Abstract
In this lecture we look at Bayesian model averaging and choice of prior distributions with a focus on g-priors or mixtures of g-priors.
Readings: Christensen Chapter 15 and Hoff Chapter 9
Review papers: Bayesian Model Averaging Hoeting et al (1999) Statistical Science
Model Uncertainty Clyde & George (2004) Statistical Science
Mixtures of g-priors for Bayesian Variable Selection Liang et al (2008) Journal of the American Statistical Association
In this lecture we look at model choice from a Bayesian perspective. We augment the likelihood and prior on parameters in the linear model using indicator variables that represent which variables are included in a model, which allows positive probability that the coefficients are exactly zero. Using the Jeffreys-Zellner’s g-prior for parameters in a model we derive closed form expressions for Bayes factors that are used in posterior probabilities. To resolve problems with the choice of $g$ we turn to mixtures of $g$ priors, such as the Cauchy distribution.
