A Bayesian Analysis of Extreme Rainfall Data

Abstract

Understanding and quantifying the behaviour of a rainfall process at extreme levels has important applications for design in civil engineering. As in the extremal analysis of any environmental process, estimates often are required of the probability of events that are rarer than those already recorded. As data on extremes are scarce, all available sources of information should be used in inference. Consequently, research has focused on the development oftechniquesthat make optimal use of available data. In this paper a daily rainfall series is analysed within a Bayesian framework, illustrating how the careful elicitation of prior expert information can supplement data and lead to improved estimates of extremal behaviour. For example, using the prior knowledge of an expert hydrologist, a Bayesian 95% interval estimate of the 1OO-year return level for daily rainfall is found to be approximately half of the width of the corresponding likelihoodbased confidence interval.

Análise Bayesiana no estudo do tempo de retorno das precipitações pluviais máximas em Jaboticabal (SP)

“…Apenas na última década, alguns autores têm sugerido o procedimento Bayesiano para incorporar o conhecimento na estrutura dos modelos na inferência de valores extremos e para reduzir as incertezas da estimação dos parâmetros e de quantis da distribuição GEV. Coles & Tawn (1996) utilizaram conhecimentos de profissionais que trabalham na área para construir suas informações à priori, as quais incorporam a dependência entre os parâmetros associados ao modelo extremo, podendo incorporar o conhecimento baseado em quantis com uma distribuição Gama. Stephenson (2002) e Stephenson & Tawn (2004), sugerem um procedimento Bayesiano para incorporar o conhecimento prévio na estrutura dos teoremas de modelos na inferência de valores extremos, reduzindo a incerteza da estimação dos parâmetros.…”

Forecasting US insured hurricane losses

“…relatively rare (Coles and Tawn, 1996;Katz et al, 2002;Coles et al, 2003). In the context of local hurricane winds, Casson and Coles (1999) used a Bayesian analysis to estimate parameters of spatial regression models.…”

Posterior propriety in Bayesian extreme value analyses using reference priors

“…A distinction can be made between subjective analyses, in which the prior distribution supplies information from an expert (Coles and Tawn, 1996) or more general experience of the quantity under study Stedinger, 2000, 2001), and so-called objective analyses (Berger, 2006). In the latter, a prior is constructed using a formal rule, for use when no subjective information is to be incorporated into the analysis.…”