Perfect Simulation for Orthogonal Model Mixing

In this article we demonstrate how to generate independent and identically distributed samples from the model space of the Bayes linear model with orthogonal predictors. We use the method of coupled Markov chains from the past as introduced by Propp and Wilson (1996). This procedure alleviates any concerns over convergence and sample mixing. We present a number of examples including a perfect simulation of Bayesian wavelet selection in a 1024 dimensional model space, a knot selection problem for spline smoothers and, a standard linear regression variable selection problem.