Multiresolution Genetic Algorithms and Markov chain Monte Carlo

This article proposes a multiresolution genetic algorithm that allows efficient estimation of parameters in large-dimensional models. Such models typically rely on complex numerical methods that require large amounts of computing power for estimating parameters. Unfortunately, the numerical maximization and sampling techniques used to fit such complex models often explore the parameter space slowly resulting in unreliable estimates. Our algorithm improves this exploration by incorporating elements of simulated tempering into a genetic algorithm framework for maximization. Our algorithm can also be adapted to perform Markov chain Monte Carlo sampling from a posterior distribution in a Bayesian setting, which can greatly improve mixing and exploration of the posterior compared to ordinary MCMC methods. The proposed algorithm can be used to estimate parameters in any model where the solution can be solved on different scales, even if the data are not inherently multiscale. We address parallel implementation of the algorithms and demonstrate their use on examples from single photon emission computed tomography and groundwater hydrology.