 Reversible-jump Markov chain Monte Carlo

Reversible-jump Markov chain Monte Carlo samples a posterior on a disjoint union of model-specific parameter spaces. A dimension-matching bijection between old parameters plus auxiliary variables and new parameters plus reverse auxiliary variables supplies a reversible proposal. Its acceptance ratio includes posterior-density, model-selection, proposal-density, and Jacobian determinant factors. The equal-dimension reversible-jump acceptance probability is the ordinary density-based special case.

Reversible-jump Markov Chain Monte Carlo (RJMCMC) is a statistical method used for Bayesian inference in models where the dimensionality of the parameter space can change. This is particularly useful in variable selection problems or model selection problems where different models may have different numbers of parameters. The key idea of RJMCMC is to allow the Markov chain to jump between models of different dimensions.