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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.

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

and of course the reference

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  • $\begingroup$ Thank you for the reply. U have already looked into Gelman et al. But I did not find it detailed enough. $\endgroup$ Feb 15 '19 at 8:11
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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.

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