  In this paper, we introduce a reversible version of a genetically modified
mode jumping Markov chain Monte Carlo algorithm (GMJMCMC) for inference on
posterior model probabilities in complex model spaces, where the number of
explanatory variables is prohibitively large for classical Markov Chain Monte
Carlo methods. Unlike the earlier proposed GMJMCMC algorithm, the introduced
algorithm is a proper MCMC and its limiting distribution corresponds to the
posterior marginal model probabilities in the explored model space under
reasonable regularity conditions.
