Deep Learning Synthetic Likelihood Approximations for Spatial Extremes
This is work done jointly with Brian Reich (NCSU) and Ben Shaby (CSU). We developed a process mixture model (PMM) which interpolates between a max stable process and a Gaussian process. The likelihood is intractable, so we develop a computational approach which uses a Vecchia approximation to simplifiy the likelihood and a simulation based approach to learn the approximate likelihood. This can then be used in a hierarchical Bayesian framework for posterior inference. In our first work we analyzed changes in streamflow across the US over the last 50 years.
In follow-up work, we concentrated on the storm-prone central US. We used precipitation as a predictor to developed a nonstationary PMM for the region. Using climate projections, we also obtained near-future forecasts of extreme streamflow for the region.