Bayesian Regression - Overview

Question

Does anyone know a comprehensive, well-written and recent book / collection of articles about Bayesian regression and variable selection?

The topics I am particularly interested in are:

• constraints of categorical variables
• ordinal bayesian regression
• interaction effects (including hierarchical models incorporating lower and higher order effects)
• generalised Bayesian regression
• cross-validation techniques
• any other topics dealt with in recent research

I am mainly interested in the mathematical background of these methods.

Answer 1

Bayesian regression is handled in pretty much every Bayesian textbook see e.g.

• Gelman et al.'s Bayesian Data Analysis
• Hoff's A First Course in Bayesian Statistical Methods
• Rossi's and Allenby's Bayesian Statistics and Marketing
• Koop's Bayesian Econometrics
• Greenberg's Introduction to Bayesian Econometrics

and of course the reference

• Zellner's An introduction to Bayesian methods in econometrics

Answer 2

Adding to Xi'an's answer, since you mention many regression models etc., the Data Analysis Using Regression and Multilevel/Hierarchical Models book by Gelman & Hill is also worth mentioning. It focuses on regression models in general, but with strong emphasis on Bayesian approach.