Spatial Semiparametric Spectral Density Estimation for Multivariate Extremes

• Activity Number: 423 - Recent Advancements in the Analysis of Extremes
• Type: Contributed
• Date/Time: Tuesday, July 31, 2018 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistics and the Environment
• Author(s): Mauricio Nascimento* and Benjamin Shaby
• Companies: Pennsylvania State University and Penn State University
• Keywords: extreme values; mixture; bayesian inference; spatial statistics

Abstract

Wildfire in California is a great problem because it results in massive loss of life and property. Last year more than a million acres were burnt, causing billions of dollars in damage. Because of this, it is important to understand the conditions that allow fires the start and conditions that allow fires to spread, and more importantly, how do they work together. Of particular interest is the situation where fire ignition conditions and spread conditions are jointly extreme. To study the tail dependence of these two conditions, we analyze data from 20 weather stations in southern California. We propose the use of a Bayesian mixture of Dirichlet distributions to model the spectral density that determines the dependence structure of the joint tail, combined with a spatial prior distribution for the mixture parameters, which results in sharing of information among the different locations. This spatial dependence allows us to not only obtain better estimates for the dependence measure but also predict the spectral density at un-observed locations.