Semivariogram Estimation Using Ant Colony Optimization and Ensemble Kriging Accounting for Parameter Uncertainty

In this presentation we revisit the problem of semivariogram estimation and present a modular, reusable, and encapsulated set of MATLAB programs that use a hybrid Ant Colony Optimization (ACO) heuristic to solve the "optimal fit" problem. Though the ACO heuristic involves a stochastic component, advantages of the heuristic over traditional gradient-search methods, like the Gauss-Newton method, include the ability to estimate model semivariogram parameters accurately without initial guesses input by the user. The ACO heuristic is also superiorly suited for strongly nonlinear optimization over spaces that may contain several local minima. The presentation will focus on the application of ACO to existing weighted least squares and restricted maximum likelihood estimation methods with a comparison of results. The presentation will also discuss parameter uncertainty, particularly in the context of restricted maximum likelihood and Bayesian methods. We compare the local linearized parameter estimates (or Cramer-Rao lower bounds) with modern Monte Carlo methods, such as acceptance-rejection. Finally, we present ensemble kriging in which conditional realizations are generated in a way that uncertainty in semi-variogram parameters is fully accounted for. Results for a variety of sample problems will be presented along with a discussion of solution accuracy and computational efficiency.