Bayesian Changepoint Analysis for Extreme Events (Typhoons, Heavy Rainfall, and Heat Waves): An RJMCMC Approach

Abstract

A hierarchical Bayesian framework is developed to identify multiple abrupt regime shifts in an extreme event series. Specifically, extreme events are modeled as a Poisson process with a gamma-distributed rate. Multiple candidate hypotheses are considered, under each of which there presumably exist a certain number of abrupt shifts of the rate. A Bayesian network involving three layers?data, parameter, and hypothesis?is formulated. A reversible jump Markov chain Monte Carlo (RJMCMC) algorithm is developed to calculate posterior probability for each hypothesis as well its associated within-hypothesis parameters. Based on the proposed RJMCMC algorithm, a simulated example is designed to illustrate the effectiveness of the method. Subsequently, the algorithm is applied to three real, rare event time series: the annual typhoon counts over the western North Pacific (WNP), the annual extreme heavy rainfall event counts at the Honolulu airport, and the annual heat wave frequency in the Chicago area. Results indicate that the typhoon activity over the WNP is very likely to have undergone a decadal variation, with two change points occurring around 1972 and 1989 characterized by the active 1960?71 epoch, the inactive 1972?88 epoch, and the moderately active 1989?2006 epoch. For the extreme rainfall case, only one shift around 1970 is found and heavy rainfall frequency has remained stationary since then. There is no evidence that the rate of the annual heat wave counts in the Chicago area has had any abrupt change during the past 50 years.