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We present a general framework for defining priors on model structure andsampling from the posterior using the Metropolis-Hastings algorithm. The keyidea is that structure priors are defined via a probability tree and that theproposal mechanism for the Metropolis-Hastings algorithm operates by traversingthis tree, thereby defining a cheaply computable acceptance probability. Wehave applied this approach to Bayesian net structure learning using a number ofpriors and tree traversal strategies. Our results show that these must bechosen appropriately for this approach to be successful.

Markov Chain Monte Carlo using Tree-Based Priors on Model Structure