Stochastic search variable selection

A partially Bayesian approach was suggested by Chipman et al. (1997). They used independent prior distributions for each main effect being active. The prior distribution selected for Pj was a mixture of normals, namely, N(0, r ) with prior probability 1 — tzj and N(0, Cj if) with prior probability ttj, where Cj greatly exceeds 1. The prior distribution for a2 was a scaled inverse-x2. They then used the Gibbs-sampling-based stochastic search variable selection method of George and McCulloch (1993) to obtain approximate posterior probabilities for Pj, that is, for each factor they obtained the posterior probability that Pj is from /V(0, cj if) rather than from N(0, r ). They treated this as a posterior probability that the corresponding factor is active and used these probabilities to evaluate the posterior probability of each model. 

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