Cox, Dennis D.2009-06-042009-06-042001Boeckenhauer, Rachel Kaye. "Estimating nonlinear functionals of a random field." (2001) Diss., Rice University. <a href="https://hdl.handle.net/1911/17941">https://hdl.handle.net/1911/17941</a>.https://hdl.handle.net/1911/17941Environmental 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.151 p.application/pdfengCopyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.StatisticsThesisTHESIS STAT. 2001 BOECKENHAUER