Chief Data Scientist, ICC & Auxiliary Professor, Department of Statistics; Director, Statistical Consulting ServiceThe Ohio State University
Parameter Estimation Algorithms for Computationally Intensive Spatial Problems
Due to modern advances in computing power, the use of increasingly complex statistical models has become practical. One class of large models that often relies on numerical techniques for parameter estimation is multi-resolution spatial models. Unfortunately, numerical maximization and sampling techniques used to estimate parameters in such complex models often explore the parameter space slowly, resulting in unreliable estimates. To combat this lack of reliability, several algorithms are introduced with the goals of improving the mixing of Markov chain Monte Carlo algorithms and improving exploration properties of genetic algorithm maximization techniques. We propose a multi-resolution genetic algorithm that incorporates elements of simulated tempering to all efficient estimation of parameters via maximization in spatial models. This algorithm is also adapted to perform Markov chain Monte Carlo sampling from a posterior distribution in a Bayesian setting resulting in improved mixing and exploration of the posterior relative to ordinary MCMC sampling. We find that these two algorithms are efficient methods of estimating parameters in computationally intensive spatial problems. Parallel implementation of these algorithms is addressed. These methods are demonstrated on inverse problem examples from the field of groundwater hydrology.