Templates for Running Bayesian Regressions
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Templates for Running Bayesian Regressions

What are Bayesian Regressions?

First, they have nothing to do with learning, have no priors to be updated (usually), and will never show an explicit Bayes Rule.

The point of Bayesian Regressions is to allow non-parametric parameter uncertainty. The distribution of each parameter will be represented by random draws from its distribution.

Some general insights:

  • The mode of the Bayesian parameters will be the MLE (or OLS) result.

  • The curvature of the parameter distributions at that peak equals the curvature of a normal distribution with the point estimate and standard error.

  • Computational Bayesian approaches make it very easy to choose different modeling assumptions (e.g., Cauchy errors and logistic regressions).

  • Bayesian regressions are useful for any dataset size, but can get prohibitively slow beyond 100k points.

The templates

Each template (except the last one) has an example part and a general part. The example can be swapped out with the general part still used.

  • Multivariate regression (multivariate.R)
  • Robust noise regression (robustnoise.R)
  • Fixed effects regression (fixedeffects.R)
  • Constrained parameter regression (paramlimits.R)

To start, install Stan using setup.R. Then run the template of your choice, and display the results with the options in display.R.