Research Seminar Speaker: Ben Shaby, Ph.D., Assistant Professor, Department of Statistics and the Institute for CyberScience at Penn State

Title: 

Max-Infinitely Divisible Models for Spatial Extremes Using Random Effects

Abstract:

Rare events can have crippling effects on economies, infrastructure, and human health and wellbeing. Their outsized impacts make extreme events critical to understand, yet their defining characteristic, rareness, means that precious little information is available to study them. Extremes of environmental processes are inherently spatial in structure, as a given event necessarily occurs over a particular spatial extent at a particular collection of locations. Characterizing their probabilistic structure therefore requires moving well beyond the well-understood models that describe marginal extremal behavior at a single location. Rather, stochastic process models are needed to describe joint tail event across space. Distinguishing between the subtly different dependence characteristics implied by current families of stochastic process models for spatial extremes is difficult or impossible based on exploratory analysis of data that is by definition scarce. Furthermore, different choices of extremal dependence classes have large consequences in the analysis they produce.

I will present stochastic models for extreme events in space that are 1) flexible enough to transition across different classes of extremal dependence, and 2) permit inference through likelihood functions that can be computed for large datasets. These modeling goals are accomplished by representing stochastic dependence relationships conditionally, which will induce desirable tail dependence properties and allow efficient inference through Markov chain Monte Carlo. I will describe models for spatial extremes using max-infinitely divisible processes, a generalization of the limiting max-stable class of processes which has received a great deal of attention. This work extends previous family of max-stable models based on a conditional hierarchical representation to the more flexible max-id class, thus accommodating a wider variety of extremal dependence characteristics while retaining the structure that makes it computationally attractive.