Estimating nonlinear functionals of a random field
Boeckenhauer, Rachel Kaye
Cox, Dennis D.
Doctor of Philosophy
Environmental data are gathered with the goal of estimating some quantity of interest. In particular, in the case of groundwater or soil contamination, it is desirable to estimate the total amount of contaminant present within a region in order to more effectively remediate the contamination. This problem has been generally unaddressed previously, and is of interest to environmental scientists. A method is introduced here to estimate the integral of a lognormal process over a region using Monte Carlo simulation of the process conditional on the observed data. The performance of the method is evaluated with an application to groundwater data. Results are compared using uniform sampling and importance sampling over the region.