Bayesian Semiparametrics for Modeling the Clustering of Extreme Values

• Activity Number: 583
• Type: Invited
• Date/Time: Thursday, August 7, 2014 : 8:30 AM to 10:20 AM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Thomas Lugrin*+ and Jonathan Tawn and Anthony Davison
• Companies: EPFL and Lancaster University and EPFL
• Keywords: clustering ; Dirichlet process ; dependence

Abstract

Risk estimates for time series with short-range dependence are often obtained using the peaks over threshold method (Davison and Smith, 1990, J. R. Statist. Soc. B). Such estimates may be badly biased, however, because they do not properly account for dependence in clusters of extremes. An alternative characterization of cluster maxima (Eastoe and Tawn, 2012, Biometrika) allows separate consideration of both the marginal distribution of exceedances over the threshold and of the dependence structure. This characterization uses the extremal index at sub-asymptotic levels, for which a formulation can be derived from the conditional model of Heffernan and Tawn (2004, J. R. Statist. Soc. B), which involves specifying the conditional distribution and two stages of inference. Here we estimate this distribution by a semiparametric Bayesian approach using a dependent Dirichlet process, allowing us to fit a model for clusters of extremes in a single step. The ideas, illustrated using simulated and real data, can result in substantially improved estimates of high quantiles for time series.