Evolutionary computation and multiple chains MCMC sampling: An overview

Evolutionary Computation (EC) has been introduced in the 1960s in the field of Artificial Intelligence, and includes a variety of algorithms (called Evolutionary Algorithms, EAs) designed to analyze complex systems and problems. These tasks are accomplished by use of metaphors related to evolutionary biology and Darwins principles, for which a population of interacting individuals evolves through generations to populations better able to adapt the environment. In the last twenty years EAs have been employed to a wide range of statistical problems; a particular application is Markov Chain Monte Carlo (MCMC) sampling with multiple chains running in parallel. This framework, motivated by situations in which target distribution exhibits multimodality, high-dimensionality or has highly correlated components, suggests many analogies with EAs if chains are allowed to interact with each other. This has led to several contributions and algorithms in literature by researchers from different fields of science. We aim at reviewing these different proposals, identifying peculiar procedures to deal with MCMC issues, for example preservation of convergence to desired equilibrium distribution, highlighting strengths and weaknesses, and unifying them in a common framework of EC.