A Parallel Evolutionary Multiple-Try Metropolis Markov Chain Monte Carlo Algorithm for Sampling Spatial Partitions
This provides an incremental improvement for researchers in spatial statistics and computational science who need to sample from complex spatial distributions more efficiently.
The paper tackles the problem of sampling spatial partitions from complex state spaces by developing a parallel evolutionary Markov Chain Monte Carlo algorithm that combines evolutionary algorithms for state space traversal with MCMC's theoretical convergence properties, achieving computational efficiency through parallelization.
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.