On Bayesian Model and Variable Selection Using MCMC

Introduction A Bayesian approach to model selection proceeds as follows. Suppose that the data y are considered to have been generated by a model m, one of a set M of competing models. Each model specifies the distribution of Y , f(yjm; fi m ) apart from an unknown parameter vector fi m 2 Bm , where Bm is the set of all possible values for the coefficients of model m. If f(m) is the prior probability of model m, then the posterior probability is given by f(mjy) = f(m)f(y jm) P m2M f(m)f(y jm