# Bayesian

Bayesian statistics blogs

## 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...

## Bayesian meta-analysis of two proportions in random control trials

November 3, 2016
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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...

## 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 ...

## 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...

## Stop saying confidence intervals are "better" than p values

July 29, 2016
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One of the common tropes one hears from advocates of confidence intervals is that they are superior, or should be preferred, to p values. In our paper "The Fallacy of Placing Confidence in Confidence Intervals", we outlined a number of interpretation p...

## A scalable particle filter in Scala

July 22, 2016
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Introduction Many modern algorithms in computational Bayesian statistics have at their heart a particle filter or some other sequential Monte Carlo (SMC) procedure. In this blog I’ve discussed particle MCMC algorithms which use a particle filter in the inner-loop in order to compute a (noisy, unbiased) estimate of the marginal likelihood of the data. These … Continue reading A scalable particle filter in Scala

## Bayesian predicted slopes with interaction in multiple linear regression

July 21, 2016
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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} ...

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

July 11, 2016
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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...

## 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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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...

## 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 ...