Bayesian

Bayesian statistics blogs

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 ...

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. 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...

Bayesian inference in the (abnormal) mind

May 15, 2016
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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...

Numerical pitfalls in computing variance

May 3, 2016
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One of the most common tasks in statistical computing is computation of sample variance. This would seem to be straightforward; there are a number of algebraically equivalent ways of representing the sum of squares $$S$$, such as \[ S = \sum_{k=1}^n (...

Matlab version of BEST

April 28, 2016
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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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