# Explaining Bayesian Regression Models to Physicians

I have estimated a rstanarm stan_lm model. The intended audience is a specialty medical journal (anesthesiology) whose readers are mostly physicians with limited statistical understanding/competence.
I am seeking a literature reference for this audience that provides a gentle, minimally mathematical, introduction to Bayesian regression, weakly informative priors, model selection (loo cv), etc. A google search has many hits, but nothing quite right. Most physician readers have heard of Rev Bayes and his theorem, but they are mostly oblivious to the steps for a Bayesian regression model.
I would point them to a Wikipedia reference, but these change from time to time making them difficult to use in a journal citation.
Any suggestions would be appreciated.
Nathan

I would cite Regression and Other Stories by Gelman, Hill, and Vehtari

http://www.stat.columbia.edu/~gelman/regression/

This has the added benefit that no reviewers can object because it hasn’t been published yet, but it does cover most of what you listed (excluding PSISLOOCV).

There isn’t a nontechnical explanation of what stan_lm does, published or otherwise. I would describe it as a beta prior on the R^2 with first shape parameter \frac{K}{2} and second shape parameter \eta, where \eta is calculated to achieve whatever you specified for the prior mode, median, or mean. The number you input for the prior mode, median, or mean is highly informative, but conditional on that, the priors on everything else in the model are as weak as I could make them.

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I appreciate your comment. I have Gelman et al 1st edition. But for my audience, that is too much. I do want to see the 2nd ed.

I have found a recent article that does a reasonable job. it might be useful to others who need a citation for the same purpose.

An introduction to using Bayesian linear regression with clinical data

Scott A. Baldwin, Michael J. Larson
Behav Res Ther 2017; 98:58-75

Talks about or mentions priors, estimation, stan, loo, etc.

I wasn’t intending to explain the R2 family priors.

Nathan

I was going to suggest Baldwin and Larsons paper, so seconding that. I think it strikes a pretty good balance between accessible and accurate.