Evolutionary Markov chain Monte Carlo

Markov chain Monte Carlo (MCMC) is a popular class of algorithms to sample from a complex distribution. A key issue in the design of MCMC algorithms is to improve the proposal mechanism and the mixing behaviour. This has led some authors to propose the use of a population of MCMC chains, while others go even further by integrating techniques from evolutionary computation (EC) into the MCMC framework. This merging of MCMC and EC leads to a class of algorithms, we call Evolutionary Markov Chain Monte Carlo (EMCMC). In this paper we first survey existing EMCMC algorithms and categorise them in two classes: family-competitive EMCMC and population-driven EMCMC. Next, we introduce, the Elitist Coupled Acceptance rule and the Fitness Ordered Tempering algorithm.