximate it to arbitrary accuracy with its series expansion.
I’d probably rather estimate the two parameters of $\mathbb E[y]= A\sin(Bx)$ than the many parameters in a long series expansion.
Note that, because the $B$ is inside the nonlinear sine function, you canno... | Why do you need non-linear regression if you can use a linear one to fit any kind of curvature to yo | Model Parsimony
If you have a sine curve, you can approximate it to arbitrary accuracy with its series expansion.
I’d probably rather estimate the two parameters of $\mathbb E[y]= A\sin(Bx)$ than the | Why do you need non-linear regression if you can use a linear one to fit any kind of curvature to your data?
Model Parsimony
If you have a sine curve, you can approximate it to arbitrary accuracy with its series expansion.
I’d probably rather estimate the two parameters of $\mathbb E[y]= A\sin(Bx)$ than the many param... | Why do you need non-linear regression if you can use a linear one to fit any kind of curvature to yo
Model Parsimony
If you have a sine curve, you can approximate it to arbitrary accuracy with its series expansion.
I’d probably rather estimate the two parameters of $\mathbb E[y]= A\sin(Bx)$ than the |
54,689 | CDF of Dirichlet Distribution | The Dirichlet distribution is either defined on the simplex of $\mathbb R^k$,
$$\mathcal S_{k-1}=\big\{\mathbf x;\ x_i\in (0,1),~i=1,2,\ldots,k,~\sum_{i=1}^k x_i=1\big\}$$
in which case the density
$$f(\mathbf x) = \frac{1}{B(\textbf{a})}\prod_{i=1}^{k}x_{i}^{a_{i}-1}$$
is with respect to the Lebesgue distribution over... | CDF of Dirichlet Distribution | The Dirichlet distribution is either defined on the simplex of $\mathbb R^k$,
$$\mathcal S_{k-1}=\big\{\mathbf x;\ x_i\in (0,1),~i=1,2,\ldots,k,~\sum_{i=1}^k x_i=1\big\}$$
in which case the density
$$ | CDF of Dirichlet Distribution
The Dirichlet distribution is either defined on the simplex of $\mathbb R^k$,
$$\mathcal S_{k-1}=\big\{\mathbf x;\ x_i\in (0,1),~i=1,2,\ldots,k,~\sum_{i=1}^k x_i=1\big\}$$
in which case the density
$$f(\mathbf x) = \frac{1}{B(\textbf{a})}\prod_{i=1}^{k}x_{i}^{a_{i}-1}$$
is with respect to ... | CDF of Dirichlet Distribution
The Dirichlet distribution is either defined on the simplex of $\mathbb R^k$,
$$\mathcal S_{k-1}=\big\{\mathbf x;\ x_i\in (0,1),~i=1,2,\ldots,k,~\sum_{i=1}^k x_i=1\big\}$$
in which case the density
$$ |
54,690 | Why do we apply the sample mean version of the CLT for a problem involving a sample size of 1? | This is an example of a poorly worded question. If one were to interpret it strictly as written, one has a sample size of $n=500$ and a population size of $N=500$, so yes, the population mean is certain to be \$750 (and so the probability that this mean is greater than \$755 is known to be zero). If you were to give ... | Why do we apply the sample mean version of the CLT for a problem involving a sample size of 1? | This is an example of a poorly worded question. If one were to interpret it strictly as written, one has a sample size of $n=500$ and a population size of $N=500$, so yes, the population mean is cert | Why do we apply the sample mean version of the CLT for a problem involving a sample size of 1?
This is an example of a poorly worded question. If one were to interpret it strictly as written, one has a sample size of $n=500$ and a population size of $N=500$, so yes, the population mean is certain to be \$750 (and so t... | Why do we apply the sample mean version of the CLT for a problem involving a sample size of 1?
This is an example of a poorly worded question. If one were to interpret it strictly as written, one has a sample size of $n=500$ and a population size of $N=500$, so yes, the population mean is cert |
54,691 | Why do we apply the sample mean version of the CLT for a problem involving a sample size of 1? | The first Comment of @COOLSerdash is correct. The wording of the problem is somewhat confusing.
Moreover, the choice of numbers leads to a z-value that needs to be rounded for use of a printed table, thus we get a noticeable rounding error in the posted answer.
You have $\bar X =\bar X_{500} \sim\mathsf{Norm}(\mu=750, ... | Why do we apply the sample mean version of the CLT for a problem involving a sample size of 1? | The first Comment of @COOLSerdash is correct. The wording of the problem is somewhat confusing.
Moreover, the choice of numbers leads to a z-value that needs to be rounded for use of a printed table, | Why do we apply the sample mean version of the CLT for a problem involving a sample size of 1?
The first Comment of @COOLSerdash is correct. The wording of the problem is somewhat confusing.
Moreover, the choice of numbers leads to a z-value that needs to be rounded for use of a printed table, thus we get a noticeable ... | Why do we apply the sample mean version of the CLT for a problem involving a sample size of 1?
The first Comment of @COOLSerdash is correct. The wording of the problem is somewhat confusing.
Moreover, the choice of numbers leads to a z-value that needs to be rounded for use of a printed table, |
54,692 | After "Statistics" by Freedman, Pisani, and Purves what book is good for ANOVA? | ANOVA is a method that arises within the context of regression models, so I recommend you read some books on regression modelling (see related answer here). It is difficult to recommend a specific book without more knowledge of your strengths and weaknesses, but you should be able to find a book or notes that derive l... | After "Statistics" by Freedman, Pisani, and Purves what book is good for ANOVA? | ANOVA is a method that arises within the context of regression models, so I recommend you read some books on regression modelling (see related answer here). It is difficult to recommend a specific bo | After "Statistics" by Freedman, Pisani, and Purves what book is good for ANOVA?
ANOVA is a method that arises within the context of regression models, so I recommend you read some books on regression modelling (see related answer here). It is difficult to recommend a specific book without more knowledge of your streng... | After "Statistics" by Freedman, Pisani, and Purves what book is good for ANOVA?
ANOVA is a method that arises within the context of regression models, so I recommend you read some books on regression modelling (see related answer here). It is difficult to recommend a specific bo |
54,693 | After "Statistics" by Freedman, Pisani, and Purves what book is good for ANOVA? | If you want more of a softer, practioner approach to the topic, I would encourage looking at the appropriate chapter within a book on DOE. Box, Hunter, Hunter is the classic reference (78 edition best). A shorter, but serviceable book is Barker Quality by Experimental Design. Both of these books have a lot of non-AN... | After "Statistics" by Freedman, Pisani, and Purves what book is good for ANOVA? | If you want more of a softer, practioner approach to the topic, I would encourage looking at the appropriate chapter within a book on DOE. Box, Hunter, Hunter is the classic reference (78 edition bes | After "Statistics" by Freedman, Pisani, and Purves what book is good for ANOVA?
If you want more of a softer, practioner approach to the topic, I would encourage looking at the appropriate chapter within a book on DOE. Box, Hunter, Hunter is the classic reference (78 edition best). A shorter, but serviceable book is ... | After "Statistics" by Freedman, Pisani, and Purves what book is good for ANOVA?
If you want more of a softer, practioner approach to the topic, I would encourage looking at the appropriate chapter within a book on DOE. Box, Hunter, Hunter is the classic reference (78 edition bes |
54,694 | 'Aspect ratio' as a measure of the 'tall-and-skinny' property of unimodal distributions | You already got my +1 for drawing attention to Westfall (2014). A few thoughts:
Unimodality is of course important, and also quite a restriction. If you have multiple peaks, then all kinds of strange things can happen. And if you don't have a peak at all (e.g., a gamma distribution with shape $k<1$), then your $f_{\tex... | 'Aspect ratio' as a measure of the 'tall-and-skinny' property of unimodal distributions | You already got my +1 for drawing attention to Westfall (2014). A few thoughts:
Unimodality is of course important, and also quite a restriction. If you have multiple peaks, then all kinds of strange | 'Aspect ratio' as a measure of the 'tall-and-skinny' property of unimodal distributions
You already got my +1 for drawing attention to Westfall (2014). A few thoughts:
Unimodality is of course important, and also quite a restriction. If you have multiple peaks, then all kinds of strange things can happen. And if you do... | 'Aspect ratio' as a measure of the 'tall-and-skinny' property of unimodal distributions
You already got my +1 for drawing attention to Westfall (2014). A few thoughts:
Unimodality is of course important, and also quite a restriction. If you have multiple peaks, then all kinds of strange |
54,695 | 'Aspect ratio' as a measure of the 'tall-and-skinny' property of unimodal distributions | Before you get to the other drawbacks of your measure, the first thing to note is that you appear to be comparing apples and oranges. The idea of using kurtosis as a measure of "peakedness" of a distribution (as flawed as that is) is that it is a measure that adjusts for variance, so the "peakedness" looks at the shap... | 'Aspect ratio' as a measure of the 'tall-and-skinny' property of unimodal distributions | Before you get to the other drawbacks of your measure, the first thing to note is that you appear to be comparing apples and oranges. The idea of using kurtosis as a measure of "peakedness" of a dist | 'Aspect ratio' as a measure of the 'tall-and-skinny' property of unimodal distributions
Before you get to the other drawbacks of your measure, the first thing to note is that you appear to be comparing apples and oranges. The idea of using kurtosis as a measure of "peakedness" of a distribution (as flawed as that is) ... | 'Aspect ratio' as a measure of the 'tall-and-skinny' property of unimodal distributions
Before you get to the other drawbacks of your measure, the first thing to note is that you appear to be comparing apples and oranges. The idea of using kurtosis as a measure of "peakedness" of a dist |
54,696 | Emperically testing a "p-test" (of multiple fair coin flips) | In general, there is no such binomial test with
significance level exactly $\alpha = 0.05,$ on
account of the discreteness of binomial distributions.
For an exact test at $\alpha = 0.05$ based on a continuous test statistic,
the distribution of P-value when $H_0$ is true would be
standard uniform and the probability th... | Emperically testing a "p-test" (of multiple fair coin flips) | In general, there is no such binomial test with
significance level exactly $\alpha = 0.05,$ on
account of the discreteness of binomial distributions.
For an exact test at $\alpha = 0.05$ based on a co | Emperically testing a "p-test" (of multiple fair coin flips)
In general, there is no such binomial test with
significance level exactly $\alpha = 0.05,$ on
account of the discreteness of binomial distributions.
For an exact test at $\alpha = 0.05$ based on a continuous test statistic,
the distribution of P-value when $... | Emperically testing a "p-test" (of multiple fair coin flips)
In general, there is no such binomial test with
significance level exactly $\alpha = 0.05,$ on
account of the discreteness of binomial distributions.
For an exact test at $\alpha = 0.05$ based on a co |
54,697 | Emperically testing a "p-test" (of multiple fair coin flips) | It is (nearly) impossible for a test statistic that has a discrete distribution to attain exactly a 5% (or any other) significance level. So instead, many so-called "exact" tests use the largest attainable significance level that is less than $\alpha$ (or 5% in your case). That is what you are seeing.
Here is a refere... | Emperically testing a "p-test" (of multiple fair coin flips) | It is (nearly) impossible for a test statistic that has a discrete distribution to attain exactly a 5% (or any other) significance level. So instead, many so-called "exact" tests use the largest attai | Emperically testing a "p-test" (of multiple fair coin flips)
It is (nearly) impossible for a test statistic that has a discrete distribution to attain exactly a 5% (or any other) significance level. So instead, many so-called "exact" tests use the largest attainable significance level that is less than $\alpha$ (or 5% ... | Emperically testing a "p-test" (of multiple fair coin flips)
It is (nearly) impossible for a test statistic that has a discrete distribution to attain exactly a 5% (or any other) significance level. So instead, many so-called "exact" tests use the largest attai |
54,698 | The prior odds were a hundred-to-one against Voldemort surviving. What is the probability of Voldemort being alive? | CORRECTION: The old solution i gave is assuming that the prior odds were referring to the conditional probability of knowing the mark exists and you are calculating the overall probability of being alive. However if that is not the case and $p(A) = \frac{1}{101}$ then you can use:
$$p(A|M) = \frac{p(M|A)\times p(A)}{p(... | The prior odds were a hundred-to-one against Voldemort surviving. What is the probability of Voldemo | CORRECTION: The old solution i gave is assuming that the prior odds were referring to the conditional probability of knowing the mark exists and you are calculating the overall probability of being al | The prior odds were a hundred-to-one against Voldemort surviving. What is the probability of Voldemort being alive?
CORRECTION: The old solution i gave is assuming that the prior odds were referring to the conditional probability of knowing the mark exists and you are calculating the overall probability of being alive.... | The prior odds were a hundred-to-one against Voldemort surviving. What is the probability of Voldemo
CORRECTION: The old solution i gave is assuming that the prior odds were referring to the conditional probability of knowing the mark exists and you are calculating the overall probability of being al |
54,699 | The prior odds were a hundred-to-one against Voldemort surviving. What is the probability of Voldemort being alive? | Studies have shown that people deal with proportions better than probabilities. Rewrite the question as
There 3030 fanfics. There are 100 times as many fanfics where Voldemort died as fanfics where Voldermort lived. In 100% of fanfics where Voldemort lived, the mark remained. In 20% of fanfics where Voldemort died, th... | The prior odds were a hundred-to-one against Voldemort surviving. What is the probability of Voldemo | Studies have shown that people deal with proportions better than probabilities. Rewrite the question as
There 3030 fanfics. There are 100 times as many fanfics where Voldemort died as fanfics where V | The prior odds were a hundred-to-one against Voldemort surviving. What is the probability of Voldemort being alive?
Studies have shown that people deal with proportions better than probabilities. Rewrite the question as
There 3030 fanfics. There are 100 times as many fanfics where Voldemort died as fanfics where Volde... | The prior odds were a hundred-to-one against Voldemort surviving. What is the probability of Voldemo
Studies have shown that people deal with proportions better than probabilities. Rewrite the question as
There 3030 fanfics. There are 100 times as many fanfics where Voldemort died as fanfics where V |
54,700 | Interpretation difference between log link and log transformation | Those models are similar, but the key different thing is we model $\log{E(Y)}$ for GLM and $E(\log Y)$ for LM. Thus, we can estimate $Y$ directly in GLM and $\log Y$ in LM.
GLM: We can directly say $E(Y)=\exp(\beta_0+\beta_1X)$. In this case, $\beta_1$ catches the effect of a unite change in $X$ on $Y$ (acutually, log ... | Interpretation difference between log link and log transformation | Those models are similar, but the key different thing is we model $\log{E(Y)}$ for GLM and $E(\log Y)$ for LM. Thus, we can estimate $Y$ directly in GLM and $\log Y$ in LM.
GLM: We can directly say $E | Interpretation difference between log link and log transformation
Those models are similar, but the key different thing is we model $\log{E(Y)}$ for GLM and $E(\log Y)$ for LM. Thus, we can estimate $Y$ directly in GLM and $\log Y$ in LM.
GLM: We can directly say $E(Y)=\exp(\beta_0+\beta_1X)$. In this case, $\beta_1$ c... | Interpretation difference between log link and log transformation
Those models are similar, but the key different thing is we model $\log{E(Y)}$ for GLM and $E(\log Y)$ for LM. Thus, we can estimate $Y$ directly in GLM and $\log Y$ in LM.
GLM: We can directly say $E |
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