What to Expect
Modeling data with nonstationary covariance structure is important to represent heterogeneity in geophysical and other environmental spatial processes. In this work, we investigate a multistage approach to modeling nonstationary covariances that is efficient for large data sets. First, we use likelihood estimation in local, moving windows to infer spatially varying covariance parameters. These surfaces of covariance parameters can then be encoded into a global covariance model specifying the second order structure for the complete spatial domain. The resulting global model allows for efficient simulation and prediction. We investigate the nonstationary spatial autoregressive (SAR) model related to Gaussian Markov random field (GMRF) methods, which is amenable to plug in local estimates and practical for large data sets. In addition we use a simulation study to establish the accuracy of local Matern parameter estimation as a reliable technique when replicate fields are available and small local windows are exploited to reduce computation. This multistage modeling approach is implemented on a nonstationary climate model output data set with the goal of emulating the variation in the numerical model ensemble using a Gaussian process.
Ashton Wiens received his B.S. in mathematics from the University of Kansas in 2015 and M.S. in applied mathematics from the University of Colorado Boulder in 2018. He is currently finishing his Ph.D. in applied mathematics at the University of Colorado Boulder, working with Professor William Kleiber. His thesis research in spatial statistics focuses on modeling large, nonstationary, and multivariate data sets with efficient numerical techniques and applications in climatology. He spent two summers working at the National Center for Atmospheric Research (NCAR) under the mentorship of Professor Douglas Nychka. He has also collaborated with researchers in many different academic fields at CU Boulder through the Laboratory for Interdisciplinary Statistical Analysis (LISA).