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 |
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9,901 | Difference between regression analysis and analysis of variance? | The analysis of variance (ANOVA) is a body of statistical method of analyzing observations assumed to be of the structure
$y_i=\beta_1x_{i1}+\beta_2x_{i2}+\dots+\beta_px_{ip}+e_i,~i=1(1)n$,which are constituted of linear combinations of $p$ unknown quantities $\beta_1,\beta_2,\dots,\beta_p$ plus errors $e_1,e_2,\dots,e... | Difference between regression analysis and analysis of variance? | The analysis of variance (ANOVA) is a body of statistical method of analyzing observations assumed to be of the structure
$y_i=\beta_1x_{i1}+\beta_2x_{i2}+\dots+\beta_px_{ip}+e_i,~i=1(1)n$,which are c | Difference between regression analysis and analysis of variance?
The analysis of variance (ANOVA) is a body of statistical method of analyzing observations assumed to be of the structure
$y_i=\beta_1x_{i1}+\beta_2x_{i2}+\dots+\beta_px_{ip}+e_i,~i=1(1)n$,which are constituted of linear combinations of $p$ unknown quanti... | Difference between regression analysis and analysis of variance?
The analysis of variance (ANOVA) is a body of statistical method of analyzing observations assumed to be of the structure
$y_i=\beta_1x_{i1}+\beta_2x_{i2}+\dots+\beta_px_{ip}+e_i,~i=1(1)n$,which are c |
9,902 | Difference between regression analysis and analysis of variance? | In regression analysis you have one variable fixed and you want to know how the variable goes with the other variable.
In analysis of variance you want to know for example: If this specific animal food influences the weight of animals... SO one fixed var and the influence on the others. | Difference between regression analysis and analysis of variance? | In regression analysis you have one variable fixed and you want to know how the variable goes with the other variable.
In analysis of variance you want to know for example: If this specific animal foo | Difference between regression analysis and analysis of variance?
In regression analysis you have one variable fixed and you want to know how the variable goes with the other variable.
In analysis of variance you want to know for example: If this specific animal food influences the weight of animals... SO one fixed var ... | Difference between regression analysis and analysis of variance?
In regression analysis you have one variable fixed and you want to know how the variable goes with the other variable.
In analysis of variance you want to know for example: If this specific animal foo |
9,903 | Is there an equivalent to Kruskal Wallis one-way test for a two-way model? | You can use a permutation test.
Form your hypothesis as a full and reduced model test and using the original data compute the F-statistic for the full and reduced model test (or another stat of interest).
Now compute the fitted values and residuals for the reduced model, then randomly permute the residuals and add th... | Is there an equivalent to Kruskal Wallis one-way test for a two-way model? | You can use a permutation test.
Form your hypothesis as a full and reduced model test and using the original data compute the F-statistic for the full and reduced model test (or another stat of inte | Is there an equivalent to Kruskal Wallis one-way test for a two-way model?
You can use a permutation test.
Form your hypothesis as a full and reduced model test and using the original data compute the F-statistic for the full and reduced model test (or another stat of interest).
Now compute the fitted values and resi... | Is there an equivalent to Kruskal Wallis one-way test for a two-way model?
You can use a permutation test.
Form your hypothesis as a full and reduced model test and using the original data compute the F-statistic for the full and reduced model test (or another stat of inte |
9,904 | Is there an equivalent to Kruskal Wallis one-way test for a two-way model? | The Kruskal-Wallis test is a special case of the proportional odds model. You can use the proportional odds model to model multiple factors, adjust for covariates, etc. | Is there an equivalent to Kruskal Wallis one-way test for a two-way model? | The Kruskal-Wallis test is a special case of the proportional odds model. You can use the proportional odds model to model multiple factors, adjust for covariates, etc. | Is there an equivalent to Kruskal Wallis one-way test for a two-way model?
The Kruskal-Wallis test is a special case of the proportional odds model. You can use the proportional odds model to model multiple factors, adjust for covariates, etc. | Is there an equivalent to Kruskal Wallis one-way test for a two-way model?
The Kruskal-Wallis test is a special case of the proportional odds model. You can use the proportional odds model to model multiple factors, adjust for covariates, etc. |
9,905 | Is there an equivalent to Kruskal Wallis one-way test for a two-way model? | Friedman's test provides a non-parametric equivalent to a one-way ANOVA with a blocking factor, but can't do anything more complex than this. | Is there an equivalent to Kruskal Wallis one-way test for a two-way model? | Friedman's test provides a non-parametric equivalent to a one-way ANOVA with a blocking factor, but can't do anything more complex than this. | Is there an equivalent to Kruskal Wallis one-way test for a two-way model?
Friedman's test provides a non-parametric equivalent to a one-way ANOVA with a blocking factor, but can't do anything more complex than this. | Is there an equivalent to Kruskal Wallis one-way test for a two-way model?
Friedman's test provides a non-parametric equivalent to a one-way ANOVA with a blocking factor, but can't do anything more complex than this. |
9,906 | Is there an equivalent to Kruskal Wallis one-way test for a two-way model? | One nonparametric test for a two-way factorial design is the Scheirer–Ray–Hare test. It is described by Sokal and Rohlf (1995), and can be found on a variety of websites, though it appears to be not particularly well known or widely discussed.
Another approach is aligned ranks transformation anova (ART anova). With cu... | Is there an equivalent to Kruskal Wallis one-way test for a two-way model? | One nonparametric test for a two-way factorial design is the Scheirer–Ray–Hare test. It is described by Sokal and Rohlf (1995), and can be found on a variety of websites, though it appears to be not p | Is there an equivalent to Kruskal Wallis one-way test for a two-way model?
One nonparametric test for a two-way factorial design is the Scheirer–Ray–Hare test. It is described by Sokal and Rohlf (1995), and can be found on a variety of websites, though it appears to be not particularly well known or widely discussed.
A... | Is there an equivalent to Kruskal Wallis one-way test for a two-way model?
One nonparametric test for a two-way factorial design is the Scheirer–Ray–Hare test. It is described by Sokal and Rohlf (1995), and can be found on a variety of websites, though it appears to be not p |
9,907 | Pitfalls in experimental design: Avoiding dead experiments | I believe what Fisher meant in his famous quote goes beyond saying "We will do a full factorial design for our study" or another design approach. Consulting a statistician when planning the experiment means thinking about every aspect of the problem in an intelligent way, including the research objective, what variable... | Pitfalls in experimental design: Avoiding dead experiments | I believe what Fisher meant in his famous quote goes beyond saying "We will do a full factorial design for our study" or another design approach. Consulting a statistician when planning the experiment | Pitfalls in experimental design: Avoiding dead experiments
I believe what Fisher meant in his famous quote goes beyond saying "We will do a full factorial design for our study" or another design approach. Consulting a statistician when planning the experiment means thinking about every aspect of the problem in an intel... | Pitfalls in experimental design: Avoiding dead experiments
I believe what Fisher meant in his famous quote goes beyond saying "We will do a full factorial design for our study" or another design approach. Consulting a statistician when planning the experiment |
9,908 | Pitfalls in experimental design: Avoiding dead experiments | Two words: Sample Size...A power analysis is a must. By including a competent statistician on your team from the get-go, you will likely save yourself a great deal of frustration when you are writing the results and discussion sections of your manuscript or report.
It is all too common for a principal investigator to ... | Pitfalls in experimental design: Avoiding dead experiments | Two words: Sample Size...A power analysis is a must. By including a competent statistician on your team from the get-go, you will likely save yourself a great deal of frustration when you are writing | Pitfalls in experimental design: Avoiding dead experiments
Two words: Sample Size...A power analysis is a must. By including a competent statistician on your team from the get-go, you will likely save yourself a great deal of frustration when you are writing the results and discussion sections of your manuscript or rep... | Pitfalls in experimental design: Avoiding dead experiments
Two words: Sample Size...A power analysis is a must. By including a competent statistician on your team from the get-go, you will likely save yourself a great deal of frustration when you are writing |
9,909 | Pitfalls in experimental design: Avoiding dead experiments | I suppose it depends on how strictly you interpret the word "design". It is sometimes taken to mean completely randomized vs. randomized blocks, etc. I don't think I've seen a study that died from that. Also, as others have mentioned, I suspect "died" is too strong, but it depends on how you interpret the term. Cer... | Pitfalls in experimental design: Avoiding dead experiments | I suppose it depends on how strictly you interpret the word "design". It is sometimes taken to mean completely randomized vs. randomized blocks, etc. I don't think I've seen a study that died from t | Pitfalls in experimental design: Avoiding dead experiments
I suppose it depends on how strictly you interpret the word "design". It is sometimes taken to mean completely randomized vs. randomized blocks, etc. I don't think I've seen a study that died from that. Also, as others have mentioned, I suspect "died" is too... | Pitfalls in experimental design: Avoiding dead experiments
I suppose it depends on how strictly you interpret the word "design". It is sometimes taken to mean completely randomized vs. randomized blocks, etc. I don't think I've seen a study that died from t |
9,910 | Pitfalls in experimental design: Avoiding dead experiments | I've seen this kind of problem in survey-like and psychological experiments.
In one case, the entire experiment had to be chalked up to a learning experience. There were problems at multiple levels that resulted in a jumble of results, but results that seemed to give some support for the hypothesis. In the end, I was a... | Pitfalls in experimental design: Avoiding dead experiments | I've seen this kind of problem in survey-like and psychological experiments.
In one case, the entire experiment had to be chalked up to a learning experience. There were problems at multiple levels th | Pitfalls in experimental design: Avoiding dead experiments
I've seen this kind of problem in survey-like and psychological experiments.
In one case, the entire experiment had to be chalked up to a learning experience. There were problems at multiple levels that resulted in a jumble of results, but results that seemed t... | Pitfalls in experimental design: Avoiding dead experiments
I've seen this kind of problem in survey-like and psychological experiments.
In one case, the entire experiment had to be chalked up to a learning experience. There were problems at multiple levels th |
9,911 | How to interpret the output of predict.coxph? | Edit: the following description applies to survival versions 3.2-8 and below. Starting with version 3.2-9, the default behavior of predict.coxph() changes with respect to treating 0/1 (dummy indicator) variables. See NEWS.
predict.coxph() computes the hazard ratio relative to the sample average for all $p$ predictor va... | How to interpret the output of predict.coxph? | Edit: the following description applies to survival versions 3.2-8 and below. Starting with version 3.2-9, the default behavior of predict.coxph() changes with respect to treating 0/1 (dummy indicator | How to interpret the output of predict.coxph?
Edit: the following description applies to survival versions 3.2-8 and below. Starting with version 3.2-9, the default behavior of predict.coxph() changes with respect to treating 0/1 (dummy indicator) variables. See NEWS.
predict.coxph() computes the hazard ratio relative ... | How to interpret the output of predict.coxph?
Edit: the following description applies to survival versions 3.2-8 and below. Starting with version 3.2-9, the default behavior of predict.coxph() changes with respect to treating 0/1 (dummy indicator |
9,912 | Getting seRious about time series with R | There is a Time Series Task View that aims to summarize all the time series packages for R. It highlights some core packages that provide some essential functionality.
I would also recommend the book by Shumway and Stoffer and the associated website, although it is not so good for forecasting.
My blog post on "Economet... | Getting seRious about time series with R | There is a Time Series Task View that aims to summarize all the time series packages for R. It highlights some core packages that provide some essential functionality.
I would also recommend the book | Getting seRious about time series with R
There is a Time Series Task View that aims to summarize all the time series packages for R. It highlights some core packages that provide some essential functionality.
I would also recommend the book by Shumway and Stoffer and the associated website, although it is not so good f... | Getting seRious about time series with R
There is a Time Series Task View that aims to summarize all the time series packages for R. It highlights some core packages that provide some essential functionality.
I would also recommend the book |
9,913 | Getting seRious about time series with R | I've found the UseR! series book Introductory Time Series with R by Cowpertwait and Metcalfe very useful in translating my time series statistics textbooks into R-speak. | Getting seRious about time series with R | I've found the UseR! series book Introductory Time Series with R by Cowpertwait and Metcalfe very useful in translating my time series statistics textbooks into R-speak. | Getting seRious about time series with R
I've found the UseR! series book Introductory Time Series with R by Cowpertwait and Metcalfe very useful in translating my time series statistics textbooks into R-speak. | Getting seRious about time series with R
I've found the UseR! series book Introductory Time Series with R by Cowpertwait and Metcalfe very useful in translating my time series statistics textbooks into R-speak. |
9,914 | Getting seRious about time series with R | For ecologists, Tree diversity analysis can be a first healthy step into the right direction. The book is free, it comes with an R package (BiodiversityR) and gives you a taste of other eco-packages (like vegan). | Getting seRious about time series with R | For ecologists, Tree diversity analysis can be a first healthy step into the right direction. The book is free, it comes with an R package (BiodiversityR) and gives you a taste of other eco-packages ( | Getting seRious about time series with R
For ecologists, Tree diversity analysis can be a first healthy step into the right direction. The book is free, it comes with an R package (BiodiversityR) and gives you a taste of other eco-packages (like vegan). | Getting seRious about time series with R
For ecologists, Tree diversity analysis can be a first healthy step into the right direction. The book is free, it comes with an R package (BiodiversityR) and gives you a taste of other eco-packages ( |
9,915 | Best way to deal with heteroscedasticity? | It's a good question, but I think it's the wrong question. Your figure makes it clear that you have a more fundamental problem than heteroscedasticity, i.e. your model has a nonlinearity that you haven't accounted for. Many of the potential problems that a model can have (nonlinearity, interactions, outliers, heterosc... | Best way to deal with heteroscedasticity? | It's a good question, but I think it's the wrong question. Your figure makes it clear that you have a more fundamental problem than heteroscedasticity, i.e. your model has a nonlinearity that you hav | Best way to deal with heteroscedasticity?
It's a good question, but I think it's the wrong question. Your figure makes it clear that you have a more fundamental problem than heteroscedasticity, i.e. your model has a nonlinearity that you haven't accounted for. Many of the potential problems that a model can have (nonl... | Best way to deal with heteroscedasticity?
It's a good question, but I think it's the wrong question. Your figure makes it clear that you have a more fundamental problem than heteroscedasticity, i.e. your model has a nonlinearity that you hav |
9,916 | Best way to deal with heteroscedasticity? | I list a number of methods of dealing with heteroscedasticity (with R examples) here: Alternatives to one-way ANOVA for heteroskedastic data. Many of those recommendations would be less ideal because you have a single continuous variable, rather than a multi-level categorical variable, but it might be nice to read thr... | Best way to deal with heteroscedasticity? | I list a number of methods of dealing with heteroscedasticity (with R examples) here: Alternatives to one-way ANOVA for heteroskedastic data. Many of those recommendations would be less ideal because | Best way to deal with heteroscedasticity?
I list a number of methods of dealing with heteroscedasticity (with R examples) here: Alternatives to one-way ANOVA for heteroskedastic data. Many of those recommendations would be less ideal because you have a single continuous variable, rather than a multi-level categorical ... | Best way to deal with heteroscedasticity?
I list a number of methods of dealing with heteroscedasticity (with R examples) here: Alternatives to one-way ANOVA for heteroskedastic data. Many of those recommendations would be less ideal because |
9,917 | Best way to deal with heteroscedasticity? | Load the sandwich package and compute the var-cov matrix of your regression with var_cov<-vcovHC(regression_result, type = "HC4") (read the manual of sandwich).
Now with the lmtest package use the coeftest function:
coeftest(regression_result, df = Inf, var_cov) | Best way to deal with heteroscedasticity? | Load the sandwich package and compute the var-cov matrix of your regression with var_cov<-vcovHC(regression_result, type = "HC4") (read the manual of sandwich).
Now with the lmtest package use the coe | Best way to deal with heteroscedasticity?
Load the sandwich package and compute the var-cov matrix of your regression with var_cov<-vcovHC(regression_result, type = "HC4") (read the manual of sandwich).
Now with the lmtest package use the coeftest function:
coeftest(regression_result, df = Inf, var_cov) | Best way to deal with heteroscedasticity?
Load the sandwich package and compute the var-cov matrix of your regression with var_cov<-vcovHC(regression_result, type = "HC4") (read the manual of sandwich).
Now with the lmtest package use the coe |
9,918 | Best way to deal with heteroscedasticity? | How does the distribution of your data looks like? Does it look like a bell curve at all? From the subject matter, can it be normally distributed at all? Duration of a phone call may not be negative, for example. So in that specific case of calls a gamma distribution describes it well. And with gamma you can use genera... | Best way to deal with heteroscedasticity? | How does the distribution of your data looks like? Does it look like a bell curve at all? From the subject matter, can it be normally distributed at all? Duration of a phone call may not be negative, | Best way to deal with heteroscedasticity?
How does the distribution of your data looks like? Does it look like a bell curve at all? From the subject matter, can it be normally distributed at all? Duration of a phone call may not be negative, for example. So in that specific case of calls a gamma distribution describes ... | Best way to deal with heteroscedasticity?
How does the distribution of your data looks like? Does it look like a bell curve at all? From the subject matter, can it be normally distributed at all? Duration of a phone call may not be negative, |
9,919 | RMSE vs. Coefficient of Determination | I have used them both, and have a few points to make.
Rmse is useful because it is simple to explain. Everybody knows what it is.
Rmse does not show relative values. If $rmse=0.2$, you must specifically know the range $\alpha <y_x< \beta$. If $\alpha=1, \beta=1000$, then 0.2 is a good value. If $\alpha=0, \beta=1$, i... | RMSE vs. Coefficient of Determination | I have used them both, and have a few points to make.
Rmse is useful because it is simple to explain. Everybody knows what it is.
Rmse does not show relative values. If $rmse=0.2$, you must specifica | RMSE vs. Coefficient of Determination
I have used them both, and have a few points to make.
Rmse is useful because it is simple to explain. Everybody knows what it is.
Rmse does not show relative values. If $rmse=0.2$, you must specifically know the range $\alpha <y_x< \beta$. If $\alpha=1, \beta=1000$, then 0.2 is a... | RMSE vs. Coefficient of Determination
I have used them both, and have a few points to make.
Rmse is useful because it is simple to explain. Everybody knows what it is.
Rmse does not show relative values. If $rmse=0.2$, you must specifica |
9,920 | RMSE vs. Coefficient of Determination | No matter what Errror measurement you give, consider giving your complete result vector in an appendix. People who like to compare against your method but prefer another error measurement can derive such value from your table.
$R^2$:
Does not reflect systematic errors. Imagine you measure diameters instead of radii of... | RMSE vs. Coefficient of Determination | No matter what Errror measurement you give, consider giving your complete result vector in an appendix. People who like to compare against your method but prefer another error measurement can derive s | RMSE vs. Coefficient of Determination
No matter what Errror measurement you give, consider giving your complete result vector in an appendix. People who like to compare against your method but prefer another error measurement can derive such value from your table.
$R^2$:
Does not reflect systematic errors. Imagine you... | RMSE vs. Coefficient of Determination
No matter what Errror measurement you give, consider giving your complete result vector in an appendix. People who like to compare against your method but prefer another error measurement can derive s |
9,921 | RMSE vs. Coefficient of Determination | Both the Root-Mean-Square-Error (RMSE) and coefficient of determination ($R^2$) offer different, yet complementary, information that should be assessed when evaluating your physical model. Neither is "better", but some reports might focus more on one metric depending on the particular application.
I would use the foll... | RMSE vs. Coefficient of Determination | Both the Root-Mean-Square-Error (RMSE) and coefficient of determination ($R^2$) offer different, yet complementary, information that should be assessed when evaluating your physical model. Neither is | RMSE vs. Coefficient of Determination
Both the Root-Mean-Square-Error (RMSE) and coefficient of determination ($R^2$) offer different, yet complementary, information that should be assessed when evaluating your physical model. Neither is "better", but some reports might focus more on one metric depending on the particu... | RMSE vs. Coefficient of Determination
Both the Root-Mean-Square-Error (RMSE) and coefficient of determination ($R^2$) offer different, yet complementary, information that should be assessed when evaluating your physical model. Neither is |
9,922 | RMSE vs. Coefficient of Determination | There is also MAE, Mean Absolute Error. Unlike RMSE, it isn't overly sensitive to large errors. From what I've read, some fields prefer RMSE, others MAE. I like to use both. | RMSE vs. Coefficient of Determination | There is also MAE, Mean Absolute Error. Unlike RMSE, it isn't overly sensitive to large errors. From what I've read, some fields prefer RMSE, others MAE. I like to use both. | RMSE vs. Coefficient of Determination
There is also MAE, Mean Absolute Error. Unlike RMSE, it isn't overly sensitive to large errors. From what I've read, some fields prefer RMSE, others MAE. I like to use both. | RMSE vs. Coefficient of Determination
There is also MAE, Mean Absolute Error. Unlike RMSE, it isn't overly sensitive to large errors. From what I've read, some fields prefer RMSE, others MAE. I like to use both. |
9,923 | RMSE vs. Coefficient of Determination | If some number is added to each element of one of the vectors, RMSE changes. Same if all elements in one of or both vectors are multiplied by a number.
R code follows;
#RMSE vs pearson's correlation
one<-rnorm(100)
two<-one+rnorm(100)
rumis<-(two - one)^2
(RMSE<-sqrt(mean(rumis)))
cor(one,two)
oneA<-one+100
rumis<-(... | RMSE vs. Coefficient of Determination | If some number is added to each element of one of the vectors, RMSE changes. Same if all elements in one of or both vectors are multiplied by a number.
R code follows;
#RMSE vs pearson's correlation
o | RMSE vs. Coefficient of Determination
If some number is added to each element of one of the vectors, RMSE changes. Same if all elements in one of or both vectors are multiplied by a number.
R code follows;
#RMSE vs pearson's correlation
one<-rnorm(100)
two<-one+rnorm(100)
rumis<-(two - one)^2
(RMSE<-sqrt(mean(rumis)))... | RMSE vs. Coefficient of Determination
If some number is added to each element of one of the vectors, RMSE changes. Same if all elements in one of or both vectors are multiplied by a number.
R code follows;
#RMSE vs pearson's correlation
o |
9,924 | RMSE vs. Coefficient of Determination | Ultimately the difference is just standardization as both lead to the choice of the same model, because RMSE times the number of observations is in the numerator or R squared, and the denominator of the latter is constant across all models (just plot one measure against the other for 10 different models). | RMSE vs. Coefficient of Determination | Ultimately the difference is just standardization as both lead to the choice of the same model, because RMSE times the number of observations is in the numerator or R squared, and the denominator of t | RMSE vs. Coefficient of Determination
Ultimately the difference is just standardization as both lead to the choice of the same model, because RMSE times the number of observations is in the numerator or R squared, and the denominator of the latter is constant across all models (just plot one measure against the other f... | RMSE vs. Coefficient of Determination
Ultimately the difference is just standardization as both lead to the choice of the same model, because RMSE times the number of observations is in the numerator or R squared, and the denominator of t |
9,925 | RMSE vs. Coefficient of Determination | Actually,for statistical scientists should know the best fit of the model,then RMSE is very important for those people in his robust research.if RMSE is very close to zero,then the model is best fitted.
The coefficient of determination is good for other scientists like agricultural and other fields. It is a value betwe... | RMSE vs. Coefficient of Determination | Actually,for statistical scientists should know the best fit of the model,then RMSE is very important for those people in his robust research.if RMSE is very close to zero,then the model is best fitte | RMSE vs. Coefficient of Determination
Actually,for statistical scientists should know the best fit of the model,then RMSE is very important for those people in his robust research.if RMSE is very close to zero,then the model is best fitted.
The coefficient of determination is good for other scientists like agricultural... | RMSE vs. Coefficient of Determination
Actually,for statistical scientists should know the best fit of the model,then RMSE is very important for those people in his robust research.if RMSE is very close to zero,then the model is best fitte |
9,926 | Subsetting R time series vectors | Use the window function:
> window(qs, 2010, c(2010, 4))
Qtr1 Qtr2 Qtr3 Qtr4
2010 104 105 106 107 | Subsetting R time series vectors | Use the window function:
> window(qs, 2010, c(2010, 4))
Qtr1 Qtr2 Qtr3 Qtr4
2010 104 105 106 107 | Subsetting R time series vectors
Use the window function:
> window(qs, 2010, c(2010, 4))
Qtr1 Qtr2 Qtr3 Qtr4
2010 104 105 106 107 | Subsetting R time series vectors
Use the window function:
> window(qs, 2010, c(2010, 4))
Qtr1 Qtr2 Qtr3 Qtr4
2010 104 105 106 107 |
9,927 | Subsetting R time series vectors | Also useful, if you are combining multiple time series and don't want to have to have to window every one to get them to match, ts.union and ts.intersect. | Subsetting R time series vectors | Also useful, if you are combining multiple time series and don't want to have to have to window every one to get them to match, ts.union and ts.intersect. | Subsetting R time series vectors
Also useful, if you are combining multiple time series and don't want to have to have to window every one to get them to match, ts.union and ts.intersect. | Subsetting R time series vectors
Also useful, if you are combining multiple time series and don't want to have to have to window every one to get them to match, ts.union and ts.intersect. |
9,928 | Is there any difference between Frequentist and Bayesian on the definition of Likelihood? | There is no difference in the definition - in both cases, the likelihood function is any function of the parameter that is proportional to the sampling density. Strictly speaking we do not require that the likelihood be equal to the sampling density; it needs only be proportional, which allows removal of multiplicativ... | Is there any difference between Frequentist and Bayesian on the definition of Likelihood? | There is no difference in the definition - in both cases, the likelihood function is any function of the parameter that is proportional to the sampling density. Strictly speaking we do not require th | Is there any difference between Frequentist and Bayesian on the definition of Likelihood?
There is no difference in the definition - in both cases, the likelihood function is any function of the parameter that is proportional to the sampling density. Strictly speaking we do not require that the likelihood be equal to ... | Is there any difference between Frequentist and Bayesian on the definition of Likelihood?
There is no difference in the definition - in both cases, the likelihood function is any function of the parameter that is proportional to the sampling density. Strictly speaking we do not require th |
9,929 | Is there any difference between Frequentist and Bayesian on the definition of Likelihood? | The likelihood function is defined independently from $-$or prior to$-$ the statistical paradigm that is used for inference, as a function, $L(\theta;x)$ (or $L(\theta|x)$), of the parameter $\theta$, function that depends on $-$or is indexed by$-$ the observation(s) $x$ available for this inference. And also implicitl... | Is there any difference between Frequentist and Bayesian on the definition of Likelihood? | The likelihood function is defined independently from $-$or prior to$-$ the statistical paradigm that is used for inference, as a function, $L(\theta;x)$ (or $L(\theta|x)$), of the parameter $\theta$, | Is there any difference between Frequentist and Bayesian on the definition of Likelihood?
The likelihood function is defined independently from $-$or prior to$-$ the statistical paradigm that is used for inference, as a function, $L(\theta;x)$ (or $L(\theta|x)$), of the parameter $\theta$, function that depends on $-$o... | Is there any difference between Frequentist and Bayesian on the definition of Likelihood?
The likelihood function is defined independently from $-$or prior to$-$ the statistical paradigm that is used for inference, as a function, $L(\theta;x)$ (or $L(\theta|x)$), of the parameter $\theta$, |
9,930 | Is there any difference between Frequentist and Bayesian on the definition of Likelihood? | As a small addendum:
The name "Likelihood" is entirely misleading, because there are very many different possible meanings. Not only the "normal language" one, but also in statistics. I can think of at least three different, but even related expressions that are all called Likelihood; even in text books.
That said, whe... | Is there any difference between Frequentist and Bayesian on the definition of Likelihood? | As a small addendum:
The name "Likelihood" is entirely misleading, because there are very many different possible meanings. Not only the "normal language" one, but also in statistics. I can think of a | Is there any difference between Frequentist and Bayesian on the definition of Likelihood?
As a small addendum:
The name "Likelihood" is entirely misleading, because there are very many different possible meanings. Not only the "normal language" one, but also in statistics. I can think of at least three different, but e... | Is there any difference between Frequentist and Bayesian on the definition of Likelihood?
As a small addendum:
The name "Likelihood" is entirely misleading, because there are very many different possible meanings. Not only the "normal language" one, but also in statistics. I can think of a |
9,931 | AUC and class imbalance in training/test dataset | It depends how you mean the word sensitive. The ROC AUC is sensitive to class imbalance in the sense that when there is a minority class, you typically define this as the positive class and it will have a strong impact on the AUC value. This is very much desirable behaviour. Accuracy is for example not sensitive in tha... | AUC and class imbalance in training/test dataset | It depends how you mean the word sensitive. The ROC AUC is sensitive to class imbalance in the sense that when there is a minority class, you typically define this as the positive class and it will ha | AUC and class imbalance in training/test dataset
It depends how you mean the word sensitive. The ROC AUC is sensitive to class imbalance in the sense that when there is a minority class, you typically define this as the positive class and it will have a strong impact on the AUC value. This is very much desirable behavi... | AUC and class imbalance in training/test dataset
It depends how you mean the word sensitive. The ROC AUC is sensitive to class imbalance in the sense that when there is a minority class, you typically define this as the positive class and it will ha |
9,932 | AUC and class imbalance in training/test dataset | I think it is not safe to say that the AUC is insensitive to class imbalance, as it introduces some confusion to the reader. In case you mean that the score itself doesn't detect class imbalance, that's wrong, that's why the AUC is there. In case you mean insensitive such that changes in the class distribution don't ha... | AUC and class imbalance in training/test dataset | I think it is not safe to say that the AUC is insensitive to class imbalance, as it introduces some confusion to the reader. In case you mean that the score itself doesn't detect class imbalance, that | AUC and class imbalance in training/test dataset
I think it is not safe to say that the AUC is insensitive to class imbalance, as it introduces some confusion to the reader. In case you mean that the score itself doesn't detect class imbalance, that's wrong, that's why the AUC is there. In case you mean insensitive suc... | AUC and class imbalance in training/test dataset
I think it is not safe to say that the AUC is insensitive to class imbalance, as it introduces some confusion to the reader. In case you mean that the score itself doesn't detect class imbalance, that |
9,933 | AUC and class imbalance in training/test dataset | (a 3-years late answer, but maybe still useful!)
ROC is sensitive to the class-imbalance issue, meaning that it favors the class with larger population solely because of its higher population. In other words, it is biased toward the larger population when it comes to classification/prediction.
This is indeed problemati... | AUC and class imbalance in training/test dataset | (a 3-years late answer, but maybe still useful!)
ROC is sensitive to the class-imbalance issue, meaning that it favors the class with larger population solely because of its higher population. In othe | AUC and class imbalance in training/test dataset
(a 3-years late answer, but maybe still useful!)
ROC is sensitive to the class-imbalance issue, meaning that it favors the class with larger population solely because of its higher population. In other words, it is biased toward the larger population when it comes to cla... | AUC and class imbalance in training/test dataset
(a 3-years late answer, but maybe still useful!)
ROC is sensitive to the class-imbalance issue, meaning that it favors the class with larger population solely because of its higher population. In othe |
9,934 | AUC and class imbalance in training/test dataset | I choose to disgaree with the answer given by @Azim. Emphirical research has shown ROC is insentive to class imbalance. This has been extensively discussed by Tom Fawcett, see Section 4.2 of his paper An introduction to ROC analysis
4.2. Class skew
ROC curves have an attractive property: they are insensitive to chang... | AUC and class imbalance in training/test dataset | I choose to disgaree with the answer given by @Azim. Emphirical research has shown ROC is insentive to class imbalance. This has been extensively discussed by Tom Fawcett, see Section 4.2 of his pape | AUC and class imbalance in training/test dataset
I choose to disgaree with the answer given by @Azim. Emphirical research has shown ROC is insentive to class imbalance. This has been extensively discussed by Tom Fawcett, see Section 4.2 of his paper An introduction to ROC analysis
4.2. Class skew
ROC curves have an a... | AUC and class imbalance in training/test dataset
I choose to disgaree with the answer given by @Azim. Emphirical research has shown ROC is insentive to class imbalance. This has been extensively discussed by Tom Fawcett, see Section 4.2 of his pape |
9,935 | Mean of the bootstrap sample vs statistic of the sample | Let's generalize, so as to focus on the crux of the matter. I will spell out the tiniest details so as to leave no doubts. The analysis requires only the following:
The arithmetic mean of a set of numbers $z_1, \ldots, z_m$ is defined to be
$$\frac{1}{m}\left(z_1 + \cdots + z_m\right).$$
Expectation is a linear ope... | Mean of the bootstrap sample vs statistic of the sample | Let's generalize, so as to focus on the crux of the matter. I will spell out the tiniest details so as to leave no doubts. The analysis requires only the following:
The arithmetic mean of a set of | Mean of the bootstrap sample vs statistic of the sample
Let's generalize, so as to focus on the crux of the matter. I will spell out the tiniest details so as to leave no doubts. The analysis requires only the following:
The arithmetic mean of a set of numbers $z_1, \ldots, z_m$ is defined to be
$$\frac{1}{m}\left(... | Mean of the bootstrap sample vs statistic of the sample
Let's generalize, so as to focus on the crux of the matter. I will spell out the tiniest details so as to leave no doubts. The analysis requires only the following:
The arithmetic mean of a set of |
9,936 | Mean of the bootstrap sample vs statistic of the sample | Since the bootstrap distribution associated with an iid sample $X_1,\ldots,X_n$ is defined as$$\hat{F}_n(x) = \frac{1}{n}\sum_{i=1}^n\mathbb{I}_{X_i\le x}\qquad X_i\stackrel{\text{iid}}{\sim}F(x)\,,$$
the mean of the bootstrap distribution $\hat{F}_n$ (conditional on the iid sample $X_1,\ldots,X_n$) is$$\mathbb{E}_{\ha... | Mean of the bootstrap sample vs statistic of the sample | Since the bootstrap distribution associated with an iid sample $X_1,\ldots,X_n$ is defined as$$\hat{F}_n(x) = \frac{1}{n}\sum_{i=1}^n\mathbb{I}_{X_i\le x}\qquad X_i\stackrel{\text{iid}}{\sim}F(x)\,,$$ | Mean of the bootstrap sample vs statistic of the sample
Since the bootstrap distribution associated with an iid sample $X_1,\ldots,X_n$ is defined as$$\hat{F}_n(x) = \frac{1}{n}\sum_{i=1}^n\mathbb{I}_{X_i\le x}\qquad X_i\stackrel{\text{iid}}{\sim}F(x)\,,$$
the mean of the bootstrap distribution $\hat{F}_n$ (conditional... | Mean of the bootstrap sample vs statistic of the sample
Since the bootstrap distribution associated with an iid sample $X_1,\ldots,X_n$ is defined as$$\hat{F}_n(x) = \frac{1}{n}\sum_{i=1}^n\mathbb{I}_{X_i\le x}\qquad X_i\stackrel{\text{iid}}{\sim}F(x)\,,$$ |
9,937 | Strategies for introducing advanced statistics to various audiences | This is a tricky question!
First, some thoughts on why this happens. I work in an area which does (or at least should) make extensive use of statistics, but where most practitioners are not statistical experts. Consequently one sees a lot of "I put a vector into excel's t-test function and this number fell out. Therefo... | Strategies for introducing advanced statistics to various audiences | This is a tricky question!
First, some thoughts on why this happens. I work in an area which does (or at least should) make extensive use of statistics, but where most practitioners are not statistica | Strategies for introducing advanced statistics to various audiences
This is a tricky question!
First, some thoughts on why this happens. I work in an area which does (or at least should) make extensive use of statistics, but where most practitioners are not statistical experts. Consequently one sees a lot of "I put a v... | Strategies for introducing advanced statistics to various audiences
This is a tricky question!
First, some thoughts on why this happens. I work in an area which does (or at least should) make extensive use of statistics, but where most practitioners are not statistica |
9,938 | Strategies for introducing advanced statistics to various audiences | Speaking from the perspective of a psychologist with only slight statistical sophistication: When you introduce the method, also introduce the tools. If you tell most researchers in my field a long story about a great new method, they're going to spend the whole time worried that the punchline is "and all you have to d... | Strategies for introducing advanced statistics to various audiences | Speaking from the perspective of a psychologist with only slight statistical sophistication: When you introduce the method, also introduce the tools. If you tell most researchers in my field a long st | Strategies for introducing advanced statistics to various audiences
Speaking from the perspective of a psychologist with only slight statistical sophistication: When you introduce the method, also introduce the tools. If you tell most researchers in my field a long story about a great new method, they're going to spend... | Strategies for introducing advanced statistics to various audiences
Speaking from the perspective of a psychologist with only slight statistical sophistication: When you introduce the method, also introduce the tools. If you tell most researchers in my field a long st |
9,939 | Strategies for introducing advanced statistics to various audiences | Thanks for this nice question Peter. I work at a medical research institution and deal with physicians who do research and publish in the medical journals. Often they are more interested in getting their paper published than "doing the statistics completely right". So when I propose an unfamilar technique they will ... | Strategies for introducing advanced statistics to various audiences | Thanks for this nice question Peter. I work at a medical research institution and deal with physicians who do research and publish in the medical journals. Often they are more interested in getting | Strategies for introducing advanced statistics to various audiences
Thanks for this nice question Peter. I work at a medical research institution and deal with physicians who do research and publish in the medical journals. Often they are more interested in getting their paper published than "doing the statistics com... | Strategies for introducing advanced statistics to various audiences
Thanks for this nice question Peter. I work at a medical research institution and deal with physicians who do research and publish in the medical journals. Often they are more interested in getting |
9,940 | Strategies for introducing advanced statistics to various audiences | There are some nice comments already made here, but I'll throw in my 2 cents. I'll preface this all by saying that I'm assuming we're talking about a situation where using the traditional "canned" techniques will damage the substantive conclusions reached by the analysis. If that's not the case, then I think that somet... | Strategies for introducing advanced statistics to various audiences | There are some nice comments already made here, but I'll throw in my 2 cents. I'll preface this all by saying that I'm assuming we're talking about a situation where using the traditional "canned" tec | Strategies for introducing advanced statistics to various audiences
There are some nice comments already made here, but I'll throw in my 2 cents. I'll preface this all by saying that I'm assuming we're talking about a situation where using the traditional "canned" techniques will damage the substantive conclusions reac... | Strategies for introducing advanced statistics to various audiences
There are some nice comments already made here, but I'll throw in my 2 cents. I'll preface this all by saying that I'm assuming we're talking about a situation where using the traditional "canned" tec |
9,941 | Strategies for introducing advanced statistics to various audiences | Some random thoughts because this is a complex issue...
I feel that a big problem is the lack of math education in a variety of professional disciplines and graduated programs. Without a mathematical understanding of statistics, it becomes a bunch of formulas to be applied according the case. Also, for getting a real u... | Strategies for introducing advanced statistics to various audiences | Some random thoughts because this is a complex issue...
I feel that a big problem is the lack of math education in a variety of professional disciplines and graduated programs. Without a mathematical | Strategies for introducing advanced statistics to various audiences
Some random thoughts because this is a complex issue...
I feel that a big problem is the lack of math education in a variety of professional disciplines and graduated programs. Without a mathematical understanding of statistics, it becomes a bunch of f... | Strategies for introducing advanced statistics to various audiences
Some random thoughts because this is a complex issue...
I feel that a big problem is the lack of math education in a variety of professional disciplines and graduated programs. Without a mathematical |
9,942 | Logistic regression or T test? | Both tests implicitly model the age-response relationship, but they do so in different ways. Which one to select depends on how you choose to model that relationship. Your choice ought to depend on an underlying theory, if there is one; on what kind of information you want to extract from the results; and on how the ... | Logistic regression or T test? | Both tests implicitly model the age-response relationship, but they do so in different ways. Which one to select depends on how you choose to model that relationship. Your choice ought to depend on | Logistic regression or T test?
Both tests implicitly model the age-response relationship, but they do so in different ways. Which one to select depends on how you choose to model that relationship. Your choice ought to depend on an underlying theory, if there is one; on what kind of information you want to extract fr... | Logistic regression or T test?
Both tests implicitly model the age-response relationship, but they do so in different ways. Which one to select depends on how you choose to model that relationship. Your choice ought to depend on |
9,943 | Logistic regression or T test? | This doesn't really answer the question but may still be of some interest. The standard assumption of a two sample $t$-test is that the conditional normal distribution of $X$ given a binary variable $Y$,
$$
X|Y=i \sim N(\mu_i,\sigma^2).
$$
This together with the assumption that $Y \sim \operatorname{bernoulli}(p)$ mar... | Logistic regression or T test? | This doesn't really answer the question but may still be of some interest. The standard assumption of a two sample $t$-test is that the conditional normal distribution of $X$ given a binary variable | Logistic regression or T test?
This doesn't really answer the question but may still be of some interest. The standard assumption of a two sample $t$-test is that the conditional normal distribution of $X$ given a binary variable $Y$,
$$
X|Y=i \sim N(\mu_i,\sigma^2).
$$
This together with the assumption that $Y \sim \... | Logistic regression or T test?
This doesn't really answer the question but may still be of some interest. The standard assumption of a two sample $t$-test is that the conditional normal distribution of $X$ given a binary variable |
9,944 | Logistic regression or T test? | The better test is the the one that better addresses your question. Neither is just better on it's face. The differences here are equivalent to those found when regressing y on x and x on y and the reasons for different results are similar. The variance being assessed depends on which variable is being treated as the r... | Logistic regression or T test? | The better test is the the one that better addresses your question. Neither is just better on it's face. The differences here are equivalent to those found when regressing y on x and x on y and the re | Logistic regression or T test?
The better test is the the one that better addresses your question. Neither is just better on it's face. The differences here are equivalent to those found when regressing y on x and x on y and the reasons for different results are similar. The variance being assessed depends on which var... | Logistic regression or T test?
The better test is the the one that better addresses your question. Neither is just better on it's face. The differences here are equivalent to those found when regressing y on x and x on y and the re |
9,945 | What is the daily job routine of the machine learning scientist? | Alex, I can't comment specifically on Germany or Switzerland, but I do work for an international company with a staff of over 100,000 people from all different countries. Most of these people have at least graduate level degrees, many have Masters and PhDs and, except for the HR and Admin staff most of us are expert in... | What is the daily job routine of the machine learning scientist? | Alex, I can't comment specifically on Germany or Switzerland, but I do work for an international company with a staff of over 100,000 people from all different countries. Most of these people have at | What is the daily job routine of the machine learning scientist?
Alex, I can't comment specifically on Germany or Switzerland, but I do work for an international company with a staff of over 100,000 people from all different countries. Most of these people have at least graduate level degrees, many have Masters and PhD... | What is the daily job routine of the machine learning scientist?
Alex, I can't comment specifically on Germany or Switzerland, but I do work for an international company with a staff of over 100,000 people from all different countries. Most of these people have at |
9,946 | What is the daily job routine of the machine learning scientist? | Before I describe my opinion of job routine, I will pick a few pieces of your post that I think are relevant (emphasis mine):
I'm a very curious person
Will work with intellectually challenging stuff
I need to be honest and say that also I hate to see someone else with a higher degree than me (vanity)
I can start a ca... | What is the daily job routine of the machine learning scientist? | Before I describe my opinion of job routine, I will pick a few pieces of your post that I think are relevant (emphasis mine):
I'm a very curious person
Will work with intellectually challenging stuff | What is the daily job routine of the machine learning scientist?
Before I describe my opinion of job routine, I will pick a few pieces of your post that I think are relevant (emphasis mine):
I'm a very curious person
Will work with intellectually challenging stuff
I need to be honest and say that also I hate to see so... | What is the daily job routine of the machine learning scientist?
Before I describe my opinion of job routine, I will pick a few pieces of your post that I think are relevant (emphasis mine):
I'm a very curious person
Will work with intellectually challenging stuff |
9,947 | What is the daily job routine of the machine learning scientist? | •What is it like to work as a data scientist/machine learner with a
master degree in the industry? What kind of work you do? Especially
when I read those ads on Amazon as a machine learning scientist, I
always wonder what they do.
The business problems do not really change depending on your degree, so you would ... | What is the daily job routine of the machine learning scientist? | •What is it like to work as a data scientist/machine learner with a
master degree in the industry? What kind of work you do? Especially
when I read those ads on Amazon as a machine learning scient | What is the daily job routine of the machine learning scientist?
•What is it like to work as a data scientist/machine learner with a
master degree in the industry? What kind of work you do? Especially
when I read those ads on Amazon as a machine learning scientist, I
always wonder what they do.
The business prob... | What is the daily job routine of the machine learning scientist?
•What is it like to work as a data scientist/machine learner with a
master degree in the industry? What kind of work you do? Especially
when I read those ads on Amazon as a machine learning scient |
9,948 | What is the daily job routine of the machine learning scientist? | Or you can try to join some research group where statisticians and machine learners are not an everyday appearance. For example infestation and disease spreading, botany or ecology, social insect or maybe social sciences?
I can´t give you exact examples, but if you are a good statistician/ML at a place where there are... | What is the daily job routine of the machine learning scientist? | Or you can try to join some research group where statisticians and machine learners are not an everyday appearance. For example infestation and disease spreading, botany or ecology, social insect or m | What is the daily job routine of the machine learning scientist?
Or you can try to join some research group where statisticians and machine learners are not an everyday appearance. For example infestation and disease spreading, botany or ecology, social insect or maybe social sciences?
I can´t give you exact examples,... | What is the daily job routine of the machine learning scientist?
Or you can try to join some research group where statisticians and machine learners are not an everyday appearance. For example infestation and disease spreading, botany or ecology, social insect or m |
9,949 | What is the daily job routine of the machine learning scientist? | I agree with the other answers. I would just emphasize that one common way (at least in the US) for people like you who hesitate between continuing with a PhD or doing the industry after their undergrad degrees is to apply for PhD, then take a leave (one year or more) if things aren't as great as they expected or simpl... | What is the daily job routine of the machine learning scientist? | I agree with the other answers. I would just emphasize that one common way (at least in the US) for people like you who hesitate between continuing with a PhD or doing the industry after their undergr | What is the daily job routine of the machine learning scientist?
I agree with the other answers. I would just emphasize that one common way (at least in the US) for people like you who hesitate between continuing with a PhD or doing the industry after their undergrad degrees is to apply for PhD, then take a leave (one ... | What is the daily job routine of the machine learning scientist?
I agree with the other answers. I would just emphasize that one common way (at least in the US) for people like you who hesitate between continuing with a PhD or doing the industry after their undergr |
9,950 | What is the daily job routine of the machine learning scientist? | To get a PhD, you have to advance the state of human knowledge. You don't just have to learn more stuff. You have to produce something original. This is a long, slow, and painful process, and not everyone succeeds at it. So you should do a PhD only if you think you have a new, creative, contribution to the field in you... | What is the daily job routine of the machine learning scientist? | To get a PhD, you have to advance the state of human knowledge. You don't just have to learn more stuff. You have to produce something original. This is a long, slow, and painful process, and not ever | What is the daily job routine of the machine learning scientist?
To get a PhD, you have to advance the state of human knowledge. You don't just have to learn more stuff. You have to produce something original. This is a long, slow, and painful process, and not everyone succeeds at it. So you should do a PhD only if you... | What is the daily job routine of the machine learning scientist?
To get a PhD, you have to advance the state of human knowledge. You don't just have to learn more stuff. You have to produce something original. This is a long, slow, and painful process, and not ever |
9,951 | What is the daily job routine of the machine learning scientist? | When you choose the /famous little company/ route, you have the freedom to establish a research department in your company.
Here, you can get annoyingly creative, as in, unrestrained... explore all your childhood fantasies, intellectually challenging stuff... you set the pace... you will be /the man/.
You don't have to... | What is the daily job routine of the machine learning scientist? | When you choose the /famous little company/ route, you have the freedom to establish a research department in your company.
Here, you can get annoyingly creative, as in, unrestrained... explore all yo | What is the daily job routine of the machine learning scientist?
When you choose the /famous little company/ route, you have the freedom to establish a research department in your company.
Here, you can get annoyingly creative, as in, unrestrained... explore all your childhood fantasies, intellectually challenging stuf... | What is the daily job routine of the machine learning scientist?
When you choose the /famous little company/ route, you have the freedom to establish a research department in your company.
Here, you can get annoyingly creative, as in, unrestrained... explore all yo |
9,952 | Spatial statistics models: CAR vs SAR | Non-spatial model
My House Value is a function of my home Gardening Investment.
SAR model
My House Value is a function of the House Values of my neighbours.
CAR model
My House Value is a function of the Gardening Investment of my neighbours. | Spatial statistics models: CAR vs SAR | Non-spatial model
My House Value is a function of my home Gardening Investment.
SAR model
My House Value is a function of the House Values of my neighbours.
CAR model
My House Value is a function of | Spatial statistics models: CAR vs SAR
Non-spatial model
My House Value is a function of my home Gardening Investment.
SAR model
My House Value is a function of the House Values of my neighbours.
CAR model
My House Value is a function of the Gardening Investment of my neighbours. | Spatial statistics models: CAR vs SAR
Non-spatial model
My House Value is a function of my home Gardening Investment.
SAR model
My House Value is a function of the House Values of my neighbours.
CAR model
My House Value is a function of |
9,953 | Spatial statistics models: CAR vs SAR | As the Encyclopedia of GIS states, the conditional autoregressive model (CAR) is appropriate for situations with first order dependency or relatively local spatial autocorrelation, and simultaneous autoregressive model (SAR) is more suitable where there are second order dependency or a more global spatial autocorrelat... | Spatial statistics models: CAR vs SAR | As the Encyclopedia of GIS states, the conditional autoregressive model (CAR) is appropriate for situations with first order dependency or relatively local spatial autocorrelation, and simultaneous au | Spatial statistics models: CAR vs SAR
As the Encyclopedia of GIS states, the conditional autoregressive model (CAR) is appropriate for situations with first order dependency or relatively local spatial autocorrelation, and simultaneous autoregressive model (SAR) is more suitable where there are second order dependency... | Spatial statistics models: CAR vs SAR
As the Encyclopedia of GIS states, the conditional autoregressive model (CAR) is appropriate for situations with first order dependency or relatively local spatial autocorrelation, and simultaneous au |
9,954 | How to test if my distribution is multimodal? | @NickCox has presented an interesting strategy (+1). I might consider it more exploratory in nature however, due to the concern that @whuber points out.
Let me suggest another strategy: You could fit a Gaussian finite mixture model. Note that this makes the very strong assumption that your data are drawn from one ... | How to test if my distribution is multimodal? | @NickCox has presented an interesting strategy (+1). I might consider it more exploratory in nature however, due to the concern that @whuber points out.
Let me suggest another strategy: You could | How to test if my distribution is multimodal?
@NickCox has presented an interesting strategy (+1). I might consider it more exploratory in nature however, due to the concern that @whuber points out.
Let me suggest another strategy: You could fit a Gaussian finite mixture model. Note that this makes the very strong... | How to test if my distribution is multimodal?
@NickCox has presented an interesting strategy (+1). I might consider it more exploratory in nature however, due to the concern that @whuber points out.
Let me suggest another strategy: You could |
9,955 | How to test if my distribution is multimodal? | Following up on the ideas in @Nick's answer and comments, you can see how wide the bandwidth needs to be to just flatten out the secondary mode:
Take this kernel density estimate as the proximal null—the distribution closest to the data yet still consistent with the null hypothesis that it's a sample from a unimodal p... | How to test if my distribution is multimodal? | Following up on the ideas in @Nick's answer and comments, you can see how wide the bandwidth needs to be to just flatten out the secondary mode:
Take this kernel density estimate as the proximal null | How to test if my distribution is multimodal?
Following up on the ideas in @Nick's answer and comments, you can see how wide the bandwidth needs to be to just flatten out the secondary mode:
Take this kernel density estimate as the proximal null—the distribution closest to the data yet still consistent with the null h... | How to test if my distribution is multimodal?
Following up on the ideas in @Nick's answer and comments, you can see how wide the bandwidth needs to be to just flatten out the secondary mode:
Take this kernel density estimate as the proximal null |
9,956 | How to test if my distribution is multimodal? | The things to worry about include:
The size of the dataset. It is not tiny, not large.
The dependence of what you see on histogram origin and bin width. With only one choice evident, you (and we) have no idea of sensitivity.
The dependence of what you see on kernel type and width and whatever other choices are made... | How to test if my distribution is multimodal? | The things to worry about include:
The size of the dataset. It is not tiny, not large.
The dependence of what you see on histogram origin and bin width. With only one choice evident, you (and we) h | How to test if my distribution is multimodal?
The things to worry about include:
The size of the dataset. It is not tiny, not large.
The dependence of what you see on histogram origin and bin width. With only one choice evident, you (and we) have no idea of sensitivity.
The dependence of what you see on kernel type... | How to test if my distribution is multimodal?
The things to worry about include:
The size of the dataset. It is not tiny, not large.
The dependence of what you see on histogram origin and bin width. With only one choice evident, you (and we) h |
9,957 | How to test if my distribution is multimodal? | LP Nonparametric Mode Identification (name of the algorithm LPMode, the ref of the paper is given below)
MaxEnt Modes [Red color triangles in the plot]: 12783.36 and 24654.28.
L2 Modes [Green color triangles in the plot]: 13054.70 and 24111.61.
Interesting to note the modal shapes, especially the second one which sho... | How to test if my distribution is multimodal? | LP Nonparametric Mode Identification (name of the algorithm LPMode, the ref of the paper is given below)
MaxEnt Modes [Red color triangles in the plot]: 12783.36 and 24654.28.
L2 Modes [Green color tr | How to test if my distribution is multimodal?
LP Nonparametric Mode Identification (name of the algorithm LPMode, the ref of the paper is given below)
MaxEnt Modes [Red color triangles in the plot]: 12783.36 and 24654.28.
L2 Modes [Green color triangles in the plot]: 13054.70 and 24111.61.
Interesting to note the mod... | How to test if my distribution is multimodal?
LP Nonparametric Mode Identification (name of the algorithm LPMode, the ref of the paper is given below)
MaxEnt Modes [Red color triangles in the plot]: 12783.36 and 24654.28.
L2 Modes [Green color tr |
9,958 | How to test if my distribution is multimodal? | I'll add that you can replace the progress bars, which don't illuminate all that much, with an iteration count instead with this:
x2.d[i] = Mclust(x2, G=2, verbose=FALSE)$loglik - Mclust(x2,
G=1, verbose=FALSE)$loglik
x1.d[i] = Mclust(x1, G=2, verbose=FALSE)$loglik - Mclust(x1,
... | How to test if my distribution is multimodal? | I'll add that you can replace the progress bars, which don't illuminate all that much, with an iteration count instead with this:
x2.d[i] = Mclust(x2, G=2, verbose=FALSE)$loglik - Mclust(x2,
| How to test if my distribution is multimodal?
I'll add that you can replace the progress bars, which don't illuminate all that much, with an iteration count instead with this:
x2.d[i] = Mclust(x2, G=2, verbose=FALSE)$loglik - Mclust(x2,
G=1, verbose=FALSE)$loglik
x1.d[i] = Mclust(x1, G=2, ... | How to test if my distribution is multimodal?
I'll add that you can replace the progress bars, which don't illuminate all that much, with an iteration count instead with this:
x2.d[i] = Mclust(x2, G=2, verbose=FALSE)$loglik - Mclust(x2,
|
9,959 | A statistics book that explains using more images than equations | The Cartoon Guide to Statistics covers the basics, including random variables, hypothesis testing and confidence intervals. | A statistics book that explains using more images than equations | The Cartoon Guide to Statistics covers the basics, including random variables, hypothesis testing and confidence intervals. | A statistics book that explains using more images than equations
The Cartoon Guide to Statistics covers the basics, including random variables, hypothesis testing and confidence intervals. | A statistics book that explains using more images than equations
The Cartoon Guide to Statistics covers the basics, including random variables, hypothesis testing and confidence intervals. |
9,960 | A statistics book that explains using more images than equations | I really like A Guide to Econometrics by Peter Kennedy. Some material in it will probably be irrelevant, but the conceptual info is excellent and useful for non-economists. For example, here's Kennedy on graphical intuition for omitted variable bias and multicolinearity in multiple regression using Ballentine/Venn diag... | A statistics book that explains using more images than equations | I really like A Guide to Econometrics by Peter Kennedy. Some material in it will probably be irrelevant, but the conceptual info is excellent and useful for non-economists. For example, here's Kennedy | A statistics book that explains using more images than equations
I really like A Guide to Econometrics by Peter Kennedy. Some material in it will probably be irrelevant, but the conceptual info is excellent and useful for non-economists. For example, here's Kennedy on graphical intuition for omitted variable bias and m... | A statistics book that explains using more images than equations
I really like A Guide to Econometrics by Peter Kennedy. Some material in it will probably be irrelevant, but the conceptual info is excellent and useful for non-economists. For example, here's Kennedy |
9,961 | A statistics book that explains using more images than equations | While reading the reviews for The Cartoon Guide to Statistics, I noticed one saying The Manga Guide To Statistics was better: http://www.amazon.com/gp/product/1593271891
The Manga Guide has fewer reviews, but gets better ones on average. (I.e. the mean number of stars is better; hopefully after reading either book you'... | A statistics book that explains using more images than equations | While reading the reviews for The Cartoon Guide to Statistics, I noticed one saying The Manga Guide To Statistics was better: http://www.amazon.com/gp/product/1593271891
The Manga Guide has fewer revi | A statistics book that explains using more images than equations
While reading the reviews for The Cartoon Guide to Statistics, I noticed one saying The Manga Guide To Statistics was better: http://www.amazon.com/gp/product/1593271891
The Manga Guide has fewer reviews, but gets better ones on average. (I.e. the mean nu... | A statistics book that explains using more images than equations
While reading the reviews for The Cartoon Guide to Statistics, I noticed one saying The Manga Guide To Statistics was better: http://www.amazon.com/gp/product/1593271891
The Manga Guide has fewer revi |
9,962 | A statistics book that explains using more images than equations | Ram Gnandesikan's book "Methods for Statistical Data Analysis of Multivariate Observations" has some equations but also a lot of graphics. Duda Hart and Stork "Pattern Classification Second Edition" has a lot of nice graphics including some color. Hastie, Tibshirani and Friedman "The Elements of Statistical Learning"... | A statistics book that explains using more images than equations | Ram Gnandesikan's book "Methods for Statistical Data Analysis of Multivariate Observations" has some equations but also a lot of graphics. Duda Hart and Stork "Pattern Classification Second Edition" | A statistics book that explains using more images than equations
Ram Gnandesikan's book "Methods for Statistical Data Analysis of Multivariate Observations" has some equations but also a lot of graphics. Duda Hart and Stork "Pattern Classification Second Edition" has a lot of nice graphics including some color. Hasti... | A statistics book that explains using more images than equations
Ram Gnandesikan's book "Methods for Statistical Data Analysis of Multivariate Observations" has some equations but also a lot of graphics. Duda Hart and Stork "Pattern Classification Second Edition" |
9,963 | A statistics book that explains using more images than equations | One book that I really like is "The Statistical Sleuth" by Ramsey and Schafer. It does still have the formulas, but the more complicated formulas have arrows pointing to the different parts with explanations of what that part of the formula means, there are lots of good graphics to help explain the concepts. It also ... | A statistics book that explains using more images than equations | One book that I really like is "The Statistical Sleuth" by Ramsey and Schafer. It does still have the formulas, but the more complicated formulas have arrows pointing to the different parts with expl | A statistics book that explains using more images than equations
One book that I really like is "The Statistical Sleuth" by Ramsey and Schafer. It does still have the formulas, but the more complicated formulas have arrows pointing to the different parts with explanations of what that part of the formula means, there ... | A statistics book that explains using more images than equations
One book that I really like is "The Statistical Sleuth" by Ramsey and Schafer. It does still have the formulas, but the more complicated formulas have arrows pointing to the different parts with expl |
9,964 | How to get the value of Mean squared error in a linear regression in R | The multiple R-squared that R reports is the coefficient of determination, which is given by the formula
$$ R^2 = 1 - \frac{SS_{\text{res}}}{SS_{\text{tot}}}.$$
The sum of squared errors is given (thanks to a previous answer) by sum(sm$residuals^2).
The mean squared error is given by mean(sm$residuals^2). You could wr... | How to get the value of Mean squared error in a linear regression in R | The multiple R-squared that R reports is the coefficient of determination, which is given by the formula
$$ R^2 = 1 - \frac{SS_{\text{res}}}{SS_{\text{tot}}}.$$
The sum of squared errors is given (th | How to get the value of Mean squared error in a linear regression in R
The multiple R-squared that R reports is the coefficient of determination, which is given by the formula
$$ R^2 = 1 - \frac{SS_{\text{res}}}{SS_{\text{tot}}}.$$
The sum of squared errors is given (thanks to a previous answer) by sum(sm$residuals^2)... | How to get the value of Mean squared error in a linear regression in R
The multiple R-squared that R reports is the coefficient of determination, which is given by the formula
$$ R^2 = 1 - \frac{SS_{\text{res}}}{SS_{\text{tot}}}.$$
The sum of squared errors is given (th |
9,965 | How to get the value of Mean squared error in a linear regression in R | Another simple method is to use the anova function.
You can get the MSE with anova(model)['Residuals', 'Mean Sq']
> print(sprintf("MSE=%0.2f", sum(lmfit$residuals^2)/lmfit$df.residual))
[1] "MSE=0.27"
> print(sprintf("MSE=%0.2f", anova(lmfit)['Residuals', 'Mean Sq']))
[1] "MSE=0.27" | How to get the value of Mean squared error in a linear regression in R | Another simple method is to use the anova function.
You can get the MSE with anova(model)['Residuals', 'Mean Sq']
> print(sprintf("MSE=%0.2f", sum(lmfit$residuals^2)/lmfit$df.residual))
[1] "MSE=0.27" | How to get the value of Mean squared error in a linear regression in R
Another simple method is to use the anova function.
You can get the MSE with anova(model)['Residuals', 'Mean Sq']
> print(sprintf("MSE=%0.2f", sum(lmfit$residuals^2)/lmfit$df.residual))
[1] "MSE=0.27"
> print(sprintf("MSE=%0.2f", anova(lmfit)['Resid... | How to get the value of Mean squared error in a linear regression in R
Another simple method is to use the anova function.
You can get the MSE with anova(model)['Residuals', 'Mean Sq']
> print(sprintf("MSE=%0.2f", sum(lmfit$residuals^2)/lmfit$df.residual))
[1] "MSE=0.27" |
9,966 | Hessian of logistic function | Here I derive all the necessary properties and identities for the solution to be self-contained, but apart from that this derivation is clean and easy. Let us formalize our notation and write the loss function a little more compactly. Consider $m$ samples $\{x_i,y_i\}$ such that $x_i\in\mathbb{R}^d$ and $y_i\in\mathbb{... | Hessian of logistic function | Here I derive all the necessary properties and identities for the solution to be self-contained, but apart from that this derivation is clean and easy. Let us formalize our notation and write the loss | Hessian of logistic function
Here I derive all the necessary properties and identities for the solution to be self-contained, but apart from that this derivation is clean and easy. Let us formalize our notation and write the loss function a little more compactly. Consider $m$ samples $\{x_i,y_i\}$ such that $x_i\in\mat... | Hessian of logistic function
Here I derive all the necessary properties and identities for the solution to be self-contained, but apart from that this derivation is clean and easy. Let us formalize our notation and write the loss |
9,967 | Calculate mean of ordinal variable | A short answer is that this is contentious. Contrary to the advice you mention, people in many fields do take means of ordinal scales and are often happy that means do what they want. Grade-point averages or the equivalent in many educational systems are one example.
However, ordinal data not being normally distribut... | Calculate mean of ordinal variable | A short answer is that this is contentious. Contrary to the advice you mention, people in many fields do take means of ordinal scales and are often happy that means do what they want. Grade-point aver | Calculate mean of ordinal variable
A short answer is that this is contentious. Contrary to the advice you mention, people in many fields do take means of ordinal scales and are often happy that means do what they want. Grade-point averages or the equivalent in many educational systems are one example.
However, ordinal... | Calculate mean of ordinal variable
A short answer is that this is contentious. Contrary to the advice you mention, people in many fields do take means of ordinal scales and are often happy that means do what they want. Grade-point aver |
9,968 | Calculate mean of ordinal variable | Suppose we take ordinal values, e.g. 1 for strongly disagree, 2 for disagree, 3 for agree, and 4 for strongly agree. If four people give the responses 1,2,3 and 4, then what would be the mean? It is (1+2+3+4)/4=2.50.
How should that be interpreted, when the four person average response is "disagree or agree"? That's wh... | Calculate mean of ordinal variable | Suppose we take ordinal values, e.g. 1 for strongly disagree, 2 for disagree, 3 for agree, and 4 for strongly agree. If four people give the responses 1,2,3 and 4, then what would be the mean? It is ( | Calculate mean of ordinal variable
Suppose we take ordinal values, e.g. 1 for strongly disagree, 2 for disagree, 3 for agree, and 4 for strongly agree. If four people give the responses 1,2,3 and 4, then what would be the mean? It is (1+2+3+4)/4=2.50.
How should that be interpreted, when the four person average respons... | Calculate mean of ordinal variable
Suppose we take ordinal values, e.g. 1 for strongly disagree, 2 for disagree, 3 for agree, and 4 for strongly agree. If four people give the responses 1,2,3 and 4, then what would be the mean? It is ( |
9,969 | Calculate mean of ordinal variable | I totally agree with @Azeem. But just to drive this point home let me elaborate a bit further.
Let's say you have ordinal data like in the example from @Azeem, where your scale ranges from 1 through 4. And let's also say you have a couple of people rating something (like Ice Cream) on this scale. Imagine that you get t... | Calculate mean of ordinal variable | I totally agree with @Azeem. But just to drive this point home let me elaborate a bit further.
Let's say you have ordinal data like in the example from @Azeem, where your scale ranges from 1 through 4 | Calculate mean of ordinal variable
I totally agree with @Azeem. But just to drive this point home let me elaborate a bit further.
Let's say you have ordinal data like in the example from @Azeem, where your scale ranges from 1 through 4. And let's also say you have a couple of people rating something (like Ice Cream) on... | Calculate mean of ordinal variable
I totally agree with @Azeem. But just to drive this point home let me elaborate a bit further.
Let's say you have ordinal data like in the example from @Azeem, where your scale ranges from 1 through 4 |
9,970 | Calculate mean of ordinal variable | I agree with the concept that arithmetic mean cannot be truly justified in ordinal scale data. Instead of calculating mean we can use mode or median in such situations which can give us more meaningful interpretation of our results. | Calculate mean of ordinal variable | I agree with the concept that arithmetic mean cannot be truly justified in ordinal scale data. Instead of calculating mean we can use mode or median in such situations which can give us more meaningfu | Calculate mean of ordinal variable
I agree with the concept that arithmetic mean cannot be truly justified in ordinal scale data. Instead of calculating mean we can use mode or median in such situations which can give us more meaningful interpretation of our results. | Calculate mean of ordinal variable
I agree with the concept that arithmetic mean cannot be truly justified in ordinal scale data. Instead of calculating mean we can use mode or median in such situations which can give us more meaningfu |
9,971 | How large a training set is needed? | The search term you are looking for is "learning curve", which gives the (average) model performance as function of the training sample size.
Learning curves depend on a lot of things, e.g.
classification method
complexity of the classifier
how well the classes are separated.
(I think for two-class LDA you may be ... | How large a training set is needed? | The search term you are looking for is "learning curve", which gives the (average) model performance as function of the training sample size.
Learning curves depend on a lot of things, e.g.
classifi | How large a training set is needed?
The search term you are looking for is "learning curve", which gives the (average) model performance as function of the training sample size.
Learning curves depend on a lot of things, e.g.
classification method
complexity of the classifier
how well the classes are separated.
(I... | How large a training set is needed?
The search term you are looking for is "learning curve", which gives the (average) model performance as function of the training sample size.
Learning curves depend on a lot of things, e.g.
classifi |
9,972 | How large a training set is needed? | Asking about training sample size implies you are going to hold back data for model validation. This is an unstable process requiring a huge sample size. Strong internal validation with the bootstrap is often preferred. If you choose that path you need to only compute the one sample size. As @cbeleites so nicely st... | How large a training set is needed? | Asking about training sample size implies you are going to hold back data for model validation. This is an unstable process requiring a huge sample size. Strong internal validation with the bootstra | How large a training set is needed?
Asking about training sample size implies you are going to hold back data for model validation. This is an unstable process requiring a huge sample size. Strong internal validation with the bootstrap is often preferred. If you choose that path you need to only compute the one samp... | How large a training set is needed?
Asking about training sample size implies you are going to hold back data for model validation. This is an unstable process requiring a huge sample size. Strong internal validation with the bootstra |
9,973 | How robust is the independent samples t-test when the distributions of the samples are non-normal? | Questions about robustness are very hard to answer well - because the assumptions may be violated in so many ways, and in each way to different degrees. Simulation work can only sample a very small portion of the possible violations.
Given the state of computing, I think it is often worth the time to run both a paramet... | How robust is the independent samples t-test when the distributions of the samples are non-normal? | Questions about robustness are very hard to answer well - because the assumptions may be violated in so many ways, and in each way to different degrees. Simulation work can only sample a very small po | How robust is the independent samples t-test when the distributions of the samples are non-normal?
Questions about robustness are very hard to answer well - because the assumptions may be violated in so many ways, and in each way to different degrees. Simulation work can only sample a very small portion of the possible... | How robust is the independent samples t-test when the distributions of the samples are non-normal?
Questions about robustness are very hard to answer well - because the assumptions may be violated in so many ways, and in each way to different degrees. Simulation work can only sample a very small po |
9,974 | How robust is the independent samples t-test when the distributions of the samples are non-normal? | @PeterFlom hit the nail dead on with his first sentence.
I'll try to give a rough summary of what studies I have seen (if you want links it could be a while):
Overall, the two sample t-test is reasonably power-robust to symmetric non-normality (the true type-I-error-rate is affected somewhat by kurtosis, the power is i... | How robust is the independent samples t-test when the distributions of the samples are non-normal? | @PeterFlom hit the nail dead on with his first sentence.
I'll try to give a rough summary of what studies I have seen (if you want links it could be a while):
Overall, the two sample t-test is reasona | How robust is the independent samples t-test when the distributions of the samples are non-normal?
@PeterFlom hit the nail dead on with his first sentence.
I'll try to give a rough summary of what studies I have seen (if you want links it could be a while):
Overall, the two sample t-test is reasonably power-robust to s... | How robust is the independent samples t-test when the distributions of the samples are non-normal?
@PeterFlom hit the nail dead on with his first sentence.
I'll try to give a rough summary of what studies I have seen (if you want links it could be a while):
Overall, the two sample t-test is reasona |
9,975 | How robust is the independent samples t-test when the distributions of the samples are non-normal? | @PeterFlom has already mentioned that simulation studies can never cover all scenarios and possibilities and therefore cannot lead to a definite answer. However, I still find it useful to actually explore an issue like this by conducting some simulations (this also happens to be exactly the type of exercise that I like... | How robust is the independent samples t-test when the distributions of the samples are non-normal? | @PeterFlom has already mentioned that simulation studies can never cover all scenarios and possibilities and therefore cannot lead to a definite answer. However, I still find it useful to actually exp | How robust is the independent samples t-test when the distributions of the samples are non-normal?
@PeterFlom has already mentioned that simulation studies can never cover all scenarios and possibilities and therefore cannot lead to a definite answer. However, I still find it useful to actually explore an issue like th... | How robust is the independent samples t-test when the distributions of the samples are non-normal?
@PeterFlom has already mentioned that simulation studies can never cover all scenarios and possibilities and therefore cannot lead to a definite answer. However, I still find it useful to actually exp |
9,976 | How robust is the independent samples t-test when the distributions of the samples are non-normal? | In your situation, the t-test will likely be robust in terms of Type I error rate, but not Type II error rate. You would probably achieve more power through either a) a Kruskal-Wallis test, or b) a normalizing transformation prior to a t-test.
I'm basing this conclusion on two Monte Carlo studies. In the first (Khan &... | How robust is the independent samples t-test when the distributions of the samples are non-normal? | In your situation, the t-test will likely be robust in terms of Type I error rate, but not Type II error rate. You would probably achieve more power through either a) a Kruskal-Wallis test, or b) a n | How robust is the independent samples t-test when the distributions of the samples are non-normal?
In your situation, the t-test will likely be robust in terms of Type I error rate, but not Type II error rate. You would probably achieve more power through either a) a Kruskal-Wallis test, or b) a normalizing transforma... | How robust is the independent samples t-test when the distributions of the samples are non-normal?
In your situation, the t-test will likely be robust in terms of Type I error rate, but not Type II error rate. You would probably achieve more power through either a) a Kruskal-Wallis test, or b) a n |
9,977 | How robust is the independent samples t-test when the distributions of the samples are non-normal? | First of all, if you assume that the distribution of the two samples is different, make sure you are using Welch's version of the t-test which assumes unequal variances between the groups. This will at least attempt to account for some of the differences that occur because of the distribution.
If we look at the formula... | How robust is the independent samples t-test when the distributions of the samples are non-normal? | First of all, if you assume that the distribution of the two samples is different, make sure you are using Welch's version of the t-test which assumes unequal variances between the groups. This will a | How robust is the independent samples t-test when the distributions of the samples are non-normal?
First of all, if you assume that the distribution of the two samples is different, make sure you are using Welch's version of the t-test which assumes unequal variances between the groups. This will at least attempt to ac... | How robust is the independent samples t-test when the distributions of the samples are non-normal?
First of all, if you assume that the distribution of the two samples is different, make sure you are using Welch's version of the t-test which assumes unequal variances between the groups. This will a |
9,978 | Kullback-Leibler divergence WITHOUT information theory | There is a purely statistical approach to Kullback-Leibler divergence: take a sample $X_1,\ldots,X_n$ iid from an unknown distribution $p^\star$ and consider the potential fit by a family of distributions, $$\mathfrak{F}=\{p_\theta\,,\ \theta\in\Theta\}$$The corresponding likelihood is defined as
$$L(\theta|x_1,\ldots,... | Kullback-Leibler divergence WITHOUT information theory | There is a purely statistical approach to Kullback-Leibler divergence: take a sample $X_1,\ldots,X_n$ iid from an unknown distribution $p^\star$ and consider the potential fit by a family of distribut | Kullback-Leibler divergence WITHOUT information theory
There is a purely statistical approach to Kullback-Leibler divergence: take a sample $X_1,\ldots,X_n$ iid from an unknown distribution $p^\star$ and consider the potential fit by a family of distributions, $$\mathfrak{F}=\{p_\theta\,,\ \theta\in\Theta\}$$The corres... | Kullback-Leibler divergence WITHOUT information theory
There is a purely statistical approach to Kullback-Leibler divergence: take a sample $X_1,\ldots,X_n$ iid from an unknown distribution $p^\star$ and consider the potential fit by a family of distribut |
9,979 | Kullback-Leibler divergence WITHOUT information theory | Here is a statistical interpretation of the Kullback-Leibler divergence, loosely taken from I.J. Good (Weight of evidence: A brief survey, Bayesian Statistics 2, 1985).
The weight of evidence.
Suppose you observe data points $x_1, x_2, \dots, x_n$ which you have reason to believe are independent samples from some unkno... | Kullback-Leibler divergence WITHOUT information theory | Here is a statistical interpretation of the Kullback-Leibler divergence, loosely taken from I.J. Good (Weight of evidence: A brief survey, Bayesian Statistics 2, 1985).
The weight of evidence.
Suppose | Kullback-Leibler divergence WITHOUT information theory
Here is a statistical interpretation of the Kullback-Leibler divergence, loosely taken from I.J. Good (Weight of evidence: A brief survey, Bayesian Statistics 2, 1985).
The weight of evidence.
Suppose you observe data points $x_1, x_2, \dots, x_n$ which you have re... | Kullback-Leibler divergence WITHOUT information theory
Here is a statistical interpretation of the Kullback-Leibler divergence, loosely taken from I.J. Good (Weight of evidence: A brief survey, Bayesian Statistics 2, 1985).
The weight of evidence.
Suppose |
9,980 | Kullback-Leibler divergence WITHOUT information theory | I have yet to see a single explanation of how these two concepts are even related.
I don't know much about information theory, but this is how I think about it: when I hear an information theory person say "length of the message," my brain says "surprise." Surprise is 1.) random and 2.) subjective.
By 1.) I mean that... | Kullback-Leibler divergence WITHOUT information theory | I have yet to see a single explanation of how these two concepts are even related.
I don't know much about information theory, but this is how I think about it: when I hear an information theory pers | Kullback-Leibler divergence WITHOUT information theory
I have yet to see a single explanation of how these two concepts are even related.
I don't know much about information theory, but this is how I think about it: when I hear an information theory person say "length of the message," my brain says "surprise." Surpris... | Kullback-Leibler divergence WITHOUT information theory
I have yet to see a single explanation of how these two concepts are even related.
I don't know much about information theory, but this is how I think about it: when I hear an information theory pers |
9,981 | Kullback-Leibler divergence WITHOUT information theory | There is (also) a purely convex analytical viewpoint on the KL divergence, which personally I find very easy to understand.
Given any convex function $F: R^k \to R$, its Bregman divergence between $p$ and $q$ ($p, q \in R$) is the quantity
$$
F(p) - F(q) - \langle \nabla F(q), p - q \rangle
$$
This has a very simple i... | Kullback-Leibler divergence WITHOUT information theory | There is (also) a purely convex analytical viewpoint on the KL divergence, which personally I find very easy to understand.
Given any convex function $F: R^k \to R$, its Bregman divergence between $p | Kullback-Leibler divergence WITHOUT information theory
There is (also) a purely convex analytical viewpoint on the KL divergence, which personally I find very easy to understand.
Given any convex function $F: R^k \to R$, its Bregman divergence between $p$ and $q$ ($p, q \in R$) is the quantity
$$
F(p) - F(q) - \langle... | Kullback-Leibler divergence WITHOUT information theory
There is (also) a purely convex analytical viewpoint on the KL divergence, which personally I find very easy to understand.
Given any convex function $F: R^k \to R$, its Bregman divergence between $p |
9,982 | Can gradient descent be applied to non-convex functions? | The function you have graphed is indeed not convex. However, it is quasiconvex.
Gradient descent is a generic method for continuous optimization, so it can be, and is very commonly, applied to nonconvex functions. With a smooth function and a reasonably selected step size, it will generate a sequence of points $x_1, x... | Can gradient descent be applied to non-convex functions? | The function you have graphed is indeed not convex. However, it is quasiconvex.
Gradient descent is a generic method for continuous optimization, so it can be, and is very commonly, applied to noncon | Can gradient descent be applied to non-convex functions?
The function you have graphed is indeed not convex. However, it is quasiconvex.
Gradient descent is a generic method for continuous optimization, so it can be, and is very commonly, applied to nonconvex functions. With a smooth function and a reasonably selected... | Can gradient descent be applied to non-convex functions?
The function you have graphed is indeed not convex. However, it is quasiconvex.
Gradient descent is a generic method for continuous optimization, so it can be, and is very commonly, applied to noncon |
9,983 | Can gradient descent be applied to non-convex functions? | Paul already mentioned one important point:
if f is convex there are no saddle points and all local minima are also global. Thus GD (with a suitable stepsize) is guaranteed to find a global minimizer.
What makes non-convex optimization hard is the presence of saddle points and local minima, where the gradient is (0,.... | Can gradient descent be applied to non-convex functions? | Paul already mentioned one important point:
if f is convex there are no saddle points and all local minima are also global. Thus GD (with a suitable stepsize) is guaranteed to find a global minimizer | Can gradient descent be applied to non-convex functions?
Paul already mentioned one important point:
if f is convex there are no saddle points and all local minima are also global. Thus GD (with a suitable stepsize) is guaranteed to find a global minimizer.
What makes non-convex optimization hard is the presence of s... | Can gradient descent be applied to non-convex functions?
Paul already mentioned one important point:
if f is convex there are no saddle points and all local minima are also global. Thus GD (with a suitable stepsize) is guaranteed to find a global minimizer |
9,984 | Is AdaBoost less or more prone to overfitting? | As you say a lot has been discussed about this matter, and there's some quite heavy theory that has gone along with it that I have to admit I never fully understood. In my practical experience AdaBoost is quite robust to overfitting, and LPBoost (Linear Programming Boosting) even more so (because the objective function... | Is AdaBoost less or more prone to overfitting? | As you say a lot has been discussed about this matter, and there's some quite heavy theory that has gone along with it that I have to admit I never fully understood. In my practical experience AdaBoos | Is AdaBoost less or more prone to overfitting?
As you say a lot has been discussed about this matter, and there's some quite heavy theory that has gone along with it that I have to admit I never fully understood. In my practical experience AdaBoost is quite robust to overfitting, and LPBoost (Linear Programming Boostin... | Is AdaBoost less or more prone to overfitting?
As you say a lot has been discussed about this matter, and there's some quite heavy theory that has gone along with it that I have to admit I never fully understood. In my practical experience AdaBoos |
9,985 | Is AdaBoost less or more prone to overfitting? | I agree with most of the points mentioned in tdc comment. however, I have to add and correct few things.
As shown in L2Boost by Peter Bühlmann, as the number of weak learners (rounds of boosting) increases, the bias converges exponentially fast while the variance increases by geometrically diminishing magnitudes which... | Is AdaBoost less or more prone to overfitting? | I agree with most of the points mentioned in tdc comment. however, I have to add and correct few things.
As shown in L2Boost by Peter Bühlmann, as the number of weak learners (rounds of boosting) inc | Is AdaBoost less or more prone to overfitting?
I agree with most of the points mentioned in tdc comment. however, I have to add and correct few things.
As shown in L2Boost by Peter Bühlmann, as the number of weak learners (rounds of boosting) increases, the bias converges exponentially fast while the variance increase... | Is AdaBoost less or more prone to overfitting?
I agree with most of the points mentioned in tdc comment. however, I have to add and correct few things.
As shown in L2Boost by Peter Bühlmann, as the number of weak learners (rounds of boosting) inc |
9,986 | When would one use Gibbs sampling instead of Metropolis-Hastings? | Firstly, let me note [somewhat pedantically] that
There are several different kinds of MCMC algorithms:
Metropolis-Hastings, Gibbs, importance/rejection sampling (related).
importance and rejection sampling methods are not MCMC algorithms because they are not based on Markov chains. Actually, importance sampling do... | When would one use Gibbs sampling instead of Metropolis-Hastings? | Firstly, let me note [somewhat pedantically] that
There are several different kinds of MCMC algorithms:
Metropolis-Hastings, Gibbs, importance/rejection sampling (related).
importance and rejectio | When would one use Gibbs sampling instead of Metropolis-Hastings?
Firstly, let me note [somewhat pedantically] that
There are several different kinds of MCMC algorithms:
Metropolis-Hastings, Gibbs, importance/rejection sampling (related).
importance and rejection sampling methods are not MCMC algorithms because the... | When would one use Gibbs sampling instead of Metropolis-Hastings?
Firstly, let me note [somewhat pedantically] that
There are several different kinds of MCMC algorithms:
Metropolis-Hastings, Gibbs, importance/rejection sampling (related).
importance and rejectio |
9,987 | What norm of the reconstruction error is minimized by the low-rank approximation matrix obtained with PCA? | Single word answer: Both.
Let's start with defining the norms. For a matrix $X$, operator $2$-norm is defined as $$\|X\|_2 = \mathrm{sup}\frac{\|Xv\|_2}{\|v\|_2} = \mathrm{max}(s_i)$$ and Frobenius norm as $$\|X\|_F = \sqrt {\sum_{ij} X_{ij}^2} = \sqrt{\mathrm{tr}(X^\top X)} = \sqrt{\sum s_i^2},$$
where $s_i$ are sing... | What norm of the reconstruction error is minimized by the low-rank approximation matrix obtained wit | Single word answer: Both.
Let's start with defining the norms. For a matrix $X$, operator $2$-norm is defined as $$\|X\|_2 = \mathrm{sup}\frac{\|Xv\|_2}{\|v\|_2} = \mathrm{max}(s_i)$$ and Frobenius n | What norm of the reconstruction error is minimized by the low-rank approximation matrix obtained with PCA?
Single word answer: Both.
Let's start with defining the norms. For a matrix $X$, operator $2$-norm is defined as $$\|X\|_2 = \mathrm{sup}\frac{\|Xv\|_2}{\|v\|_2} = \mathrm{max}(s_i)$$ and Frobenius norm as $$\|X\... | What norm of the reconstruction error is minimized by the low-rank approximation matrix obtained wit
Single word answer: Both.
Let's start with defining the norms. For a matrix $X$, operator $2$-norm is defined as $$\|X\|_2 = \mathrm{sup}\frac{\|Xv\|_2}{\|v\|_2} = \mathrm{max}(s_i)$$ and Frobenius n |
9,988 | Do Bayesians accept Kolmogorov's axioms? | In my opinion, Cox-Jaynes interpretation of probability provides a rigorous foundation for Bayesian probability:
Cox, Richard T. "Probability, frequency and reasonable expectation." American Journal of Physics 14.1 (1946): 1–13.
Jaynes, Edwin T. Probability theory: the logic of science. Cambridge University Press, 200... | Do Bayesians accept Kolmogorov's axioms? | In my opinion, Cox-Jaynes interpretation of probability provides a rigorous foundation for Bayesian probability:
Cox, Richard T. "Probability, frequency and reasonable expectation." American Journal | Do Bayesians accept Kolmogorov's axioms?
In my opinion, Cox-Jaynes interpretation of probability provides a rigorous foundation for Bayesian probability:
Cox, Richard T. "Probability, frequency and reasonable expectation." American Journal of Physics 14.1 (1946): 1–13.
Jaynes, Edwin T. Probability theory: the logic of... | Do Bayesians accept Kolmogorov's axioms?
In my opinion, Cox-Jaynes interpretation of probability provides a rigorous foundation for Bayesian probability:
Cox, Richard T. "Probability, frequency and reasonable expectation." American Journal |
9,989 | Do Bayesians accept Kolmogorov's axioms? | After the development of Probability Theory it was necessary to show that looser concepts answering to the name of "probability" measured up to the rigorously defined concept they had inspired. "Subjective" Bayesian probabilities were considered by Ramsey and de Finetti, who independently showed that a quantification o... | Do Bayesians accept Kolmogorov's axioms? | After the development of Probability Theory it was necessary to show that looser concepts answering to the name of "probability" measured up to the rigorously defined concept they had inspired. "Subje | Do Bayesians accept Kolmogorov's axioms?
After the development of Probability Theory it was necessary to show that looser concepts answering to the name of "probability" measured up to the rigorously defined concept they had inspired. "Subjective" Bayesian probabilities were considered by Ramsey and de Finetti, who ind... | Do Bayesians accept Kolmogorov's axioms?
After the development of Probability Theory it was necessary to show that looser concepts answering to the name of "probability" measured up to the rigorously defined concept they had inspired. "Subje |
9,990 | Have I correctly specified my model in lmer? | Tow nested within station when tow is random and station is fixed
station+(1|station:tow) is correct. As @John said in his answer, (1|station/tow) would expand to (1|station)+(1|station:tow) (main effect of station plus interaction between tow and station), which you don't want because you have already specified statio... | Have I correctly specified my model in lmer? | Tow nested within station when tow is random and station is fixed
station+(1|station:tow) is correct. As @John said in his answer, (1|station/tow) would expand to (1|station)+(1|station:tow) (main eff | Have I correctly specified my model in lmer?
Tow nested within station when tow is random and station is fixed
station+(1|station:tow) is correct. As @John said in his answer, (1|station/tow) would expand to (1|station)+(1|station:tow) (main effect of station plus interaction between tow and station), which you don't w... | Have I correctly specified my model in lmer?
Tow nested within station when tow is random and station is fixed
station+(1|station:tow) is correct. As @John said in his answer, (1|station/tow) would expand to (1|station)+(1|station:tow) (main eff |
9,991 | Have I correctly specified my model in lmer? | Some of the things in formula are a bit confusing. The : is for interactions between two terms while the * is for main effects and interactions. The / is another one for interactions but what it does is generate an interaction between the numerator and all of the terms in the denominator (e.g. A/(B+C) = A:B + A:C). The... | Have I correctly specified my model in lmer? | Some of the things in formula are a bit confusing. The : is for interactions between two terms while the * is for main effects and interactions. The / is another one for interactions but what it does | Have I correctly specified my model in lmer?
Some of the things in formula are a bit confusing. The : is for interactions between two terms while the * is for main effects and interactions. The / is another one for interactions but what it does is generate an interaction between the numerator and all of the terms in th... | Have I correctly specified my model in lmer?
Some of the things in formula are a bit confusing. The : is for interactions between two terms while the * is for main effects and interactions. The / is another one for interactions but what it does |
9,992 | Interpreting interaction terms in logit regression with categorical variables | I assume that PreferA = 1 when one prefered A and 0 otherwise and that ControlFALSE = 1 when treated and 0 when control.
The odds of preffering A when a person did not do so previously and did not receive a treatment (ControlFALSE=0 and PreferA=0) is $\exp(3.135)= 23$, i.e. there are 23 such persons who prefer A for ev... | Interpreting interaction terms in logit regression with categorical variables | I assume that PreferA = 1 when one prefered A and 0 otherwise and that ControlFALSE = 1 when treated and 0 when control.
The odds of preffering A when a person did not do so previously and did not rec | Interpreting interaction terms in logit regression with categorical variables
I assume that PreferA = 1 when one prefered A and 0 otherwise and that ControlFALSE = 1 when treated and 0 when control.
The odds of preffering A when a person did not do so previously and did not receive a treatment (ControlFALSE=0 and Prefe... | Interpreting interaction terms in logit regression with categorical variables
I assume that PreferA = 1 when one prefered A and 0 otherwise and that ControlFALSE = 1 when treated and 0 when control.
The odds of preffering A when a person did not do so previously and did not rec |
9,993 | Interpreting interaction terms in logit regression with categorical variables | I also found this paper to be helpful in interpreting interaction in logistic regression:
Chen, J. J. (2003). Communicating complex information: the interpretation of statistical interaction in multiple logistic regression analysis. American journal of public health, 93(9), 1376-1377. | Interpreting interaction terms in logit regression with categorical variables | I also found this paper to be helpful in interpreting interaction in logistic regression:
Chen, J. J. (2003). Communicating complex information: the interpretation of statistical interaction in multi | Interpreting interaction terms in logit regression with categorical variables
I also found this paper to be helpful in interpreting interaction in logistic regression:
Chen, J. J. (2003). Communicating complex information: the interpretation of statistical interaction in multiple logistic regression analysis. American... | Interpreting interaction terms in logit regression with categorical variables
I also found this paper to be helpful in interpreting interaction in logistic regression:
Chen, J. J. (2003). Communicating complex information: the interpretation of statistical interaction in multi |
9,994 | Interpreting interaction terms in logit regression with categorical variables | My own preference, when trying to interpret interactions in logistic regression, is to look at the predicted probabilities for each combination of categorical variables. In your case, this would be just 4 probabilities:
Prefer A, control true
Prefer A, control false
Prefer B, control true
Prefer B, control false
Whe... | Interpreting interaction terms in logit regression with categorical variables | My own preference, when trying to interpret interactions in logistic regression, is to look at the predicted probabilities for each combination of categorical variables. In your case, this would be ju | Interpreting interaction terms in logit regression with categorical variables
My own preference, when trying to interpret interactions in logistic regression, is to look at the predicted probabilities for each combination of categorical variables. In your case, this would be just 4 probabilities:
Prefer A, control tr... | Interpreting interaction terms in logit regression with categorical variables
My own preference, when trying to interpret interactions in logistic regression, is to look at the predicted probabilities for each combination of categorical variables. In your case, this would be ju |
9,995 | How does the formula for generating correlated random variables work? | Suppose you want to find a linear combination of $X_1$ and $X_2$ such that
$$
\text{corr}(\alpha X_1 + \beta X_2, X_1) = \rho
$$
Notice that if you multiply both $\alpha$ and $\beta$ by the same (non-zero) constant, the correlation will not change. Thus, we're going to add a condition to preserve variance: $\text{var}(... | How does the formula for generating correlated random variables work? | Suppose you want to find a linear combination of $X_1$ and $X_2$ such that
$$
\text{corr}(\alpha X_1 + \beta X_2, X_1) = \rho
$$
Notice that if you multiply both $\alpha$ and $\beta$ by the same (non- | How does the formula for generating correlated random variables work?
Suppose you want to find a linear combination of $X_1$ and $X_2$ such that
$$
\text{corr}(\alpha X_1 + \beta X_2, X_1) = \rho
$$
Notice that if you multiply both $\alpha$ and $\beta$ by the same (non-zero) constant, the correlation will not change. T... | How does the formula for generating correlated random variables work?
Suppose you want to find a linear combination of $X_1$ and $X_2$ such that
$$
\text{corr}(\alpha X_1 + \beta X_2, X_1) = \rho
$$
Notice that if you multiply both $\alpha$ and $\beta$ by the same (non- |
9,996 | How does the formula for generating correlated random variables work? | The equation is a simplified bivariate form of Cholesky decomposition. This simplified equation is sometimes called the Kaiser-Dickman algorithm (Kaiser & Dickman, 1962).
Note that $X_1$ and $X_2$ must have the same variance for this algorithm to work properly. Also, the algorithm is typically used with normal varia... | How does the formula for generating correlated random variables work? | The equation is a simplified bivariate form of Cholesky decomposition. This simplified equation is sometimes called the Kaiser-Dickman algorithm (Kaiser & Dickman, 1962).
Note that $X_1$ and $X_2$ | How does the formula for generating correlated random variables work?
The equation is a simplified bivariate form of Cholesky decomposition. This simplified equation is sometimes called the Kaiser-Dickman algorithm (Kaiser & Dickman, 1962).
Note that $X_1$ and $X_2$ must have the same variance for this algorithm to ... | How does the formula for generating correlated random variables work?
The equation is a simplified bivariate form of Cholesky decomposition. This simplified equation is sometimes called the Kaiser-Dickman algorithm (Kaiser & Dickman, 1962).
Note that $X_1$ and $X_2$ |
9,997 | How does the formula for generating correlated random variables work? | Correlation coefficient is the $\cos$ between two series if they are treated as vectors (with $n^{th}$ data point being $n^{th}$ dimension of a vector). The above formula simply creates a decomposition of a vector into its $\cos\theta$, $sin\theta$ components (with respect to $X_1,X_2$).
if $\rho = cos \theta$ ,
then... | How does the formula for generating correlated random variables work? | Correlation coefficient is the $\cos$ between two series if they are treated as vectors (with $n^{th}$ data point being $n^{th}$ dimension of a vector). The above formula simply creates a decompositi | How does the formula for generating correlated random variables work?
Correlation coefficient is the $\cos$ between two series if they are treated as vectors (with $n^{th}$ data point being $n^{th}$ dimension of a vector). The above formula simply creates a decomposition of a vector into its $\cos\theta$, $sin\theta$ ... | How does the formula for generating correlated random variables work?
Correlation coefficient is the $\cos$ between two series if they are treated as vectors (with $n^{th}$ data point being $n^{th}$ dimension of a vector). The above formula simply creates a decompositi |
9,998 | What is covariate? | From Wikipedia:
Depending on the context, an independent variable is sometimes called a "predictor variable", regressor, covariate, "controlled variable", "manipulated variable", "explanatory variable", exposure variable (see reliability theory), "risk factor" (see medical statistics), "feature" (in machine learning a... | What is covariate? | From Wikipedia:
Depending on the context, an independent variable is sometimes called a "predictor variable", regressor, covariate, "controlled variable", "manipulated variable", "explanatory variabl | What is covariate?
From Wikipedia:
Depending on the context, an independent variable is sometimes called a "predictor variable", regressor, covariate, "controlled variable", "manipulated variable", "explanatory variable", exposure variable (see reliability theory), "risk factor" (see medical statistics), "feature" (in... | What is covariate?
From Wikipedia:
Depending on the context, an independent variable is sometimes called a "predictor variable", regressor, covariate, "controlled variable", "manipulated variable", "explanatory variabl |
9,999 | What is covariate? | the way linear regression is generally run (there are ways to ask for different slope calculations) you are getting the unique impact of one predictor on the dependent variable. Its shared impact with other predictors on the DV (or indirect impact as with structural equation models I believe) is not part of the slope. ... | What is covariate? | the way linear regression is generally run (there are ways to ask for different slope calculations) you are getting the unique impact of one predictor on the dependent variable. Its shared impact with | What is covariate?
the way linear regression is generally run (there are ways to ask for different slope calculations) you are getting the unique impact of one predictor on the dependent variable. Its shared impact with other predictors on the DV (or indirect impact as with structural equation models I believe) is not ... | What is covariate?
the way linear regression is generally run (there are ways to ask for different slope calculations) you are getting the unique impact of one predictor on the dependent variable. Its shared impact with |
10,000 | What is covariate? | In general terms, covariates are characteristics of the participants
in an experiment. If you collect data on characteristics before you
run an experiment, you could use that data to see how your treatment
affects different groups or populations. Or, you could use that data
to control for the influence of any c... | What is covariate? | In general terms, covariates are characteristics of the participants
in an experiment. If you collect data on characteristics before you
run an experiment, you could use that data to see how your | What is covariate?
In general terms, covariates are characteristics of the participants
in an experiment. If you collect data on characteristics before you
run an experiment, you could use that data to see how your treatment
affects different groups or populations. Or, you could use that data
to control for the... | What is covariate?
In general terms, covariates are characteristics of the participants
in an experiment. If you collect data on characteristics before you
run an experiment, you could use that data to see how your |
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