Blog Archives

Bayesian assessment of null values

December 21, 2016
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Bayesian assessment of null values

A blog post by Christian Robert considered an ancient (2011!) article titled "Bayesian assessment of null values via parameter estimation and model comparison." Here I'll try to clarify the ideas from way back then through the lens of more recent diagr...

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The Bayesian New Statistics: Hypothesis Testing, Estimation, Meta-Analysis, and Power Analysis from a Bayesian Perspective

December 16, 2016
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The Bayesian New Statistics: Hypothesis Testing, Estimation, Meta-Analysis, and Power Analysis from a Bayesian Perspective

Two conceptual distinctions in the practice of data analysis. Rows show point-value hypothesis testing versus estimating magnitude with uncertainty. Columns show frequentist versus Bayesian methods. Cells indicate the typical information provided by ea...

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Is it legitimate to view the data and then decide on a distribution for the dependent variable?

November 17, 2016
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An emailer asks, In Bayesian parameter estimation, is it legitimate to view the data and then decide on a distribution for the dependent variable? I have heard that this is not “fully Bayesian”. The shortest questions often probe some of the most d...

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Bayesian meta-analysis of two proportions in random control trials

November 3, 2016
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Bayesian meta-analysis of two proportions in random control trials

For an article that's accepted pending final revision (available here at OSF), I developed a Bayesian meta-analysis of two proportions in random control trials. This blog post summarizes and links to the complete R scripts.We consider scenarios in whic...

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Should researchers be correcting for multiple tests, even when they themselves did not run the tests, but all of the tests were run on the same data?

October 25, 2016
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A graduate student, named Caitlin Ducate, in my frequentist statistics class asks:In Criminal Justice, it's common to use large data sets like the Uniform Crime Report (UCR) or versions of the National Longitudinal Survey (NLS) because the nature of ...

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Posterior predictive distribution for multiple linear regression

October 22, 2016
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Suppose you've done a (robust) Bayesian multiple linear regression, and now you want the posterior distribution on the predicted value of \(y\) for some probe value of \( \langle x_1,x_2,x_3, ... \rangle \). That is, not the posterior distribution on t...

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Bayesian predicted slopes with interaction in multiple linear regression

July 21, 2016
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Bayesian predicted slopes with interaction in multiple linear regression

Suppose we have a multiple linear regression with interaction: \[\hat{y} = \beta_0 + \beta_1 x_1 + \beta_2 x_2 + \beta_{1\times 2} x_1 x_2 \] Notice that the slope on \(x_1\) is not just \(\beta_1\), it's \(\beta_1 + \beta_{1\times 2} x_2\): \[\hat{y} ...

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MCMC effective sample size for difference of parameters (in Bayesian posterior distribution)

July 11, 2016
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MCMC effective sample size for difference of parameters (in Bayesian posterior distribution)

We'd like the MCMC representation of a posterior distribution to have large effective sample size (ESS) for the relevant parameters. (I recommend ESS > 10,000 for reasonably stable estimates of the limits of the 95% highest density interval.) In man...

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Bayesian variable selection in multiple linear regression: Model with highest R^2 is not necessarily highest posterior probability

July 10, 2016
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Bayesian variable selection in multiple linear regression: Model with highest R^2 is not necessarily highest posterior probability

Chapter 18 of DBDA2E includes sections on Bayesian variable selection in multiple linear regression. The idea is that each predictor (a.k.a., "variable") has an inclusion coefficient \(\delta_j\) that can be 0 or 1 (along with its regression coefficien...

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Brexit: "Bayesian" statistics renamed "Laplacian" statistics

June 27, 2016
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With the U.K. leaving the E.U., it's time for "Bayesian" to exit its titular role and be replaced by "Laplacian".  ;-) Various historians (e.g., Dale, 1999; McGrayne, 2011; as cited in DBDA2E) have argued that despite Bayes and Price having ...

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