A Parallel Evolutionary Multiple-Try Metropolis Markov Chain Monte Carlo Algorithm for Sampling Spatial Partitions

TL;DR

This paper introduces a novel parallel evolutionary MCMC algorithm that combines optimization heuristics with Markov chain sampling, enabling efficient exploration of complex spatial partitions using parallel computation.

Contribution

It presents a new EMCMC algorithm that integrates evolutionary algorithms with Markov Chain Monte Carlo, enhanced by parallel architecture for sampling complex spatial state spaces.

Findings

Effective sampling of complex spatial partitions.

Parallel architecture improves computational efficiency.

Combines optimization heuristics with MCMC for better exploration.

Abstract

We develop an Evolutionary Markov Chain Monte Carlo (EMCMC) algorithm for sampling spatial partitions that lie within a large and complex spatial state space. Our algorithm combines the advantages of evolutionary algorithms (EAs) as optimization heuristics for state space traversal and the theoretical convergence properties of Markov Chain Monte Carlo algorithms for sampling from unknown distributions. Local optimality information that is identified via a directed search by our optimization heuristic is used to adaptively update a Markov chain in a promising direction within the framework of a Multiple-Try Metropolis Markov Chain model that incorporates a generalized Metropolis-Hasting ratio. We further expand the reach of our EMCMC algorithm by harnessing the computational power afforded by massively parallel architecture through the integration of a parallel EA framework that guides Markov chains running in parallel.