@article{heaton_christensen_terres_2017, title={Nonstationary Gaussian Process Models Using Spatial Hierarchical Clustering from Finite Differences}, volume={59}, ISSN={["1537-2723"]}, DOI={10.1080/00401706.2015.1102763}, abstractNote={Modern digital data production methods, such as computer simulation and remote sensing, have vastly increased the size and complexity of data collected over spatial domains. Analysis of these large spatial datasets for scientific inquiry is typically carried out using the Gaussian process. However, nonstationary behavior and computational requirements for large spatial datasets can prohibit efficient implementation of Gaussian process models. To perform computationally feasible inference for large spatial data, we consider partitioning a spatial region into disjoint sets using hierarchical clustering of observations and finite differences as a measure of dissimilarity. Intuitively, directions with large finite differences indicate directions of rapid increase or decrease and are, therefore, appropriate for partitioning the spatial region. Spatial contiguity of the resulting clusters is enforced by only clustering Voronoi neighbors. Following spatial clustering, we propose a nonstationary Gaussian process model across the clusters, which allows the computational burden of model fitting to be distributed across multiple cores and nodes. The methodology is primarily motivated and illustrated by an application to the validation of digital temperature data over the city of Houston as well as simulated datasets. Supplementary materials for this article are available online.}, number={1}, journal={TECHNOMETRICS}, author={Heaton, Matthew J. and Christensen, William F. and Terres, Maria A.}, year={2017}, month={Feb}, pages={93–101} }
 @article{terres_gelfand_2016, title={Spatial process gradients and their use in sensitivity analysis for environmental processes}, volume={168}, ISSN={["1873-1171"]}, DOI={10.1016/j.jspi.2015.07.003}, abstractNote={This paper develops methodology for local sensitivity analysis based on directional derivatives associated with spatial processes. Formal gradient analysis for spatial processes was elaborated in previous papers, focusing on distribution theory for directional derivatives associated with a response variable assumed to follow a Gaussian process model. In the current work, these ideas are extended to additionally accommodate a continuous covariate whose directional derivatives are also of interest and to relate the behavior of the directional derivatives of the response surface to those of the covariate surface. It is of interest to assess whether, in some sense, the gradients of the response follow those of the explanatory variable. The joint Gaussian structure of all variables, including the directional derivatives, allows for explicit distribution theory and, hence, kriging across the spatial region using multivariate normal theory. Working within a Bayesian hierarchical modeling framework, posterior samples enable all gradient analysis to occur post model fitting. As a proof of concept, we show how our methodology can be applied to a standard geostatistical modeling setting using a simulation example. For a real data illustration, we work with point pattern data, deferring our gradient analysis to the intensity surface, adopting a log-Gaussian Cox process model. In particular, we relate elevation data to point patterns associated with several tree species in Duke Forest.}, journal={JOURNAL OF STATISTICAL PLANNING AND INFERENCE}, author={Terres, Maria A. and Gelfand, Alan E.}, year={2016}, month={Jan}, pages={106–119} }
 @article{terres_lawrence_hosack_haywood_babcock_2015, title={Assessing habitat use by snapper (Chrysophrys auratus) from baited underwater video data in a coastal marine park}, volume={10}, number={8}, journal={PLoS One}, author={Terres, M. A. and Lawrence, E. and Hosack, G. R. and Haywood, M. D. E. and Babcock, R. C.}, year={2015} }