Graduation date: 2006This research addresses sample process variance estimation on continuous domains and for non-probability samples in particular. The motivation for the research is a scenario in which a program has collected non-probability samples for which there is interest in characterizing how much an extrapolation to the domain would vary given similarly arranged collections of observations. This research does not address the risk of bias and a key assumption is that the observations could represent the response on the domain of interest. This excludes any hot-spot monitoring programs. The research is presented as a collection of three manuscripts. The first (to be published in Environmetrics (2006)) reviews and compares model- and design-based approaches for sampling and estimation in the context of continuous domains and promotes a model-assisted sample-process variance estimator. The next two manuscripts are written to be companion papers. With the objective of quantifying uncertainty of an estimator based on a non-probability sample, the proposed approach is to first characterize a class of sets of locations that are similarly arranged to the collection of locations in the non-probability sample, and then to predict variability of an estimate over that class of sets using the covariance structure indicated by the non-probability sample (assuming the covariance structure is indicative of the covariance structure on the study region). The first of the companion papers discusses characterizing classes of similarly arranged sets with the specification of a metric density. Goodness-of-fit tests are demonstrated on several types of patterns (dispersed, random and clustered) and on a non-probability collection of locations surveyed by Oregon Department of Fish & Wildlife on the Alsea River basin in Oregon. The second paper addresses predicting the variability of an estimate over sets in a class of sets (using a Monte Carlo process on a simulated response with appropriate covariance structure).