Reversible Genetically Modified Mode Jumping MCMC
This work addresses computational challenges in Bayesian model selection for high-dimensional data, representing an incremental improvement over prior methods.
The paper tackles the problem of inferring posterior model probabilities in complex model spaces with many variables by introducing a reversible version of the GMJMCMC algorithm, resulting in a proper MCMC method with a limiting distribution that matches these probabilities under certain conditions.
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.