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 |
|---|---|---|---|---|---|---|
44,401 | Solving a practical machine learning problem | I have seen statements like "We pick representative samples...". This
is an absurd statement...
I agree with you on this. And I don't think representative sampling is what they do (anymore). My understanding is that they analyse big data with distributed computing, using technology like Hadoop, Spark, and MLLib. I a... | Solving a practical machine learning problem | I have seen statements like "We pick representative samples...". This
is an absurd statement...
I agree with you on this. And I don't think representative sampling is what they do (anymore). My und | Solving a practical machine learning problem
I have seen statements like "We pick representative samples...". This
is an absurd statement...
I agree with you on this. And I don't think representative sampling is what they do (anymore). My understanding is that they analyse big data with distributed computing, using ... | Solving a practical machine learning problem
I have seen statements like "We pick representative samples...". This
is an absurd statement...
I agree with you on this. And I don't think representative sampling is what they do (anymore). My und |
44,402 | Solving a practical machine learning problem | Beyond subsampling and divide-and-conquer distributed computing, both important and useful, there are many other ways of solving such problems. To name just a couple, parallel coordinate descent (iterate on each variable independently, combine solutions later), and online methods, like stochastic gradient descent (SGD)... | Solving a practical machine learning problem | Beyond subsampling and divide-and-conquer distributed computing, both important and useful, there are many other ways of solving such problems. To name just a couple, parallel coordinate descent (iter | Solving a practical machine learning problem
Beyond subsampling and divide-and-conquer distributed computing, both important and useful, there are many other ways of solving such problems. To name just a couple, parallel coordinate descent (iterate on each variable independently, combine solutions later), and online me... | Solving a practical machine learning problem
Beyond subsampling and divide-and-conquer distributed computing, both important and useful, there are many other ways of solving such problems. To name just a couple, parallel coordinate descent (iter |
44,403 | Solving a practical machine learning problem | Massively parallel matrix inversion is actually doable with open source software such as MUMPS, although I'm not sure how it would scale to 10bio rows. It's used for large scale finite elements in automotive so it's industrial strength for sure.
As for the class of algorithms used, it's a multifrontal approach (divide ... | Solving a practical machine learning problem | Massively parallel matrix inversion is actually doable with open source software such as MUMPS, although I'm not sure how it would scale to 10bio rows. It's used for large scale finite elements in aut | Solving a practical machine learning problem
Massively parallel matrix inversion is actually doable with open source software such as MUMPS, although I'm not sure how it would scale to 10bio rows. It's used for large scale finite elements in automotive so it's industrial strength for sure.
As for the class of algorithm... | Solving a practical machine learning problem
Massively parallel matrix inversion is actually doable with open source software such as MUMPS, although I'm not sure how it would scale to 10bio rows. It's used for large scale finite elements in aut |
44,404 | Solving a practical machine learning problem | Thank you all for your comments. Turns out Apache spark does L1 penalized regressions. I found links to training videos here which some of you may find helpful.
Turns out the folk at Google who seriously studied this problem and founded the Map-Reduce architecture were Jeff Dean and Sanjay Ghemawat, both of whom have ... | Solving a practical machine learning problem | Thank you all for your comments. Turns out Apache spark does L1 penalized regressions. I found links to training videos here which some of you may find helpful.
Turns out the folk at Google who serio | Solving a practical machine learning problem
Thank you all for your comments. Turns out Apache spark does L1 penalized regressions. I found links to training videos here which some of you may find helpful.
Turns out the folk at Google who seriously studied this problem and founded the Map-Reduce architecture were Jeff... | Solving a practical machine learning problem
Thank you all for your comments. Turns out Apache spark does L1 penalized regressions. I found links to training videos here which some of you may find helpful.
Turns out the folk at Google who serio |
44,405 | What to claim when we don't reject the null hypothesis? [duplicate] | "We fail to reject the null" is the correct answer. Rather than say, for example, "there is no difference" we should write "no difference was detected".
Clearly, with not enough replicates or large measurement error you are likely to not be able to detect even large effects. So maybe the difference is there, but you fa... | What to claim when we don't reject the null hypothesis? [duplicate] | "We fail to reject the null" is the correct answer. Rather than say, for example, "there is no difference" we should write "no difference was detected".
Clearly, with not enough replicates or large me | What to claim when we don't reject the null hypothesis? [duplicate]
"We fail to reject the null" is the correct answer. Rather than say, for example, "there is no difference" we should write "no difference was detected".
Clearly, with not enough replicates or large measurement error you are likely to not be able to det... | What to claim when we don't reject the null hypothesis? [duplicate]
"We fail to reject the null" is the correct answer. Rather than say, for example, "there is no difference" we should write "no difference was detected".
Clearly, with not enough replicates or large me |
44,406 | What to claim when we don't reject the null hypothesis? [duplicate] | I would include three things:
The phrase "Insufficient evidence to reject". Shows that with more evidence, e.g. more data, or repeating the experiment with a different random selection of data, you might have rejected.
The significance level. At a higher significance level you might have rejected the null hypothesis.
... | What to claim when we don't reject the null hypothesis? [duplicate] | I would include three things:
The phrase "Insufficient evidence to reject". Shows that with more evidence, e.g. more data, or repeating the experiment with a different random selection of data, you m | What to claim when we don't reject the null hypothesis? [duplicate]
I would include three things:
The phrase "Insufficient evidence to reject". Shows that with more evidence, e.g. more data, or repeating the experiment with a different random selection of data, you might have rejected.
The significance level. At a hig... | What to claim when we don't reject the null hypothesis? [duplicate]
I would include three things:
The phrase "Insufficient evidence to reject". Shows that with more evidence, e.g. more data, or repeating the experiment with a different random selection of data, you m |
44,407 | Do I have to learn SAS if I want to go into industry? | you have to figure what is that you're interested in:
programming statistics in R
programming statistics
statistics
programming
If your answer is 2-4, then it shouldn't matter which language you use. if you already know R and don't want to learn SAS, then get certified in SAS. this will increase your chances of get... | Do I have to learn SAS if I want to go into industry? | you have to figure what is that you're interested in:
programming statistics in R
programming statistics
statistics
programming
If your answer is 2-4, then it shouldn't matter which language you u | Do I have to learn SAS if I want to go into industry?
you have to figure what is that you're interested in:
programming statistics in R
programming statistics
statistics
programming
If your answer is 2-4, then it shouldn't matter which language you use. if you already know R and don't want to learn SAS, then get ce... | Do I have to learn SAS if I want to go into industry?
you have to figure what is that you're interested in:
programming statistics in R
programming statistics
statistics
programming
If your answer is 2-4, then it shouldn't matter which language you u |
44,408 | Do I have to learn SAS if I want to go into industry? | SAS is extremely expensive as an enterprise wide solution. It is used by some large organisations specially in banking and insurance. Many companies today are taking a different approach, looking for less expensive and scalable solutions. Open source is getting a lot of traction even in large organisations.
I would sta... | Do I have to learn SAS if I want to go into industry? | SAS is extremely expensive as an enterprise wide solution. It is used by some large organisations specially in banking and insurance. Many companies today are taking a different approach, looking for | Do I have to learn SAS if I want to go into industry?
SAS is extremely expensive as an enterprise wide solution. It is used by some large organisations specially in banking and insurance. Many companies today are taking a different approach, looking for less expensive and scalable solutions. Open source is getting a lo... | Do I have to learn SAS if I want to go into industry?
SAS is extremely expensive as an enterprise wide solution. It is used by some large organisations specially in banking and insurance. Many companies today are taking a different approach, looking for |
44,409 | Intuition for consequences of multicollinearity | Let us first distinguish between perfect multi-collinearity (model matrix not of full rank, so that usual matrix inversions fail. Usually due to misspecification of the predictors) and non-perfect multi-collinearity (some of the predictors are correlated without leading to computational problems). This answer is about ... | Intuition for consequences of multicollinearity | Let us first distinguish between perfect multi-collinearity (model matrix not of full rank, so that usual matrix inversions fail. Usually due to misspecification of the predictors) and non-perfect mul | Intuition for consequences of multicollinearity
Let us first distinguish between perfect multi-collinearity (model matrix not of full rank, so that usual matrix inversions fail. Usually due to misspecification of the predictors) and non-perfect multi-collinearity (some of the predictors are correlated without leading t... | Intuition for consequences of multicollinearity
Let us first distinguish between perfect multi-collinearity (model matrix not of full rank, so that usual matrix inversions fail. Usually due to misspecification of the predictors) and non-perfect mul |
44,410 | Intuition for consequences of multicollinearity | Another problem, in addition to those @Michael gave, is that when there is strong near-colinearity, small changes in the input data can lead to large changes in the output.
I made up some data (taking wild guesses at the average lengths of legs and torso (in inches) and weight (in pounds) for adult humans).
set.seed(1... | Intuition for consequences of multicollinearity | Another problem, in addition to those @Michael gave, is that when there is strong near-colinearity, small changes in the input data can lead to large changes in the output.
I made up some data (takin | Intuition for consequences of multicollinearity
Another problem, in addition to those @Michael gave, is that when there is strong near-colinearity, small changes in the input data can lead to large changes in the output.
I made up some data (taking wild guesses at the average lengths of legs and torso (in inches) and ... | Intuition for consequences of multicollinearity
Another problem, in addition to those @Michael gave, is that when there is strong near-colinearity, small changes in the input data can lead to large changes in the output.
I made up some data (takin |
44,411 | Learning probability bad reasoning. Conditional and unconditional | For (a), a simple way to look at is that you've reduced your probability space to only the combinations that have at least one boy:
BB = 1/3
BG = 1/3
GB = 1/3
GG is no longer a possibility based on the fact that your neighbor said he had at least one boy. Of the possibilities remaining, you're left with a 2/3 probabi... | Learning probability bad reasoning. Conditional and unconditional | For (a), a simple way to look at is that you've reduced your probability space to only the combinations that have at least one boy:
BB = 1/3
BG = 1/3
GB = 1/3
GG is no longer a possibility based on t | Learning probability bad reasoning. Conditional and unconditional
For (a), a simple way to look at is that you've reduced your probability space to only the combinations that have at least one boy:
BB = 1/3
BG = 1/3
GB = 1/3
GG is no longer a possibility based on the fact that your neighbor said he had at least one bo... | Learning probability bad reasoning. Conditional and unconditional
For (a), a simple way to look at is that you've reduced your probability space to only the combinations that have at least one boy:
BB = 1/3
BG = 1/3
GB = 1/3
GG is no longer a possibility based on t |
44,412 | Learning probability bad reasoning. Conditional and unconditional | Another way to show this (part a ) is to write the Bayes rule as follows:
P(B|G) = P(G)P(B|G) / P(~G)P(B|~G) + P(G)P(B|G)
= (0.5 * 0.5) / (0.5*0.25 + 0.5*0.5) = 2/3 | Learning probability bad reasoning. Conditional and unconditional | Another way to show this (part a ) is to write the Bayes rule as follows:
P(B|G) = P(G)P(B|G) / P(~G)P(B|~G) + P(G)P(B|G)
= (0.5 * 0.5) / (0.5*0.25 + 0.5*0.5) = 2/3 | Learning probability bad reasoning. Conditional and unconditional
Another way to show this (part a ) is to write the Bayes rule as follows:
P(B|G) = P(G)P(B|G) / P(~G)P(B|~G) + P(G)P(B|G)
= (0.5 * 0.5) / (0.5*0.25 + 0.5*0.5) = 2/3 | Learning probability bad reasoning. Conditional and unconditional
Another way to show this (part a ) is to write the Bayes rule as follows:
P(B|G) = P(G)P(B|G) / P(~G)P(B|~G) + P(G)P(B|G)
= (0.5 * 0.5) / (0.5*0.25 + 0.5*0.5) = 2/3 |
44,413 | Questions on standard deviation of a time series | Thirty years ago, John Emerson provided a simple explanation of an extremely useful generalization of this phenomenon. Here is the essence of it.
Suppose you have batches of data (which could include a set of windows across a time series, for instance) and you summarize each with some measure of its "level" (a mean or... | Questions on standard deviation of a time series | Thirty years ago, John Emerson provided a simple explanation of an extremely useful generalization of this phenomenon. Here is the essence of it.
Suppose you have batches of data (which could include | Questions on standard deviation of a time series
Thirty years ago, John Emerson provided a simple explanation of an extremely useful generalization of this phenomenon. Here is the essence of it.
Suppose you have batches of data (which could include a set of windows across a time series, for instance) and you summarize... | Questions on standard deviation of a time series
Thirty years ago, John Emerson provided a simple explanation of an extremely useful generalization of this phenomenon. Here is the essence of it.
Suppose you have batches of data (which could include |
44,414 | Questions on standard deviation of a time series | Level here is to be understood as mean.
This is an approximation at best, but it does not depend on data being a time series, let alone economic data!
For a fairly detailed discussion in a wider setting, see
J.H. Curtiss. 1943.
On transformations used in the analysis of variance.
Annals of Mathematical Statistics 14: 1... | Questions on standard deviation of a time series | Level here is to be understood as mean.
This is an approximation at best, but it does not depend on data being a time series, let alone economic data!
For a fairly detailed discussion in a wider setti | Questions on standard deviation of a time series
Level here is to be understood as mean.
This is an approximation at best, but it does not depend on data being a time series, let alone economic data!
For a fairly detailed discussion in a wider setting, see
J.H. Curtiss. 1943.
On transformations used in the analysis of ... | Questions on standard deviation of a time series
Level here is to be understood as mean.
This is an approximation at best, but it does not depend on data being a time series, let alone economic data!
For a fairly detailed discussion in a wider setti |
44,415 | Questions on standard deviation of a time series | We can view the time series as a realization of a sequence of random variables $Y_t$, where $Y_t$ has expected value $X_t$ (the level) and, in the case you describe, standard deviation proportional to $X_t$ - let's say it is $c X_t$ for some constant $c$. So for a fixed value of $t$, we can view $X_t$ as a constant and... | Questions on standard deviation of a time series | We can view the time series as a realization of a sequence of random variables $Y_t$, where $Y_t$ has expected value $X_t$ (the level) and, in the case you describe, standard deviation proportional to | Questions on standard deviation of a time series
We can view the time series as a realization of a sequence of random variables $Y_t$, where $Y_t$ has expected value $X_t$ (the level) and, in the case you describe, standard deviation proportional to $X_t$ - let's say it is $c X_t$ for some constant $c$. So for a fixed ... | Questions on standard deviation of a time series
We can view the time series as a realization of a sequence of random variables $Y_t$, where $Y_t$ has expected value $X_t$ (the level) and, in the case you describe, standard deviation proportional to |
44,416 | Which model should I use to fit my data ? ordinal and non-ordinal, not normal and not homoscedastic | Here is an example using the R rms package orm function. The three variables are defined in the original question above. First we see which of 3 families yields the most parallelism.
require(rms)
row <- 0
for(gvar in list(pred_1, pred_2)) {
row <- row + 1; col <- 0
for(fun in list(qlogis, qnorm, function(y) -log(... | Which model should I use to fit my data ? ordinal and non-ordinal, not normal and not homoscedastic | Here is an example using the R rms package orm function. The three variables are defined in the original question above. First we see which of 3 families yields the most parallelism.
require(rms)
ro | Which model should I use to fit my data ? ordinal and non-ordinal, not normal and not homoscedastic
Here is an example using the R rms package orm function. The three variables are defined in the original question above. First we see which of 3 families yields the most parallelism.
require(rms)
row <- 0
for(gvar in l... | Which model should I use to fit my data ? ordinal and non-ordinal, not normal and not homoscedastic
Here is an example using the R rms package orm function. The three variables are defined in the original question above. First we see which of 3 families yields the most parallelism.
require(rms)
ro |
44,417 | Which model should I use to fit my data ? ordinal and non-ordinal, not normal and not homoscedastic | For regular (OLS) regression your response variable does not have to be normally distributed. The model assumes that the residuals from your model are normally distributed. You can first run regular regression and check the residuals, e.g.
m1 <- lm(resp~pred1 + pred2)
plot(m1)
This might be "good enough" but technical... | Which model should I use to fit my data ? ordinal and non-ordinal, not normal and not homoscedastic | For regular (OLS) regression your response variable does not have to be normally distributed. The model assumes that the residuals from your model are normally distributed. You can first run regular r | Which model should I use to fit my data ? ordinal and non-ordinal, not normal and not homoscedastic
For regular (OLS) regression your response variable does not have to be normally distributed. The model assumes that the residuals from your model are normally distributed. You can first run regular regression and check ... | Which model should I use to fit my data ? ordinal and non-ordinal, not normal and not homoscedastic
For regular (OLS) regression your response variable does not have to be normally distributed. The model assumes that the residuals from your model are normally distributed. You can first run regular r |
44,418 | Alternative to Kolmogorov-Smirnov test when parameters are estimated from the data | One option is to still use the KS test statistic, but instead of using the standard p-value from the KS test (which as you say is not appropriate when estimating from the data), calculate the p-value using a permutation test. The basic steps would be:
Calculate the KS test statistic for the data as is (divided by the ... | Alternative to Kolmogorov-Smirnov test when parameters are estimated from the data | One option is to still use the KS test statistic, but instead of using the standard p-value from the KS test (which as you say is not appropriate when estimating from the data), calculate the p-value | Alternative to Kolmogorov-Smirnov test when parameters are estimated from the data
One option is to still use the KS test statistic, but instead of using the standard p-value from the KS test (which as you say is not appropriate when estimating from the data), calculate the p-value using a permutation test. The basic ... | Alternative to Kolmogorov-Smirnov test when parameters are estimated from the data
One option is to still use the KS test statistic, but instead of using the standard p-value from the KS test (which as you say is not appropriate when estimating from the data), calculate the p-value |
44,419 | Alternative to Kolmogorov-Smirnov test when parameters are estimated from the data | I can't make much sense of the question on any level. The detail about the values being integers is really important!
It appears that you are using a random number generator for uniform integers with different ranges (else how do you know that your distribution is uniform?). When you sample from a distribution on [0,... | Alternative to Kolmogorov-Smirnov test when parameters are estimated from the data | I can't make much sense of the question on any level. The detail about the values being integers is really important!
It appears that you are using a random number generator for uniform integers wit | Alternative to Kolmogorov-Smirnov test when parameters are estimated from the data
I can't make much sense of the question on any level. The detail about the values being integers is really important!
It appears that you are using a random number generator for uniform integers with different ranges (else how do you k... | Alternative to Kolmogorov-Smirnov test when parameters are estimated from the data
I can't make much sense of the question on any level. The detail about the values being integers is really important!
It appears that you are using a random number generator for uniform integers wit |
44,420 | Alternative to Kolmogorov-Smirnov test when parameters are estimated from the data | It may be possible that a distribution-free test like the Wilcoxon-Mann-Whitney, which is a test based on rank, not value. In your example, multiplying all the values from Data1 will not change their respective iinternal ranks, but now they will be on the same "scale" as Data2. As such, the MWW test may provide you wit... | Alternative to Kolmogorov-Smirnov test when parameters are estimated from the data | It may be possible that a distribution-free test like the Wilcoxon-Mann-Whitney, which is a test based on rank, not value. In your example, multiplying all the values from Data1 will not change their | Alternative to Kolmogorov-Smirnov test when parameters are estimated from the data
It may be possible that a distribution-free test like the Wilcoxon-Mann-Whitney, which is a test based on rank, not value. In your example, multiplying all the values from Data1 will not change their respective iinternal ranks, but now t... | Alternative to Kolmogorov-Smirnov test when parameters are estimated from the data
It may be possible that a distribution-free test like the Wilcoxon-Mann-Whitney, which is a test based on rank, not value. In your example, multiplying all the values from Data1 will not change their |
44,421 | Can one measure the degree of empirical data being Gaussian? | There are an infinite number of ways of being non-Gaussian.
For example, you mentioned skewness and kurtosis - while those measures are certainly ways of identifying distributions that aren't Gaussian, and they can be combined into a single measure of deviation from Gaussian-ness* (and even form the basis of some commo... | Can one measure the degree of empirical data being Gaussian? | There are an infinite number of ways of being non-Gaussian.
For example, you mentioned skewness and kurtosis - while those measures are certainly ways of identifying distributions that aren't Gaussian | Can one measure the degree of empirical data being Gaussian?
There are an infinite number of ways of being non-Gaussian.
For example, you mentioned skewness and kurtosis - while those measures are certainly ways of identifying distributions that aren't Gaussian, and they can be combined into a single measure of deviati... | Can one measure the degree of empirical data being Gaussian?
There are an infinite number of ways of being non-Gaussian.
For example, you mentioned skewness and kurtosis - while those measures are certainly ways of identifying distributions that aren't Gaussian |
44,422 | Does lm() use partial correlation - R Squared Change? | Another function that you might find useful is lm.sumSquares in the lmSupport package. Basically, if you have the following model:
mod1 <- lm(dv ~ iv1 + iv2 + iv3, data = d)
Executing the following will give you the delta R squared (the semipartial correlation squared) and PRE (the partial correlation squared) for iv... | Does lm() use partial correlation - R Squared Change? | Another function that you might find useful is lm.sumSquares in the lmSupport package. Basically, if you have the following model:
mod1 <- lm(dv ~ iv1 + iv2 + iv3, data = d)
Executing the following | Does lm() use partial correlation - R Squared Change?
Another function that you might find useful is lm.sumSquares in the lmSupport package. Basically, if you have the following model:
mod1 <- lm(dv ~ iv1 + iv2 + iv3, data = d)
Executing the following will give you the delta R squared (the semipartial correlation squ... | Does lm() use partial correlation - R Squared Change?
Another function that you might find useful is lm.sumSquares in the lmSupport package. Basically, if you have the following model:
mod1 <- lm(dv ~ iv1 + iv2 + iv3, data = d)
Executing the following |
44,423 | Does lm() use partial correlation - R Squared Change? | R doesn't use partial correlations to determine reported p-values from lm.
Indeed, you can examine the code that computes the p-values for yourself; if you type
> summary.lm
you will see the code of the function includes the following:
ans$coefficients <- cbind(est, se, tval, 2 * pt(abs(tval),
rdf, lower.tai... | Does lm() use partial correlation - R Squared Change? | R doesn't use partial correlations to determine reported p-values from lm.
Indeed, you can examine the code that computes the p-values for yourself; if you type
> summary.lm
you will see the code of | Does lm() use partial correlation - R Squared Change?
R doesn't use partial correlations to determine reported p-values from lm.
Indeed, you can examine the code that computes the p-values for yourself; if you type
> summary.lm
you will see the code of the function includes the following:
ans$coefficients <- cbin... | Does lm() use partial correlation - R Squared Change?
R doesn't use partial correlations to determine reported p-values from lm.
Indeed, you can examine the code that computes the p-values for yourself; if you type
> summary.lm
you will see the code of |
44,424 | Does lm() use partial correlation - R Squared Change? | I'm no R expert but I've looked into this same issue (your 2nd and 3rd questions) and found the following.
You do need first to run the lm command for each model separately.
If a formal test of the F associated with the change is of interest to you, you can formally compare successive models using anova, e.g., anova(M... | Does lm() use partial correlation - R Squared Change? | I'm no R expert but I've looked into this same issue (your 2nd and 3rd questions) and found the following.
You do need first to run the lm command for each model separately.
If a formal test of the F | Does lm() use partial correlation - R Squared Change?
I'm no R expert but I've looked into this same issue (your 2nd and 3rd questions) and found the following.
You do need first to run the lm command for each model separately.
If a formal test of the F associated with the change is of interest to you, you can formall... | Does lm() use partial correlation - R Squared Change?
I'm no R expert but I've looked into this same issue (your 2nd and 3rd questions) and found the following.
You do need first to run the lm command for each model separately.
If a formal test of the F |
44,425 | Does the Tukey HSD test correct for multiple comparisons? | It is not necessary to correct for multiple comparisons when using Tukey's HSD. The procedure was developed specifically to account for multiple comparison and maintains experiment-wise alpha at the specified level (conventionally .05). Page 210 of Maxwell and Delaney's book on experimental design has explanations and ... | Does the Tukey HSD test correct for multiple comparisons? | It is not necessary to correct for multiple comparisons when using Tukey's HSD. The procedure was developed specifically to account for multiple comparison and maintains experiment-wise alpha at the s | Does the Tukey HSD test correct for multiple comparisons?
It is not necessary to correct for multiple comparisons when using Tukey's HSD. The procedure was developed specifically to account for multiple comparison and maintains experiment-wise alpha at the specified level (conventionally .05). Page 210 of Maxwell and D... | Does the Tukey HSD test correct for multiple comparisons?
It is not necessary to correct for multiple comparisons when using Tukey's HSD. The procedure was developed specifically to account for multiple comparison and maintains experiment-wise alpha at the s |
44,426 | Increase sample size for significant correlation | I take it that you are investigating whether the correlation between two quantities is larger than $0$ and that you wish to know how many patients you need for your study to be able to show that it really is larger. In other words, I assume that you are using a one-sided test.
First of all, even if you collect a millio... | Increase sample size for significant correlation | I take it that you are investigating whether the correlation between two quantities is larger than $0$ and that you wish to know how many patients you need for your study to be able to show that it re | Increase sample size for significant correlation
I take it that you are investigating whether the correlation between two quantities is larger than $0$ and that you wish to know how many patients you need for your study to be able to show that it really is larger. In other words, I assume that you are using a one-sided... | Increase sample size for significant correlation
I take it that you are investigating whether the correlation between two quantities is larger than $0$ and that you wish to know how many patients you need for your study to be able to show that it re |
44,427 | Increase sample size for significant correlation | It depends on the test that was performed and the assumptions you make. I will assume that you want to calculate the sample size that would give a significant p-value at 0.05 given that the value of $\rho$ is still 0.2.
You can use the approximation
$$t = \rho\sqrt{\frac{n-2}{1-\rho^2}}$$
where $t$ has an approximate S... | Increase sample size for significant correlation | It depends on the test that was performed and the assumptions you make. I will assume that you want to calculate the sample size that would give a significant p-value at 0.05 given that the value of $ | Increase sample size for significant correlation
It depends on the test that was performed and the assumptions you make. I will assume that you want to calculate the sample size that would give a significant p-value at 0.05 given that the value of $\rho$ is still 0.2.
You can use the approximation
$$t = \rho\sqrt{\frac... | Increase sample size for significant correlation
It depends on the test that was performed and the assumptions you make. I will assume that you want to calculate the sample size that would give a significant p-value at 0.05 given that the value of $ |
44,428 | Practical significance, especially with percents: "standard" measure and threshold | I do a lot of statistical consulting and am commonly ask the question "How many subjects do I need to recruit?" I always address the sample size question in terms of "clinical" or "practical" significance. To address that I ask them to describe how large a difference "effect size" would they want to have to claim a d... | Practical significance, especially with percents: "standard" measure and threshold | I do a lot of statistical consulting and am commonly ask the question "How many subjects do I need to recruit?" I always address the sample size question in terms of "clinical" or "practical" signifi | Practical significance, especially with percents: "standard" measure and threshold
I do a lot of statistical consulting and am commonly ask the question "How many subjects do I need to recruit?" I always address the sample size question in terms of "clinical" or "practical" significance. To address that I ask them to... | Practical significance, especially with percents: "standard" measure and threshold
I do a lot of statistical consulting and am commonly ask the question "How many subjects do I need to recruit?" I always address the sample size question in terms of "clinical" or "practical" signifi |
44,429 | Practical significance, especially with percents: "standard" measure and threshold | I don't think there is any kind of test for practical significance because it really depends on the field or the problem. Sorry.
For example, if you find that implementing a certain policy increases revenue by $0.0000001, (some negligibly small amount) even though this might be statistically significant, i.e, p-value <... | Practical significance, especially with percents: "standard" measure and threshold | I don't think there is any kind of test for practical significance because it really depends on the field or the problem. Sorry.
For example, if you find that implementing a certain policy increases r | Practical significance, especially with percents: "standard" measure and threshold
I don't think there is any kind of test for practical significance because it really depends on the field or the problem. Sorry.
For example, if you find that implementing a certain policy increases revenue by $0.0000001, (some negligibl... | Practical significance, especially with percents: "standard" measure and threshold
I don't think there is any kind of test for practical significance because it really depends on the field or the problem. Sorry.
For example, if you find that implementing a certain policy increases r |
44,430 | Practical significance, especially with percents: "standard" measure and threshold | More than likely, if you're writing a paper, you're well on your way to what you need for practical significance. You've reviewed the literature and studied the subject matter and people have said, either explicitly or implicitly, what a practically significant amount is. All you need to do is cite that literature an... | Practical significance, especially with percents: "standard" measure and threshold | More than likely, if you're writing a paper, you're well on your way to what you need for practical significance. You've reviewed the literature and studied the subject matter and people have said, e | Practical significance, especially with percents: "standard" measure and threshold
More than likely, if you're writing a paper, you're well on your way to what you need for practical significance. You've reviewed the literature and studied the subject matter and people have said, either explicitly or implicitly, what ... | Practical significance, especially with percents: "standard" measure and threshold
More than likely, if you're writing a paper, you're well on your way to what you need for practical significance. You've reviewed the literature and studied the subject matter and people have said, e |
44,431 | Practical significance, especially with percents: "standard" measure and threshold | After further reading, here is one possible answer to my own question. If you have other answers along the same lines, please post them as well.
Cohen's h from Cohen (1988).
$h = |2\arcsin\sqrt{p_1}-2\arcsin\sqrt{p_2}|$
Qualification of effect sizes, with the disclaimer that they might be different in other disciplines... | Practical significance, especially with percents: "standard" measure and threshold | After further reading, here is one possible answer to my own question. If you have other answers along the same lines, please post them as well.
Cohen's h from Cohen (1988).
$h = |2\arcsin\sqrt{p_1}-2 | Practical significance, especially with percents: "standard" measure and threshold
After further reading, here is one possible answer to my own question. If you have other answers along the same lines, please post them as well.
Cohen's h from Cohen (1988).
$h = |2\arcsin\sqrt{p_1}-2\arcsin\sqrt{p_2}|$
Qualification of ... | Practical significance, especially with percents: "standard" measure and threshold
After further reading, here is one possible answer to my own question. If you have other answers along the same lines, please post them as well.
Cohen's h from Cohen (1988).
$h = |2\arcsin\sqrt{p_1}-2 |
44,432 | Outlier removal prior to mixed-effect modelling | Having taken a look at paper cited, it's not quite as bad as I thought -- they basically suggest normality testing as a way to identify extreme outliers that might screw up the analysis, and they say that mixed modeling allows less "aggressive" outlier identification/removal. (They use the terms "minimal trimming" and... | Outlier removal prior to mixed-effect modelling | Having taken a look at paper cited, it's not quite as bad as I thought -- they basically suggest normality testing as a way to identify extreme outliers that might screw up the analysis, and they say | Outlier removal prior to mixed-effect modelling
Having taken a look at paper cited, it's not quite as bad as I thought -- they basically suggest normality testing as a way to identify extreme outliers that might screw up the analysis, and they say that mixed modeling allows less "aggressive" outlier identification/remo... | Outlier removal prior to mixed-effect modelling
Having taken a look at paper cited, it's not quite as bad as I thought -- they basically suggest normality testing as a way to identify extreme outliers that might screw up the analysis, and they say |
44,433 | Outlier removal prior to mixed-effect modelling | If you are absolutely certain that nobody will ever critically review your analysis, consider it skeptically, or just need to be convinced of your results, then go ahead and remove the outliers (but if this is the case then there is probably no need to do the analysis at all).
If you remove outliers then you open yours... | Outlier removal prior to mixed-effect modelling | If you are absolutely certain that nobody will ever critically review your analysis, consider it skeptically, or just need to be convinced of your results, then go ahead and remove the outliers (but i | Outlier removal prior to mixed-effect modelling
If you are absolutely certain that nobody will ever critically review your analysis, consider it skeptically, or just need to be convinced of your results, then go ahead and remove the outliers (but if this is the case then there is probably no need to do the analysis at ... | Outlier removal prior to mixed-effect modelling
If you are absolutely certain that nobody will ever critically review your analysis, consider it skeptically, or just need to be convinced of your results, then go ahead and remove the outliers (but i |
44,434 | Is there a test for independence in a Bernoulli process? | I think you can devise a big number of tests, and the good choice depends on the alternate hypothesis you have in mind... I just have a few remarks. I place this post under community wiki as I feel it can be improved a lot.
The first think I would think to: divide your sample in n subsamples of size k; if the experime... | Is there a test for independence in a Bernoulli process? | I think you can devise a big number of tests, and the good choice depends on the alternate hypothesis you have in mind... I just have a few remarks. I place this post under community wiki as I feel it | Is there a test for independence in a Bernoulli process?
I think you can devise a big number of tests, and the good choice depends on the alternate hypothesis you have in mind... I just have a few remarks. I place this post under community wiki as I feel it can be improved a lot.
The first think I would think to: divi... | Is there a test for independence in a Bernoulli process?
I think you can devise a big number of tests, and the good choice depends on the alternate hypothesis you have in mind... I just have a few remarks. I place this post under community wiki as I feel it |
44,435 | Is there a test for independence in a Bernoulli process? | Let the sequence of values be realizations of random variables $X_i$, $1\le i\le n$, each identically distributed as a Bernoulli($p$) variable (with $p$ unknown). When they are independent, the sequence is a Markov chain with transition probabilities
$$\Pr(x \to 0) = 1-p, \quad \Pr(x \to 1) = p$$
for $x = 0,1$. The s... | Is there a test for independence in a Bernoulli process? | Let the sequence of values be realizations of random variables $X_i$, $1\le i\le n$, each identically distributed as a Bernoulli($p$) variable (with $p$ unknown). When they are independent, the seque | Is there a test for independence in a Bernoulli process?
Let the sequence of values be realizations of random variables $X_i$, $1\le i\le n$, each identically distributed as a Bernoulli($p$) variable (with $p$ unknown). When they are independent, the sequence is a Markov chain with transition probabilities
$$\Pr(x \to... | Is there a test for independence in a Bernoulli process?
Let the sequence of values be realizations of random variables $X_i$, $1\le i\le n$, each identically distributed as a Bernoulli($p$) variable (with $p$ unknown). When they are independent, the seque |
44,436 | Can you compare p-values of Kolmogorov Smirnov tests of normality of two variables to say which is more normal? | Read this article:
Murdock, D, Tsai, Y, and Adcock, J (2008) _P-Values are Random
Variables_. The American Statistician. (62) 242-245.
It talks about the fact that if the null hypothesis is true then the p-value is a uniform random variable. This means that you are just as likely to see a p-value of 0.09, 0.06, 0.... | Can you compare p-values of Kolmogorov Smirnov tests of normality of two variables to say which is m | Read this article:
Murdock, D, Tsai, Y, and Adcock, J (2008) _P-Values are Random
Variables_. The American Statistician. (62) 242-245.
It talks about the fact that if the null hypothesis is true t | Can you compare p-values of Kolmogorov Smirnov tests of normality of two variables to say which is more normal?
Read this article:
Murdock, D, Tsai, Y, and Adcock, J (2008) _P-Values are Random
Variables_. The American Statistician. (62) 242-245.
It talks about the fact that if the null hypothesis is true then the ... | Can you compare p-values of Kolmogorov Smirnov tests of normality of two variables to say which is m
Read this article:
Murdock, D, Tsai, Y, and Adcock, J (2008) _P-Values are Random
Variables_. The American Statistician. (62) 242-245.
It talks about the fact that if the null hypothesis is true t |
44,437 | Can you compare p-values of Kolmogorov Smirnov tests of normality of two variables to say which is more normal? | In general, the lower the p-value, the less belief you attach to your null hypothesis (in fact, the p-value is the chance that, if the null hypothesis were true, a test statistic so extreme (or more) as the one obtained from your sample would be obtained).
As such, it is reasonable to say that the lower the p-value, th... | Can you compare p-values of Kolmogorov Smirnov tests of normality of two variables to say which is m | In general, the lower the p-value, the less belief you attach to your null hypothesis (in fact, the p-value is the chance that, if the null hypothesis were true, a test statistic so extreme (or more) | Can you compare p-values of Kolmogorov Smirnov tests of normality of two variables to say which is more normal?
In general, the lower the p-value, the less belief you attach to your null hypothesis (in fact, the p-value is the chance that, if the null hypothesis were true, a test statistic so extreme (or more) as the o... | Can you compare p-values of Kolmogorov Smirnov tests of normality of two variables to say which is m
In general, the lower the p-value, the less belief you attach to your null hypothesis (in fact, the p-value is the chance that, if the null hypothesis were true, a test statistic so extreme (or more) |
44,438 | Can you compare p-values of Kolmogorov Smirnov tests of normality of two variables to say which is more normal? | The smaller p value represents stronger evidence against the null hypothesis, but it may not be that the first distribution is "better or more normal" than the second. Instead, it may be less easily distinguished from a normal distribution.
Note that the amount of evidence against the null hypothesis in a p value of 0.... | Can you compare p-values of Kolmogorov Smirnov tests of normality of two variables to say which is m | The smaller p value represents stronger evidence against the null hypothesis, but it may not be that the first distribution is "better or more normal" than the second. Instead, it may be less easily d | Can you compare p-values of Kolmogorov Smirnov tests of normality of two variables to say which is more normal?
The smaller p value represents stronger evidence against the null hypothesis, but it may not be that the first distribution is "better or more normal" than the second. Instead, it may be less easily distingui... | Can you compare p-values of Kolmogorov Smirnov tests of normality of two variables to say which is m
The smaller p value represents stronger evidence against the null hypothesis, but it may not be that the first distribution is "better or more normal" than the second. Instead, it may be less easily d |
44,439 | What university level statistics courses are considered advanced/hard? | It really depends what your company is doing. Are you looking for machine learning experts? Data visualisation experts? Data mining experts?
When I interview statistics PhDs I like to ask them questions about linear regression, as I feel that anyone claiming to be an expert in statistics should at the very minimum be a... | What university level statistics courses are considered advanced/hard? | It really depends what your company is doing. Are you looking for machine learning experts? Data visualisation experts? Data mining experts?
When I interview statistics PhDs I like to ask them questio | What university level statistics courses are considered advanced/hard?
It really depends what your company is doing. Are you looking for machine learning experts? Data visualisation experts? Data mining experts?
When I interview statistics PhDs I like to ask them questions about linear regression, as I feel that anyone... | What university level statistics courses are considered advanced/hard?
It really depends what your company is doing. Are you looking for machine learning experts? Data visualisation experts? Data mining experts?
When I interview statistics PhDs I like to ask them questio |
44,440 | What university level statistics courses are considered advanced/hard? | I agree with Chris on most of what he says. Additionally, I'd like to add that without knowing the institutions or universities in detail, just looking at grades would be very misleading. I could easily give a relevant example; I have recently graduated with a masters in engineering mathematics; and taken a variety of ... | What university level statistics courses are considered advanced/hard? | I agree with Chris on most of what he says. Additionally, I'd like to add that without knowing the institutions or universities in detail, just looking at grades would be very misleading. I could easi | What university level statistics courses are considered advanced/hard?
I agree with Chris on most of what he says. Additionally, I'd like to add that without knowing the institutions or universities in detail, just looking at grades would be very misleading. I could easily give a relevant example; I have recently gradu... | What university level statistics courses are considered advanced/hard?
I agree with Chris on most of what he says. Additionally, I'd like to add that without knowing the institutions or universities in detail, just looking at grades would be very misleading. I could easi |
44,441 | What university level statistics courses are considered advanced/hard? | Chris really nailed the data minining stuff. If you need someone who can also look at experimental data, you can stop all but the most versatile of statisticians dead in their tracks by asking them to explain a split-plot experiment. | What university level statistics courses are considered advanced/hard? | Chris really nailed the data minining stuff. If you need someone who can also look at experimental data, you can stop all but the most versatile of statisticians dead in their tracks by asking them t | What university level statistics courses are considered advanced/hard?
Chris really nailed the data minining stuff. If you need someone who can also look at experimental data, you can stop all but the most versatile of statisticians dead in their tracks by asking them to explain a split-plot experiment. | What university level statistics courses are considered advanced/hard?
Chris really nailed the data minining stuff. If you need someone who can also look at experimental data, you can stop all but the most versatile of statisticians dead in their tracks by asking them t |
44,442 | Is there a name for 10% best individual grades? | If I understand you correctly, you may refer to Percentiles, perhaps espacially Quartiles.
Perhaps you can elaborate a little more on which percentages should be enclosed in each bin, to get a more accurate answer.
UPDATE: Based on the comments below decile seems to be the term you want. For your data these can easily ... | Is there a name for 10% best individual grades? | If I understand you correctly, you may refer to Percentiles, perhaps espacially Quartiles.
Perhaps you can elaborate a little more on which percentages should be enclosed in each bin, to get a more ac | Is there a name for 10% best individual grades?
If I understand you correctly, you may refer to Percentiles, perhaps espacially Quartiles.
Perhaps you can elaborate a little more on which percentages should be enclosed in each bin, to get a more accurate answer.
UPDATE: Based on the comments below decile seems to be th... | Is there a name for 10% best individual grades?
If I understand you correctly, you may refer to Percentiles, perhaps espacially Quartiles.
Perhaps you can elaborate a little more on which percentages should be enclosed in each bin, to get a more ac |
44,443 | Is there a name for 10% best individual grades? | You have the answer you asked for, but along with how to communicate this information you might also want to think about how to asses the reliability & precision of the scores. If the evaluators aren't really using the same standards, the scores will furnish a misleading measure of the quality of the speakers no matter... | Is there a name for 10% best individual grades? | You have the answer you asked for, but along with how to communicate this information you might also want to think about how to asses the reliability & precision of the scores. If the evaluators aren' | Is there a name for 10% best individual grades?
You have the answer you asked for, but along with how to communicate this information you might also want to think about how to asses the reliability & precision of the scores. If the evaluators aren't really using the same standards, the scores will furnish a misleading ... | Is there a name for 10% best individual grades?
You have the answer you asked for, but along with how to communicate this information you might also want to think about how to asses the reliability & precision of the scores. If the evaluators aren' |
44,444 | Is there a name for 10% best individual grades? | In addition to the existing answers, you may find it useful to read up about test norms, a well established topic in psychology and education.
Test Norms: Their Use and Interpretation.
http://psychassessment.com.au/PDF/Chapter%2004.pdf
Google 'test norms' | Is there a name for 10% best individual grades? | In addition to the existing answers, you may find it useful to read up about test norms, a well established topic in psychology and education.
Test Norms: Their Use and Interpretation.
http://psychas | Is there a name for 10% best individual grades?
In addition to the existing answers, you may find it useful to read up about test norms, a well established topic in psychology and education.
Test Norms: Their Use and Interpretation.
http://psychassessment.com.au/PDF/Chapter%2004.pdf
Google 'test norms' | Is there a name for 10% best individual grades?
In addition to the existing answers, you may find it useful to read up about test norms, a well established topic in psychology and education.
Test Norms: Their Use and Interpretation.
http://psychas |
44,445 | Is there a name for 10% best individual grades? | I'd like to add another cautionary note, and a suggestion. When asked for a 1-5 rating, I usually think up some scale, like:
worst ever
real bad
ok
great
awesome
If your raters did similarly, taking an average is somewhat questionable; the difference between "worst ever" and "real bad" may be larger than the differen... | Is there a name for 10% best individual grades? | I'd like to add another cautionary note, and a suggestion. When asked for a 1-5 rating, I usually think up some scale, like:
worst ever
real bad
ok
great
awesome
If your raters did similarly, taking | Is there a name for 10% best individual grades?
I'd like to add another cautionary note, and a suggestion. When asked for a 1-5 rating, I usually think up some scale, like:
worst ever
real bad
ok
great
awesome
If your raters did similarly, taking an average is somewhat questionable; the difference between "worst ever... | Is there a name for 10% best individual grades?
I'd like to add another cautionary note, and a suggestion. When asked for a 1-5 rating, I usually think up some scale, like:
worst ever
real bad
ok
great
awesome
If your raters did similarly, taking |
44,446 | How to read large dataset in R [closed] | Two basic things:
That complaint addresses all of the memory in the R session, not just the one object that you're loading. And unless you're using something like ff, everything in your session is in memory.
One Windows, you need to specify how much memory can be used by R. Have a look at help(memory.limit). Even t... | How to read large dataset in R [closed] | Two basic things:
That complaint addresses all of the memory in the R session, not just the one object that you're loading. And unless you're using something like ff, everything in your session is i | How to read large dataset in R [closed]
Two basic things:
That complaint addresses all of the memory in the R session, not just the one object that you're loading. And unless you're using something like ff, everything in your session is in memory.
One Windows, you need to specify how much memory can be used by R. Ha... | How to read large dataset in R [closed]
Two basic things:
That complaint addresses all of the memory in the R session, not just the one object that you're loading. And unless you're using something like ff, everything in your session is i |
44,447 | How to read large dataset in R [closed] | What platform are you running R on? How much physical and virtual memory does the machine have?
Also, you might find the following relevant: http://stat.ethz.ch/R-manual/R-devel/library/base/html/Memory-limits.html | How to read large dataset in R [closed] | What platform are you running R on? How much physical and virtual memory does the machine have?
Also, you might find the following relevant: http://stat.ethz.ch/R-manual/R-devel/library/base/html/Memo | How to read large dataset in R [closed]
What platform are you running R on? How much physical and virtual memory does the machine have?
Also, you might find the following relevant: http://stat.ethz.ch/R-manual/R-devel/library/base/html/Memory-limits.html | How to read large dataset in R [closed]
What platform are you running R on? How much physical and virtual memory does the machine have?
Also, you might find the following relevant: http://stat.ethz.ch/R-manual/R-devel/library/base/html/Memo |
44,448 | How to read large dataset in R [closed] | I,m totally agree with Dirk answer. One suggestion. I have found very useful the use of programming languages such as AWK or others when assessing large databases. So, I was able to filter the data I wanted to include in my analysis, reducing the final size of dataset.
Moreover, in your code you are duplicating the sam... | How to read large dataset in R [closed] | I,m totally agree with Dirk answer. One suggestion. I have found very useful the use of programming languages such as AWK or others when assessing large databases. So, I was able to filter the data I | How to read large dataset in R [closed]
I,m totally agree with Dirk answer. One suggestion. I have found very useful the use of programming languages such as AWK or others when assessing large databases. So, I was able to filter the data I wanted to include in my analysis, reducing the final size of dataset.
Moreover, ... | How to read large dataset in R [closed]
I,m totally agree with Dirk answer. One suggestion. I have found very useful the use of programming languages such as AWK or others when assessing large databases. So, I was able to filter the data I |
44,449 | How to read large dataset in R [closed] | Since you're on 64-bit Windows, make sure that you have installed and are running the 64-bit version of R for Windows. Then, follow the instructions on Gary King's page:
How do I increase the memory for R? | How to read large dataset in R [closed] | Since you're on 64-bit Windows, make sure that you have installed and are running the 64-bit version of R for Windows. Then, follow the instructions on Gary King's page:
How do I increase the memory | How to read large dataset in R [closed]
Since you're on 64-bit Windows, make sure that you have installed and are running the 64-bit version of R for Windows. Then, follow the instructions on Gary King's page:
How do I increase the memory for R? | How to read large dataset in R [closed]
Since you're on 64-bit Windows, make sure that you have installed and are running the 64-bit version of R for Windows. Then, follow the instructions on Gary King's page:
How do I increase the memory |
44,450 | How to read large dataset in R [closed] | You can always use the filehash package which dumps the large dataset in the disk rather than in the system's memory. You need to be prepared to deal with the tradeoff though, due to slow read HDD times. | How to read large dataset in R [closed] | You can always use the filehash package which dumps the large dataset in the disk rather than in the system's memory. You need to be prepared to deal with the tradeoff though, due to slow read HDD tim | How to read large dataset in R [closed]
You can always use the filehash package which dumps the large dataset in the disk rather than in the system's memory. You need to be prepared to deal with the tradeoff though, due to slow read HDD times. | How to read large dataset in R [closed]
You can always use the filehash package which dumps the large dataset in the disk rather than in the system's memory. You need to be prepared to deal with the tradeoff though, due to slow read HDD tim |
44,451 | Orthogonal parametrization | In Maximum Likelihood, the term orthogonal parameters is used when you can achieve a clean factorization of a multi-parameter likelihood function. Say your data have two parameters $\theta$ and $\lambda$. If you can rewrite the joint likelihood:
$L(\theta, \lambda) = L_{1}(\theta) L_{2}(\lambda)$
then we call $\theta... | Orthogonal parametrization | In Maximum Likelihood, the term orthogonal parameters is used when you can achieve a clean factorization of a multi-parameter likelihood function. Say your data have two parameters $\theta$ and $\lam | Orthogonal parametrization
In Maximum Likelihood, the term orthogonal parameters is used when you can achieve a clean factorization of a multi-parameter likelihood function. Say your data have two parameters $\theta$ and $\lambda$. If you can rewrite the joint likelihood:
$L(\theta, \lambda) = L_{1}(\theta) L_{2}(\la... | Orthogonal parametrization
In Maximum Likelihood, the term orthogonal parameters is used when you can achieve a clean factorization of a multi-parameter likelihood function. Say your data have two parameters $\theta$ and $\lam |
44,452 | Orthogonal parametrization | This is a good, if underspecified question.
Simply put, obtaining an orthogonal parametrization allows for parameters of interest to be conveniently related to other parameters, particularly in establishing needed minimizations. Whether or not this is useful depends on what you are trying to do (in the case of some p... | Orthogonal parametrization | This is a good, if underspecified question.
Simply put, obtaining an orthogonal parametrization allows for parameters of interest to be conveniently related to other parameters, particularly in esta | Orthogonal parametrization
This is a good, if underspecified question.
Simply put, obtaining an orthogonal parametrization allows for parameters of interest to be conveniently related to other parameters, particularly in establishing needed minimizations. Whether or not this is useful depends on what you are trying t... | Orthogonal parametrization
This is a good, if underspecified question.
Simply put, obtaining an orthogonal parametrization allows for parameters of interest to be conveniently related to other parameters, particularly in esta |
44,453 | Overestimating the lower values and underestimating the higher values in Regression | This is just an effect of a model which only partially explains the observations. In such a case, this sort of effect is common. Possible choices include accepting that some things are random or trying to find better explanations for the observations; it may be impossible to get a better result with the data you have.... | Overestimating the lower values and underestimating the higher values in Regression | This is just an effect of a model which only partially explains the observations. In such a case, this sort of effect is common. Possible choices include accepting that some things are random or tryi | Overestimating the lower values and underestimating the higher values in Regression
This is just an effect of a model which only partially explains the observations. In such a case, this sort of effect is common. Possible choices include accepting that some things are random or trying to find better explanations for t... | Overestimating the lower values and underestimating the higher values in Regression
This is just an effect of a model which only partially explains the observations. In such a case, this sort of effect is common. Possible choices include accepting that some things are random or tryi |
44,454 | Overestimating the lower values and underestimating the higher values in Regression | I suspect that there is not a very strong "signal" in your data, meaning that for a given place in x-space there is a big variance in $y$, and therefore $y$ cannot be predicted very precisely. The implication is then that where big values of $y$ ("observed") occur, this is often not because the corresponding x-values t... | Overestimating the lower values and underestimating the higher values in Regression | I suspect that there is not a very strong "signal" in your data, meaning that for a given place in x-space there is a big variance in $y$, and therefore $y$ cannot be predicted very precisely. The imp | Overestimating the lower values and underestimating the higher values in Regression
I suspect that there is not a very strong "signal" in your data, meaning that for a given place in x-space there is a big variance in $y$, and therefore $y$ cannot be predicted very precisely. The implication is then that where big valu... | Overestimating the lower values and underestimating the higher values in Regression
I suspect that there is not a very strong "signal" in your data, meaning that for a given place in x-space there is a big variance in $y$, and therefore $y$ cannot be predicted very precisely. The imp |
44,455 | Overestimating the lower values and underestimating the higher values in Regression | [Edited as I misread the original question]
The way a Random Forest works, simplified, is that the computer tries to sort the observations into buckets, then calculates the average value within each bucket, and uses that as the score for everything in that bucket. This is done repeatedly, getting different bucketing ru... | Overestimating the lower values and underestimating the higher values in Regression | [Edited as I misread the original question]
The way a Random Forest works, simplified, is that the computer tries to sort the observations into buckets, then calculates the average value within each b | Overestimating the lower values and underestimating the higher values in Regression
[Edited as I misread the original question]
The way a Random Forest works, simplified, is that the computer tries to sort the observations into buckets, then calculates the average value within each bucket, and uses that as the score fo... | Overestimating the lower values and underestimating the higher values in Regression
[Edited as I misread the original question]
The way a Random Forest works, simplified, is that the computer tries to sort the observations into buckets, then calculates the average value within each b |
44,456 | What is the R squared of a regression where none of the variables are collinear? | (Most of this a linear algebra question is disguise!)
If the $100\times100$ matrix $X$ is full-rank, that means the columns form a basis for $\mathbb R^{100}$. Since $y\in\mathbb R^{100}$, $y$ can be written as some linear combination of any basis for $\mathbb R^{100}$, such as the set of columns of $X$.
That is, the c... | What is the R squared of a regression where none of the variables are collinear? | (Most of this a linear algebra question is disguise!)
If the $100\times100$ matrix $X$ is full-rank, that means the columns form a basis for $\mathbb R^{100}$. Since $y\in\mathbb R^{100}$, $y$ can be | What is the R squared of a regression where none of the variables are collinear?
(Most of this a linear algebra question is disguise!)
If the $100\times100$ matrix $X$ is full-rank, that means the columns form a basis for $\mathbb R^{100}$. Since $y\in\mathbb R^{100}$, $y$ can be written as some linear combination of a... | What is the R squared of a regression where none of the variables are collinear?
(Most of this a linear algebra question is disguise!)
If the $100\times100$ matrix $X$ is full-rank, that means the columns form a basis for $\mathbb R^{100}$. Since $y\in\mathbb R^{100}$, $y$ can be |
44,457 | What is the R squared of a regression where none of the variables are collinear? | If none of the explanatory variables is colinear (i.e., each pair has zero correlation) then the coefficient-of-determination for the regresion is equal to the sum of the coefficients-of-determination for individual simple linear regessions of each explanatory variable against the response variable. If you would like ... | What is the R squared of a regression where none of the variables are collinear? | If none of the explanatory variables is colinear (i.e., each pair has zero correlation) then the coefficient-of-determination for the regresion is equal to the sum of the coefficients-of-determination | What is the R squared of a regression where none of the variables are collinear?
If none of the explanatory variables is colinear (i.e., each pair has zero correlation) then the coefficient-of-determination for the regresion is equal to the sum of the coefficients-of-determination for individual simple linear regession... | What is the R squared of a regression where none of the variables are collinear?
If none of the explanatory variables is colinear (i.e., each pair has zero correlation) then the coefficient-of-determination for the regresion is equal to the sum of the coefficients-of-determination |
44,458 | Central limit theorem and strong law of large numbers | In short: No.
A bit longer: Convergence in distribution does not directly imply, by any way, convergence almost-surely.
Much longer:
Given a random vector $X$, whose components are independent and identically distributed and its first two moments are finite - then the CLT says that asymptotically, the sample mean $\bar... | Central limit theorem and strong law of large numbers | In short: No.
A bit longer: Convergence in distribution does not directly imply, by any way, convergence almost-surely.
Much longer:
Given a random vector $X$, whose components are independent and ide | Central limit theorem and strong law of large numbers
In short: No.
A bit longer: Convergence in distribution does not directly imply, by any way, convergence almost-surely.
Much longer:
Given a random vector $X$, whose components are independent and identically distributed and its first two moments are finite - then t... | Central limit theorem and strong law of large numbers
In short: No.
A bit longer: Convergence in distribution does not directly imply, by any way, convergence almost-surely.
Much longer:
Given a random vector $X$, whose components are independent and ide |
44,459 | Central limit theorem and strong law of large numbers | As you suppose that $X_i$ are i.i.d. such that CLT holds then you suppose that $EX_1$ exists (because it is a term in CLT). Hence $X_i$ are i.i.d. with finite expectation and SLLN holds true. | Central limit theorem and strong law of large numbers | As you suppose that $X_i$ are i.i.d. such that CLT holds then you suppose that $EX_1$ exists (because it is a term in CLT). Hence $X_i$ are i.i.d. with finite expectation and SLLN holds true. | Central limit theorem and strong law of large numbers
As you suppose that $X_i$ are i.i.d. such that CLT holds then you suppose that $EX_1$ exists (because it is a term in CLT). Hence $X_i$ are i.i.d. with finite expectation and SLLN holds true. | Central limit theorem and strong law of large numbers
As you suppose that $X_i$ are i.i.d. such that CLT holds then you suppose that $EX_1$ exists (because it is a term in CLT). Hence $X_i$ are i.i.d. with finite expectation and SLLN holds true. |
44,460 | What happens if I change the range of a flat prior for Bayesian inference? | If you start with a uniform prior over the support of the parameter, you get the normalized likelihood back as the posterior (I'm going to restrict my attention to cases where the likelihood can be normalized to a density).
So if you start with some $\theta$ with support on $(0,1)$ and a likelihood that's proportional ... | What happens if I change the range of a flat prior for Bayesian inference? | If you start with a uniform prior over the support of the parameter, you get the normalized likelihood back as the posterior (I'm going to restrict my attention to cases where the likelihood can be no | What happens if I change the range of a flat prior for Bayesian inference?
If you start with a uniform prior over the support of the parameter, you get the normalized likelihood back as the posterior (I'm going to restrict my attention to cases where the likelihood can be normalized to a density).
So if you start with ... | What happens if I change the range of a flat prior for Bayesian inference?
If you start with a uniform prior over the support of the parameter, you get the normalized likelihood back as the posterior (I'm going to restrict my attention to cases where the likelihood can be no |
44,461 | What happens if I change the range of a flat prior for Bayesian inference? | Comments:
If the prior distribution has support $[.1,1],$ then the posterior distribution has support contained in or equal to $[.1,1],$ so the posterior distribution could not be any ordinary (two-parameter) beta distribution.
Also, if one tries to use a normal prior for a binomial success
probability then it has to b... | What happens if I change the range of a flat prior for Bayesian inference? | Comments:
If the prior distribution has support $[.1,1],$ then the posterior distribution has support contained in or equal to $[.1,1],$ so the posterior distribution could not be any ordinary (two-pa | What happens if I change the range of a flat prior for Bayesian inference?
Comments:
If the prior distribution has support $[.1,1],$ then the posterior distribution has support contained in or equal to $[.1,1],$ so the posterior distribution could not be any ordinary (two-parameter) beta distribution.
Also, if one trie... | What happens if I change the range of a flat prior for Bayesian inference?
Comments:
If the prior distribution has support $[.1,1],$ then the posterior distribution has support contained in or equal to $[.1,1],$ so the posterior distribution could not be any ordinary (two-pa |
44,462 | What happens if I change the range of a flat prior for Bayesian inference? | The standard proportionality result for the posterior still holds, but the posterior is now concentrated on the same restricted set as the prior. To see this, consider the general case where you restrict your prior to the set $\mathscr{D}$. If you use a prior proportionate to $\pi(\theta) \cdot \mathbb{I}(\theta \in ... | What happens if I change the range of a flat prior for Bayesian inference? | The standard proportionality result for the posterior still holds, but the posterior is now concentrated on the same restricted set as the prior. To see this, consider the general case where you rest | What happens if I change the range of a flat prior for Bayesian inference?
The standard proportionality result for the posterior still holds, but the posterior is now concentrated on the same restricted set as the prior. To see this, consider the general case where you restrict your prior to the set $\mathscr{D}$. If... | What happens if I change the range of a flat prior for Bayesian inference?
The standard proportionality result for the posterior still holds, but the posterior is now concentrated on the same restricted set as the prior. To see this, consider the general case where you rest |
44,463 | Probability after n steps | I think it's normal to see changes wrt parity because if in any of the previous states you hit $3$, you'll stay there, and otherwise, you'll end up alternating between 1 and 2. So, for example, for $n=1$, it's impossible to be in state $1$ because $X_0=1$ and you can only go to state $2$ or $3$.
Taking the power of the... | Probability after n steps | I think it's normal to see changes wrt parity because if in any of the previous states you hit $3$, you'll stay there, and otherwise, you'll end up alternating between 1 and 2. So, for example, for $n | Probability after n steps
I think it's normal to see changes wrt parity because if in any of the previous states you hit $3$, you'll stay there, and otherwise, you'll end up alternating between 1 and 2. So, for example, for $n=1$, it's impossible to be in state $1$ because $X_0=1$ and you can only go to state $2$ or $3... | Probability after n steps
I think it's normal to see changes wrt parity because if in any of the previous states you hit $3$, you'll stay there, and otherwise, you'll end up alternating between 1 and 2. So, for example, for $n |
44,464 | Probability after n steps | Gunes gives the answer by reasoning (which is probably what you should do for this exam).
A more general and straightforward method (but which requires more computation time) is the following:
You decompose the begin state as a sum of eigenvectors. Then you describe the evolution in terms of the evolution of those eige... | Probability after n steps | Gunes gives the answer by reasoning (which is probably what you should do for this exam).
A more general and straightforward method (but which requires more computation time) is the following:
You dec | Probability after n steps
Gunes gives the answer by reasoning (which is probably what you should do for this exam).
A more general and straightforward method (but which requires more computation time) is the following:
You decompose the begin state as a sum of eigenvectors. Then you describe the evolution in terms of t... | Probability after n steps
Gunes gives the answer by reasoning (which is probably what you should do for this exam).
A more general and straightforward method (but which requires more computation time) is the following:
You dec |
44,465 | Probability after n steps | The very fact that the Markov chain can be characterized by a constant transition matrix means that it is homogeneous. It may be easier to understand the concepts that you're struggling with with a simpler matrix. Consider
$$A=\frac 1 3\left(\begin{array}{ccc}1 &2 \\ 2 & 1\end{array}\right)$$
This matrix will switch th... | Probability after n steps | The very fact that the Markov chain can be characterized by a constant transition matrix means that it is homogeneous. It may be easier to understand the concepts that you're struggling with with a si | Probability after n steps
The very fact that the Markov chain can be characterized by a constant transition matrix means that it is homogeneous. It may be easier to understand the concepts that you're struggling with with a simpler matrix. Consider
$$A=\frac 1 3\left(\begin{array}{ccc}1 &2 \\ 2 & 1\end{array}\right)$$
... | Probability after n steps
The very fact that the Markov chain can be characterized by a constant transition matrix means that it is homogeneous. It may be easier to understand the concepts that you're struggling with with a si |
44,466 | How to express descriptive statistics as statistical functionals - and why? | $dF(x) = f(x)dx$ is true when the probability measure of the random variable (or equivalently the CDF, $F(x)$) is absolutely continuous with respect to the Lebesgue Measure. What that means is that for all sets with Lebesgue measure zero, the measure also assigns measure 0. You can think of this as meaning that the Leb... | How to express descriptive statistics as statistical functionals - and why? | $dF(x) = f(x)dx$ is true when the probability measure of the random variable (or equivalently the CDF, $F(x)$) is absolutely continuous with respect to the Lebesgue Measure. What that means is that fo | How to express descriptive statistics as statistical functionals - and why?
$dF(x) = f(x)dx$ is true when the probability measure of the random variable (or equivalently the CDF, $F(x)$) is absolutely continuous with respect to the Lebesgue Measure. What that means is that for all sets with Lebesgue measure zero, the m... | How to express descriptive statistics as statistical functionals - and why?
$dF(x) = f(x)dx$ is true when the probability measure of the random variable (or equivalently the CDF, $F(x)$) is absolutely continuous with respect to the Lebesgue Measure. What that means is that fo |
44,467 | How to express descriptive statistics as statistical functionals - and why? | First a correction to the question: when writing
$$T_1(F) = \int x\text d F \qquad \text{or} \qquad T_2(F) = \int (x-T_1(F))^2\,\text d F$$
these quantities are not statistics but functionals of the distribution of the data. For instance, $T_1(F)=\mathbb E [X]$ is the mean of $F$. Functionals are thus generalised momen... | How to express descriptive statistics as statistical functionals - and why? | First a correction to the question: when writing
$$T_1(F) = \int x\text d F \qquad \text{or} \qquad T_2(F) = \int (x-T_1(F))^2\,\text d F$$
these quantities are not statistics but functionals of the d | How to express descriptive statistics as statistical functionals - and why?
First a correction to the question: when writing
$$T_1(F) = \int x\text d F \qquad \text{or} \qquad T_2(F) = \int (x-T_1(F))^2\,\text d F$$
these quantities are not statistics but functionals of the distribution of the data. For instance, $T_1(... | How to express descriptive statistics as statistical functionals - and why?
First a correction to the question: when writing
$$T_1(F) = \int x\text d F \qquad \text{or} \qquad T_2(F) = \int (x-T_1(F))^2\,\text d F$$
these quantities are not statistics but functionals of the d |
44,468 | Clarification - Random Variable | I think Mr Blitzstein, when writing
$$P (X=a_j \text{ for some } j)=1$$
really meant that $X$ is always one of $a_1, a_2, \ldots$. So it always is $a_j$ for some $j$.
I'd write
$$ P(X \in \{a_1, a_2, \ldots\})=1$$ | Clarification - Random Variable | I think Mr Blitzstein, when writing
$$P (X=a_j \text{ for some } j)=1$$
really meant that $X$ is always one of $a_1, a_2, \ldots$. So it always is $a_j$ for some $j$.
I'd write
$$ P(X \in \{a_1, a_2, | Clarification - Random Variable
I think Mr Blitzstein, when writing
$$P (X=a_j \text{ for some } j)=1$$
really meant that $X$ is always one of $a_1, a_2, \ldots$. So it always is $a_j$ for some $j$.
I'd write
$$ P(X \in \{a_1, a_2, \ldots\})=1$$ | Clarification - Random Variable
I think Mr Blitzstein, when writing
$$P (X=a_j \text{ for some } j)=1$$
really meant that $X$ is always one of $a_1, a_2, \ldots$. So it always is $a_j$ for some $j$.
I'd write
$$ P(X \in \{a_1, a_2, |
44,469 | Clarification - Random Variable | The notation is the book is intentionally avoiding sums, but in this case it leads to confusion. I prefer the second expression below.
$$
P(X = a_j \text{ for some }a_j) = \sum_{i = 1}^n P\left(X = a_i\right) \,=\, 1
$$
In you formula, if I interpret "for some $j$", it is not correct. The variable X is not equal to a ... | Clarification - Random Variable | The notation is the book is intentionally avoiding sums, but in this case it leads to confusion. I prefer the second expression below.
$$
P(X = a_j \text{ for some }a_j) = \sum_{i = 1}^n P\left(X = a | Clarification - Random Variable
The notation is the book is intentionally avoiding sums, but in this case it leads to confusion. I prefer the second expression below.
$$
P(X = a_j \text{ for some }a_j) = \sum_{i = 1}^n P\left(X = a_i\right) \,=\, 1
$$
In you formula, if I interpret "for some $j$", it is not correct. T... | Clarification - Random Variable
The notation is the book is intentionally avoiding sums, but in this case it leads to confusion. I prefer the second expression below.
$$
P(X = a_j \text{ for some }a_j) = \sum_{i = 1}^n P\left(X = a |
44,470 | Variational Autoencoder and Covariance Matrix | The diagonal covariance matrix is an explicit statement about the kind of latent representation the researcher wants the model to learn: a representation that can be modeled as independent Gaussians.
Additionally, @Firebug points out in comments that a symmetric, PD matrix can be diagonalized without any loss of inform... | Variational Autoencoder and Covariance Matrix | The diagonal covariance matrix is an explicit statement about the kind of latent representation the researcher wants the model to learn: a representation that can be modeled as independent Gaussians.
| Variational Autoencoder and Covariance Matrix
The diagonal covariance matrix is an explicit statement about the kind of latent representation the researcher wants the model to learn: a representation that can be modeled as independent Gaussians.
Additionally, @Firebug points out in comments that a symmetric, PD matrix ... | Variational Autoencoder and Covariance Matrix
The diagonal covariance matrix is an explicit statement about the kind of latent representation the researcher wants the model to learn: a representation that can be modeled as independent Gaussians.
|
44,471 | Variational Autoencoder and Covariance Matrix | I'm working on something like this now.
Let's say the researcher wants a full covariance latent variable $Z ~ N(mu, \Sigma)$. Like the multiplication trick from VAE, we can have a matrix multiplication trick. Still sample from a high dimensional unit Gaussian, $e \sim N(0, I)$.
There is this property of linear transf... | Variational Autoencoder and Covariance Matrix | I'm working on something like this now.
Let's say the researcher wants a full covariance latent variable $Z ~ N(mu, \Sigma)$. Like the multiplication trick from VAE, we can have a matrix multiplicati | Variational Autoencoder and Covariance Matrix
I'm working on something like this now.
Let's say the researcher wants a full covariance latent variable $Z ~ N(mu, \Sigma)$. Like the multiplication trick from VAE, we can have a matrix multiplication trick. Still sample from a high dimensional unit Gaussian, $e \sim N(0,... | Variational Autoencoder and Covariance Matrix
I'm working on something like this now.
Let's say the researcher wants a full covariance latent variable $Z ~ N(mu, \Sigma)$. Like the multiplication trick from VAE, we can have a matrix multiplicati |
44,472 | Variational Autoencoder and Covariance Matrix | A variational autoencoder is based on variational inference. The zero covariance is an assumption, mean-field variational family, which makes optimization easier, since the latent variables are independent.
Check chapter 2.3 of this paper: https://arxiv.org/abs/1601.00670
They also briefly dive into other families:
On... | Variational Autoencoder and Covariance Matrix | A variational autoencoder is based on variational inference. The zero covariance is an assumption, mean-field variational family, which makes optimization easier, since the latent variables are indepe | Variational Autoencoder and Covariance Matrix
A variational autoencoder is based on variational inference. The zero covariance is an assumption, mean-field variational family, which makes optimization easier, since the latent variables are independent.
Check chapter 2.3 of this paper: https://arxiv.org/abs/1601.00670
T... | Variational Autoencoder and Covariance Matrix
A variational autoencoder is based on variational inference. The zero covariance is an assumption, mean-field variational family, which makes optimization easier, since the latent variables are indepe |
44,473 | What is the best way to display confidence intervals around a proportion? | A pretty standard approach (most common for relative effect measures such as odds ratios, risk ratios, rate ratios and hazard ratios) is to use a figure with axes that show probabilities (i.e. all the axis labels show probabilities), but which are on the logit scale. I.e. the distance from 0.5 to 0.73 (0 to 1 on the lo... | What is the best way to display confidence intervals around a proportion? | A pretty standard approach (most common for relative effect measures such as odds ratios, risk ratios, rate ratios and hazard ratios) is to use a figure with axes that show probabilities (i.e. all the | What is the best way to display confidence intervals around a proportion?
A pretty standard approach (most common for relative effect measures such as odds ratios, risk ratios, rate ratios and hazard ratios) is to use a figure with axes that show probabilities (i.e. all the axis labels show probabilities), but which ar... | What is the best way to display confidence intervals around a proportion?
A pretty standard approach (most common for relative effect measures such as odds ratios, risk ratios, rate ratios and hazard ratios) is to use a figure with axes that show probabilities (i.e. all the |
44,474 | What is the best way to display confidence intervals around a proportion? | I would say that it is beneficial to show the asymmetric confidence intervals in order for readers to (better) realize that the odds ratio is asymmetric around its null value. Especially showing the figure rather than reporting the 95% CIs in the text makes this stronger/clearer.
The same of course holds for other type... | What is the best way to display confidence intervals around a proportion? | I would say that it is beneficial to show the asymmetric confidence intervals in order for readers to (better) realize that the odds ratio is asymmetric around its null value. Especially showing the f | What is the best way to display confidence intervals around a proportion?
I would say that it is beneficial to show the asymmetric confidence intervals in order for readers to (better) realize that the odds ratio is asymmetric around its null value. Especially showing the figure rather than reporting the 95% CIs in the... | What is the best way to display confidence intervals around a proportion?
I would say that it is beneficial to show the asymmetric confidence intervals in order for readers to (better) realize that the odds ratio is asymmetric around its null value. Especially showing the f |
44,475 | Is there any special case where ridge regression can shrink coefficients to zero? | Suppose, as in the case of least squares methods, you are trying to solve a statistical estimation problem for a (vector-valued) parameter $\beta$ by minimizing an objective function $Q(\beta)$ (such as the sum of squares of the residuals). Ridge Regression "regularizes" the problem by adding a non-negative linear co... | Is there any special case where ridge regression can shrink coefficients to zero? | Suppose, as in the case of least squares methods, you are trying to solve a statistical estimation problem for a (vector-valued) parameter $\beta$ by minimizing an objective function $Q(\beta)$ (such | Is there any special case where ridge regression can shrink coefficients to zero?
Suppose, as in the case of least squares methods, you are trying to solve a statistical estimation problem for a (vector-valued) parameter $\beta$ by minimizing an objective function $Q(\beta)$ (such as the sum of squares of the residual... | Is there any special case where ridge regression can shrink coefficients to zero?
Suppose, as in the case of least squares methods, you are trying to solve a statistical estimation problem for a (vector-valued) parameter $\beta$ by minimizing an objective function $Q(\beta)$ (such |
44,476 | Is there any special case where ridge regression can shrink coefficients to zero? | Traditional OLS ridge regression indeed will only return zero coefficients when a traditional OLS regression would also give you zero coefficients - the shrinkage for the other coefficients can approach zero but never actually become equal to zero. Likewise, if you use nonnegative least square ridge regression coeffici... | Is there any special case where ridge regression can shrink coefficients to zero? | Traditional OLS ridge regression indeed will only return zero coefficients when a traditional OLS regression would also give you zero coefficients - the shrinkage for the other coefficients can approa | Is there any special case where ridge regression can shrink coefficients to zero?
Traditional OLS ridge regression indeed will only return zero coefficients when a traditional OLS regression would also give you zero coefficients - the shrinkage for the other coefficients can approach zero but never actually become equa... | Is there any special case where ridge regression can shrink coefficients to zero?
Traditional OLS ridge regression indeed will only return zero coefficients when a traditional OLS regression would also give you zero coefficients - the shrinkage for the other coefficients can approa |
44,477 | Is there any special case where ridge regression can shrink coefficients to zero? | I think it can, and it does it actually very frequently (shrink some coefficient near zero). If you do an internet search for "images" and search for "ridge regression coefficient path" you will see the visual output of a large quantity of ridge regression models and their respective coefficient path output.
What you ... | Is there any special case where ridge regression can shrink coefficients to zero? | I think it can, and it does it actually very frequently (shrink some coefficient near zero). If you do an internet search for "images" and search for "ridge regression coefficient path" you will see | Is there any special case where ridge regression can shrink coefficients to zero?
I think it can, and it does it actually very frequently (shrink some coefficient near zero). If you do an internet search for "images" and search for "ridge regression coefficient path" you will see the visual output of a large quantity ... | Is there any special case where ridge regression can shrink coefficients to zero?
I think it can, and it does it actually very frequently (shrink some coefficient near zero). If you do an internet search for "images" and search for "ridge regression coefficient path" you will see |
44,478 | In the R randomForest package for random forest feature selection, how is the dataset split for training and testing? | It does not use a separate training and testing set. Instead, standard accuracy estimation in random forests takes advantage of an important feature: bagging, or bootstrap aggregation.
To construct a random forest, a large number of data subsets are generated by sampling with replacement from the full dataset. A separ... | In the R randomForest package for random forest feature selection, how is the dataset split for trai | It does not use a separate training and testing set. Instead, standard accuracy estimation in random forests takes advantage of an important feature: bagging, or bootstrap aggregation.
To construct a | In the R randomForest package for random forest feature selection, how is the dataset split for training and testing?
It does not use a separate training and testing set. Instead, standard accuracy estimation in random forests takes advantage of an important feature: bagging, or bootstrap aggregation.
To construct a r... | In the R randomForest package for random forest feature selection, how is the dataset split for trai
It does not use a separate training and testing set. Instead, standard accuracy estimation in random forests takes advantage of an important feature: bagging, or bootstrap aggregation.
To construct a |
44,479 | In the R randomForest package for random forest feature selection, how is the dataset split for training and testing? | In order to calculate mean decrease in accuracy randomForest doesn't use train and test sets per se it uses something called the out of bag sample. Since each tree is built using a bootstrap sample (a sample of the same size as your dataset sampled with replacement) there will be records that are in your dataset that ... | In the R randomForest package for random forest feature selection, how is the dataset split for trai | In order to calculate mean decrease in accuracy randomForest doesn't use train and test sets per se it uses something called the out of bag sample. Since each tree is built using a bootstrap sample ( | In the R randomForest package for random forest feature selection, how is the dataset split for training and testing?
In order to calculate mean decrease in accuracy randomForest doesn't use train and test sets per se it uses something called the out of bag sample. Since each tree is built using a bootstrap sample (a ... | In the R randomForest package for random forest feature selection, how is the dataset split for trai
In order to calculate mean decrease in accuracy randomForest doesn't use train and test sets per se it uses something called the out of bag sample. Since each tree is built using a bootstrap sample ( |
44,480 | In the R randomForest package for random forest feature selection, how is the dataset split for training and testing? | If you want to have a more detailed description you can read the Wikipedia article that answers your questions:
https://en.wikipedia.org/wiki/Random_forest
and this post:
this is a nice post for a more detailed explanation:
https://www.quora.com/What-is-the-out-of-bag-error-in-random-forests-What-does-it-mean-Whats-a-t... | In the R randomForest package for random forest feature selection, how is the dataset split for trai | If you want to have a more detailed description you can read the Wikipedia article that answers your questions:
https://en.wikipedia.org/wiki/Random_forest
and this post:
this is a nice post for a mor | In the R randomForest package for random forest feature selection, how is the dataset split for training and testing?
If you want to have a more detailed description you can read the Wikipedia article that answers your questions:
https://en.wikipedia.org/wiki/Random_forest
and this post:
this is a nice post for a more ... | In the R randomForest package for random forest feature selection, how is the dataset split for trai
If you want to have a more detailed description you can read the Wikipedia article that answers your questions:
https://en.wikipedia.org/wiki/Random_forest
and this post:
this is a nice post for a mor |
44,481 | Why is it called standard “error” and not standard “uncertainty”? | The question "why is this term used, rather than this other term" is, like much terminology, a matter of historical happenstance. Sometimes the outcome is felicitous and sometimes less so. I think that with a little context it makes reasonable sense in this case.
Yule used it in 1897$^{[1]}$, in the context of a partic... | Why is it called standard “error” and not standard “uncertainty”? | The question "why is this term used, rather than this other term" is, like much terminology, a matter of historical happenstance. Sometimes the outcome is felicitous and sometimes less so. I think tha | Why is it called standard “error” and not standard “uncertainty”?
The question "why is this term used, rather than this other term" is, like much terminology, a matter of historical happenstance. Sometimes the outcome is felicitous and sometimes less so. I think that with a little context it makes reasonable sense in t... | Why is it called standard “error” and not standard “uncertainty”?
The question "why is this term used, rather than this other term" is, like much terminology, a matter of historical happenstance. Sometimes the outcome is felicitous and sometimes less so. I think tha |
44,482 | Is a loss function the flip side of a coin to a utility function, or are they not related? | Loss is a negative utility. If you need an authoritative source for this, check the Statistical Decision Theory book by James O. Berger (p. 53):
Once $U(\theta, a)$ has been obtained, the loss function can simply be
defined as
$$ L(\theta, a) = -U(\theta, a). \tag{2.3} $$
The same is stated by Christian P. Robert i... | Is a loss function the flip side of a coin to a utility function, or are they not related? | Loss is a negative utility. If you need an authoritative source for this, check the Statistical Decision Theory book by James O. Berger (p. 53):
Once $U(\theta, a)$ has been obtained, the loss functi | Is a loss function the flip side of a coin to a utility function, or are they not related?
Loss is a negative utility. If you need an authoritative source for this, check the Statistical Decision Theory book by James O. Berger (p. 53):
Once $U(\theta, a)$ has been obtained, the loss function can simply be
defined as... | Is a loss function the flip side of a coin to a utility function, or are they not related?
Loss is a negative utility. If you need an authoritative source for this, check the Statistical Decision Theory book by James O. Berger (p. 53):
Once $U(\theta, a)$ has been obtained, the loss functi |
44,483 | Is a loss function the flip side of a coin to a utility function, or are they not related? | $U(x)=-\mathcal{L}(x)$. I cannot imagine you will find anything on the internet. I believe you can find a formal treatment of these functions in Geweke's "Contemporary Bayesian Econometrics and Statistics." | Is a loss function the flip side of a coin to a utility function, or are they not related? | $U(x)=-\mathcal{L}(x)$. I cannot imagine you will find anything on the internet. I believe you can find a formal treatment of these functions in Geweke's "Contemporary Bayesian Econometrics and Stat | Is a loss function the flip side of a coin to a utility function, or are they not related?
$U(x)=-\mathcal{L}(x)$. I cannot imagine you will find anything on the internet. I believe you can find a formal treatment of these functions in Geweke's "Contemporary Bayesian Econometrics and Statistics." | Is a loss function the flip side of a coin to a utility function, or are they not related?
$U(x)=-\mathcal{L}(x)$. I cannot imagine you will find anything on the internet. I believe you can find a formal treatment of these functions in Geweke's "Contemporary Bayesian Econometrics and Stat |
44,484 | R caret Naive Bayes (untuned) results differ from klaR | The problem lies in the fact that you use a different specification in the models.
In fit1 and fit2 you use the x and y combination, in fit3 the formula notation
If you switch all models in the formula notation (type ~ ., data = spam) you will see an Accuracy of 0.7135
If you switch all models in the x / y notation (sp... | R caret Naive Bayes (untuned) results differ from klaR | The problem lies in the fact that you use a different specification in the models.
In fit1 and fit2 you use the x and y combination, in fit3 the formula notation
If you switch all models in the formul | R caret Naive Bayes (untuned) results differ from klaR
The problem lies in the fact that you use a different specification in the models.
In fit1 and fit2 you use the x and y combination, in fit3 the formula notation
If you switch all models in the formula notation (type ~ ., data = spam) you will see an Accuracy of 0.... | R caret Naive Bayes (untuned) results differ from klaR
The problem lies in the fact that you use a different specification in the models.
In fit1 and fit2 you use the x and y combination, in fit3 the formula notation
If you switch all models in the formul |
44,485 | R caret Naive Bayes (untuned) results differ from klaR | From my knowledge, for the first two models, you shouldn't be giving the whole spam data frame as the training variables (the class labels are considered as a feature in this case). Instead, you should use:
fit1 <- naiveBayes(spam[,-58], spam$type, type="raw")
this way it will produce the same results with (type ~., d... | R caret Naive Bayes (untuned) results differ from klaR | From my knowledge, for the first two models, you shouldn't be giving the whole spam data frame as the training variables (the class labels are considered as a feature in this case). Instead, you shoul | R caret Naive Bayes (untuned) results differ from klaR
From my knowledge, for the first two models, you shouldn't be giving the whole spam data frame as the training variables (the class labels are considered as a feature in this case). Instead, you should use:
fit1 <- naiveBayes(spam[,-58], spam$type, type="raw")
thi... | R caret Naive Bayes (untuned) results differ from klaR
From my knowledge, for the first two models, you shouldn't be giving the whole spam data frame as the training variables (the class labels are considered as a feature in this case). Instead, you shoul |
44,486 | R caret Naive Bayes (untuned) results differ from klaR | The difference is whether x includes the full matrix including class variable, or whether y is specifically excluded from x.
# y included in x -> Accuracy : 0.7266
fit3 <- train(
x=spam,
y=spam$type,
method = "nb",
trControl = trainControl(method="none"),
tuneGrid = data.frame(usekernel=FALSE,fL=0,adjus... | R caret Naive Bayes (untuned) results differ from klaR | The difference is whether x includes the full matrix including class variable, or whether y is specifically excluded from x.
# y included in x -> Accuracy : 0.7266
fit3 <- train(
x=spam,
y=spam | R caret Naive Bayes (untuned) results differ from klaR
The difference is whether x includes the full matrix including class variable, or whether y is specifically excluded from x.
# y included in x -> Accuracy : 0.7266
fit3 <- train(
x=spam,
y=spam$type,
method = "nb",
trControl = trainControl(method="none... | R caret Naive Bayes (untuned) results differ from klaR
The difference is whether x includes the full matrix including class variable, or whether y is specifically excluded from x.
# y included in x -> Accuracy : 0.7266
fit3 <- train(
x=spam,
y=spam |
44,487 | Interpretation of bs(x) and gam Results | bs stands for basis spline. A complete understanding takes a bit of a digression into linear algebra.
First, a natural cubic spline is a very specific, rather rigid, species of curve. natural cubic splines come equipped with a collection of knots $x_1, x_2, \ldots, x_n$, and the definition is as follows.
To the left... | Interpretation of bs(x) and gam Results | bs stands for basis spline. A complete understanding takes a bit of a digression into linear algebra.
First, a natural cubic spline is a very specific, rather rigid, species of curve. natural cubic | Interpretation of bs(x) and gam Results
bs stands for basis spline. A complete understanding takes a bit of a digression into linear algebra.
First, a natural cubic spline is a very specific, rather rigid, species of curve. natural cubic splines come equipped with a collection of knots $x_1, x_2, \ldots, x_n$, and th... | Interpretation of bs(x) and gam Results
bs stands for basis spline. A complete understanding takes a bit of a digression into linear algebra.
First, a natural cubic spline is a very specific, rather rigid, species of curve. natural cubic |
44,488 | Why do degrees of freedom impact statistical power? | In the Anderson and Rubin Statistic case you compute the test statistic directly from the model without using an estimator: your assumption is that at $\beta=\beta_0$ you have $\mathbb{E}\left( Z^\prime[Y-X\beta]\right)=0$. For each instrument $z_k$ you have a central limit theorem (CLT) $\sqrt{n}(\frac{1}{n}\sum_iz_{k... | Why do degrees of freedom impact statistical power? | In the Anderson and Rubin Statistic case you compute the test statistic directly from the model without using an estimator: your assumption is that at $\beta=\beta_0$ you have $\mathbb{E}\left( Z^\pri | Why do degrees of freedom impact statistical power?
In the Anderson and Rubin Statistic case you compute the test statistic directly from the model without using an estimator: your assumption is that at $\beta=\beta_0$ you have $\mathbb{E}\left( Z^\prime[Y-X\beta]\right)=0$. For each instrument $z_k$ you have a central... | Why do degrees of freedom impact statistical power?
In the Anderson and Rubin Statistic case you compute the test statistic directly from the model without using an estimator: your assumption is that at $\beta=\beta_0$ you have $\mathbb{E}\left( Z^\pri |
44,489 | Why do degrees of freedom impact statistical power? | In regression there are two kinds of degrees of freedom. As described well below, the denominator or error or residual d.f. is relevant to regression models that have residuals and residual variance. As shown above, this is strongly a function of the sample size, and the more the merrier. On the other hand, numerato... | Why do degrees of freedom impact statistical power? | In regression there are two kinds of degrees of freedom. As described well below, the denominator or error or residual d.f. is relevant to regression models that have residuals and residual variance. | Why do degrees of freedom impact statistical power?
In regression there are two kinds of degrees of freedom. As described well below, the denominator or error or residual d.f. is relevant to regression models that have residuals and residual variance. As shown above, this is strongly a function of the sample size, an... | Why do degrees of freedom impact statistical power?
In regression there are two kinds of degrees of freedom. As described well below, the denominator or error or residual d.f. is relevant to regression models that have residuals and residual variance. |
44,490 | Why do degrees of freedom impact statistical power? | Definition & Overview
Degrees of freedom is the number of values that are free to vary when when the value of some statistic, like $\bar{X}$ or $\hat{\sigma}^2$, is known. In other words, it is the number of values that need to be known in order to know all of the values.
Sometimes, such as in the $t$-distribution, d... | Why do degrees of freedom impact statistical power? | Definition & Overview
Degrees of freedom is the number of values that are free to vary when when the value of some statistic, like $\bar{X}$ or $\hat{\sigma}^2$, is known. In other words, it is the n | Why do degrees of freedom impact statistical power?
Definition & Overview
Degrees of freedom is the number of values that are free to vary when when the value of some statistic, like $\bar{X}$ or $\hat{\sigma}^2$, is known. In other words, it is the number of values that need to be known in order to know all of the va... | Why do degrees of freedom impact statistical power?
Definition & Overview
Degrees of freedom is the number of values that are free to vary when when the value of some statistic, like $\bar{X}$ or $\hat{\sigma}^2$, is known. In other words, it is the n |
44,491 | How do you interpret a significant but weak correlation? | More meaningful in this case is the $\text{R}^2$ which explains the proportion of variation in your observations accounted by the association. For example if your $R$ was 0.1 (p= 0.005) due to the large sample size, it means 1% of the variation in tail lesions in pigs is accounted for by abscesses. In a multifactorial ... | How do you interpret a significant but weak correlation? | More meaningful in this case is the $\text{R}^2$ which explains the proportion of variation in your observations accounted by the association. For example if your $R$ was 0.1 (p= 0.005) due to the lar | How do you interpret a significant but weak correlation?
More meaningful in this case is the $\text{R}^2$ which explains the proportion of variation in your observations accounted by the association. For example if your $R$ was 0.1 (p= 0.005) due to the large sample size, it means 1% of the variation in tail lesions in... | How do you interpret a significant but weak correlation?
More meaningful in this case is the $\text{R}^2$ which explains the proportion of variation in your observations accounted by the association. For example if your $R$ was 0.1 (p= 0.005) due to the lar |
44,492 | How do you interpret a significant but weak correlation? | You could say it like this:
The association is small, but not zero.
However, I don't know that I'd call a V of 0.288 "small".
Don't confuse "statistically significant" with important. Statistical significance is very different from practical importance. | How do you interpret a significant but weak correlation? | You could say it like this:
The association is small, but not zero.
However, I don't know that I'd call a V of 0.288 "small".
Don't confuse "statistically significant" with important. Statistical | How do you interpret a significant but weak correlation?
You could say it like this:
The association is small, but not zero.
However, I don't know that I'd call a V of 0.288 "small".
Don't confuse "statistically significant" with important. Statistical significance is very different from practical importance. | How do you interpret a significant but weak correlation?
You could say it like this:
The association is small, but not zero.
However, I don't know that I'd call a V of 0.288 "small".
Don't confuse "statistically significant" with important. Statistical |
44,493 | How do you interpret a significant but weak correlation? | Adding on to @Glen_b 's excellent answer and your comments there.
As he said, it is significant but weak because the sample size is large enough to make a small effect significant. But now you need a way of showing the effect size. V is one such way, but it isn't intuitive to many and is not as well known as some other... | How do you interpret a significant but weak correlation? | Adding on to @Glen_b 's excellent answer and your comments there.
As he said, it is significant but weak because the sample size is large enough to make a small effect significant. But now you need a | How do you interpret a significant but weak correlation?
Adding on to @Glen_b 's excellent answer and your comments there.
As he said, it is significant but weak because the sample size is large enough to make a small effect significant. But now you need a way of showing the effect size. V is one such way, but it isn't... | How do you interpret a significant but weak correlation?
Adding on to @Glen_b 's excellent answer and your comments there.
As he said, it is significant but weak because the sample size is large enough to make a small effect significant. But now you need a |
44,494 | How do you interpret a significant but weak correlation? | I like to comment on the perceived usefulness of the relationship. For instance:
The association is statistically significant but not practically relevant.
That being said, your association doesn't seem to be that weak. | How do you interpret a significant but weak correlation? | I like to comment on the perceived usefulness of the relationship. For instance:
The association is statistically significant but not practically relevant.
That being said, your association doesn't | How do you interpret a significant but weak correlation?
I like to comment on the perceived usefulness of the relationship. For instance:
The association is statistically significant but not practically relevant.
That being said, your association doesn't seem to be that weak. | How do you interpret a significant but weak correlation?
I like to comment on the perceived usefulness of the relationship. For instance:
The association is statistically significant but not practically relevant.
That being said, your association doesn't |
44,495 | How to get Sub-Training and Sub-Test from cross validation in Caret | So using 10-fold CV will split the data into 10 different sets of roughly the same size. The model is fit on 90% and the remaining 10% is used to estimate accuracy. This process continues "round robin" 9 more times.
The accuracy is the average of the 10 holdouts for each tuning value. For example:
> set.seed(1)
> train... | How to get Sub-Training and Sub-Test from cross validation in Caret | So using 10-fold CV will split the data into 10 different sets of roughly the same size. The model is fit on 90% and the remaining 10% is used to estimate accuracy. This process continues "round robin | How to get Sub-Training and Sub-Test from cross validation in Caret
So using 10-fold CV will split the data into 10 different sets of roughly the same size. The model is fit on 90% and the remaining 10% is used to estimate accuracy. This process continues "round robin" 9 more times.
The accuracy is the average of the 1... | How to get Sub-Training and Sub-Test from cross validation in Caret
So using 10-fold CV will split the data into 10 different sets of roughly the same size. The model is fit on 90% and the remaining 10% is used to estimate accuracy. This process continues "round robin |
44,496 | How to determine the confidence interval or significance of a covariance estimate | John's answer is correct. I will just try and explain it a bit more clearly.
The covariance, $\sigma(x, y)$, is given as: $$\sigma(x, y)=E[(x-\mu_x)(y-\mu_y)]$$ to consider if a value f the covariance is significantly different from zero first consider what are the limits on the covariance. The range of covariance poss... | How to determine the confidence interval or significance of a covariance estimate | John's answer is correct. I will just try and explain it a bit more clearly.
The covariance, $\sigma(x, y)$, is given as: $$\sigma(x, y)=E[(x-\mu_x)(y-\mu_y)]$$ to consider if a value f the covariance | How to determine the confidence interval or significance of a covariance estimate
John's answer is correct. I will just try and explain it a bit more clearly.
The covariance, $\sigma(x, y)$, is given as: $$\sigma(x, y)=E[(x-\mu_x)(y-\mu_y)]$$ to consider if a value f the covariance is significantly different from zero ... | How to determine the confidence interval or significance of a covariance estimate
John's answer is correct. I will just try and explain it a bit more clearly.
The covariance, $\sigma(x, y)$, is given as: $$\sigma(x, y)=E[(x-\mu_x)(y-\mu_y)]$$ to consider if a value f the covariance |
44,497 | How to determine the confidence interval or significance of a covariance estimate | Correlation can be calculated as the covariance divided by the geometric mean variance. It's the proportion of covariance given the variance. Therefore, the correlation includes the covariance you want to assess in a standardized way and has known solutions for your questions. If there's an issue with the scaling of th... | How to determine the confidence interval or significance of a covariance estimate | Correlation can be calculated as the covariance divided by the geometric mean variance. It's the proportion of covariance given the variance. Therefore, the correlation includes the covariance you wan | How to determine the confidence interval or significance of a covariance estimate
Correlation can be calculated as the covariance divided by the geometric mean variance. It's the proportion of covariance given the variance. Therefore, the correlation includes the covariance you want to assess in a standardized way and ... | How to determine the confidence interval or significance of a covariance estimate
Correlation can be calculated as the covariance divided by the geometric mean variance. It's the proportion of covariance given the variance. Therefore, the correlation includes the covariance you wan |
44,498 | How to calculate log-normal parameters using the mean and std of the given distribution | Let m and s be the mean and sd of $X$ on the original scale. The appropriate mean and sd on the log scale can be found after a little algebra to be
$E(\log(X)) = \log(m) - \frac{1}{2} \log [ (s/m)^2 +1]$
$sd(\log(X)) = \sqrt{\log [(s/m)^2 +1]}$ | How to calculate log-normal parameters using the mean and std of the given distribution | Let m and s be the mean and sd of $X$ on the original scale. The appropriate mean and sd on the log scale can be found after a little algebra to be
$E(\log(X)) = \log(m) - \frac{1}{2} \log [ (s/m)^2 | How to calculate log-normal parameters using the mean and std of the given distribution
Let m and s be the mean and sd of $X$ on the original scale. The appropriate mean and sd on the log scale can be found after a little algebra to be
$E(\log(X)) = \log(m) - \frac{1}{2} \log [ (s/m)^2 +1]$
$sd(\log(X)) = \sqrt{\log [... | How to calculate log-normal parameters using the mean and std of the given distribution
Let m and s be the mean and sd of $X$ on the original scale. The appropriate mean and sd on the log scale can be found after a little algebra to be
$E(\log(X)) = \log(m) - \frac{1}{2} \log [ (s/m)^2 |
44,499 | Probability that the square of a random integer ends in 1 | In fact that answer is not sufficiently justified given the information in the question.
It depends on the distribution over the positive integers. The question says "randomly chosen", and the burning question is "what the heck does that mean"?
The positive integers can't all be chosen with equal probability*, so the a... | Probability that the square of a random integer ends in 1 | In fact that answer is not sufficiently justified given the information in the question.
It depends on the distribution over the positive integers. The question says "randomly chosen", and the burning | Probability that the square of a random integer ends in 1
In fact that answer is not sufficiently justified given the information in the question.
It depends on the distribution over the positive integers. The question says "randomly chosen", and the burning question is "what the heck does that mean"?
The positive inte... | Probability that the square of a random integer ends in 1
In fact that answer is not sufficiently justified given the information in the question.
It depends on the distribution over the positive integers. The question says "randomly chosen", and the burning |
44,500 | Probability that the square of a random integer ends in 1 | When a mathematician asks to pick a "random integer" or "random natural number," they usually have in mind a limiting process in which the numbers all "become equally probable." The process can be quite general: I believe all that you need is that (a) the relative probabilities of any two sets should converge and (b) ... | Probability that the square of a random integer ends in 1 | When a mathematician asks to pick a "random integer" or "random natural number," they usually have in mind a limiting process in which the numbers all "become equally probable." The process can be qu | Probability that the square of a random integer ends in 1
When a mathematician asks to pick a "random integer" or "random natural number," they usually have in mind a limiting process in which the numbers all "become equally probable." The process can be quite general: I believe all that you need is that (a) the relat... | Probability that the square of a random integer ends in 1
When a mathematician asks to pick a "random integer" or "random natural number," they usually have in mind a limiting process in which the numbers all "become equally probable." The process can be qu |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.