Statistics Seminar

Abstract: Extreme value analysis is critical for understanding the effects of climate change. Exploiting the spatiotemporal structure of climate data can improve estimates by borrowing strength across nearby locations and provide estimates of the probability of simultaneous extreme events. A fundamental probability model for spatially-dependent extremes is the max-stable processes. While this model is theoretically justified, it leads to an intractable likelihood function. We propose to use deep learning to overcome this computational challenge. The approximation is based on simulating millions of draws from the prior and then the data-generating process, and then using deep learning density regression to approximate the posterior distribution. We verify through extensive simulation experiments that this approach leads to reliable Bayesian inference, and discuss extensions to other spatial processes with intractable likelihoods including the autologistic model for binary data and SIR model for the spread of an infectious disease.