Title: Inference for Max-Stable Random Fields and Applications
Advisor: Associate Professor Stilian Stoev
Committee Members: Professor Tailen Hsing, Assistant Professor Veronica Berrocal
Abstract: Extreme values over a spatial domain are of key interest in many geophysical and environmental science applications. Over the last 30 years advancements in multivariate extreme value theory have shown that max-stable random fields are fundamental statistical models for spatial extremes. Inference for these models, however, remains a challenging problem due to the lack of tractable multivariate likelihoods. Recent progress has been made utilizing composite likelihood inference (Padoan et al., 2010), but is limited to cases where pairwise likelihoods exist. In this proposal, we review several max-stable random field models and introduce a computational approach to inference that can be applied in a more general setting. We discuss some implementation issues, as well as future extensions, theoretical and methodological problems.