Blog Archives

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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Some Bayesian approaches to replication analysis and planning (talk video)

May 30, 2016
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Some Bayesian approaches to replication analysis and planning (talk video)

Some Bayesian approaches to replication analysis and planning. A talk presented at the Association for Psychological Science, Friday May 27, 2016. This video (below) is a pre-recording while sitting at my desk; the actual talk included some spontaneous...

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Bayesian inference in the (abnormal) mind

May 15, 2016
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Bayesian inference in the (abnormal) mind

The (abnormal) mind can be modeled as a Bayesian inference engine, as summarized in the post, Bayesian reasoning implicated in some mental disorders. Excerpt:“The brain is a guessing machine [i.e., Bayesian inference engine - JKK], trying at each mom...

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Matlab version of BEST

April 28, 2016
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Matlab version of BEST

Nils Winter has created a Matlab interface to BEST (Bayesian estimation for two groups of metric-scale data). You can read about it at his GitHub README. 

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Bayesian estimation of log-normal parameters – Update

April 19, 2016
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Bayesian estimation of log-normal parameters – Update

Using the log-normal density can be confusing because it's parameterized in terms of the mean and precision of the log-scale data, not the original-scale data. Thus, if your data, y, are nicely described by a log-normal distribution, the estimated m...

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The remains of R. A. Fisher are visited by Bayesians again

January 29, 2016
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The remains of R. A. Fisher are visited by Bayesians again

Thanks to Phillip Alday, the second edition of Doing Bayesian Data Analysis has visited the remains of R. A. Fisher at St. Peter's Cathedral in Adelaide. Here is a photo that Phillip snapped: In a previous post, the first edition visited Fisher's ...

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(A pointer to) bayes.js: A Small Library for Doing MCMC in the Browser

December 31, 2015
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(A pointer to) bayes.js: A Small Library for Doing MCMC in the Browser

Screen shot from bayes.js blog post.This is just a pointer to a new post at Rasmus Bååth's Blog that might interest readers of DBDA2E. bayes.js: A small JavaScript library that implements an adaptive MCMC sampler and a couple of probability distribut...

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