Simulated Sintering: Markov Chain Monte Carlo With Spaces of Varying Dimensions

In an effort to extend the tempering methodology, we propose simulated sintering as a general framework for designing Markov chain Monte Carlo algorithms. To implement sintering, one identifies a family of probability distributions, all related to the target one and defined on spaces of different dimensions. Then, a Markov chain is constructed to move across these spaces, with the hope that the fast mixing of transitions in lower-dimensional spaces facilitates the simulation from the target distribution. Two types of sintering are discussed: conditional sintering, which is motivated by the multigrid Monte Carlo idea and can be regarded as a generalization of the Gibbs sampler; and marginal sintering, which can be achieved by reversible jump MCMC. To help mixing in a reversible jump MCMC algorithm, we suggest incorporating the dynamic weighting method proposed by Wong and Liang. Examples in graphical modeling and computational biology illustrate how these techniques can be applied.