, Volume 11, Issue 3, pp 217-233

First online:

Bayesian inference for clustered extremes

  • Lee FawcettAffiliated withSchool of Mathematics and Statistics, Newcastle University
  • , David WalshawAffiliated withSchool of Mathematics and Statistics, Newcastle University Email author 

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We consider Bayesian inference for the extremes of dependent stationary series. We discuss the virtues of the Bayesian approach to inference for the extremal index, and for related characteristics of clustering behaviour. We develop an inference procedure based on an automatic declustering scheme, and using simulated data we implement and assess this procedure, making inferences for the extremal index, and for two cluster functionals. We then apply our procedure to a set of real data, specifically a time series of wind-speed measurements, where the clusters correspond to storms. Here the two cluster functionals selected previously correspond to the mean storm length and the mean inter-storm interval. We also consider inference for long-period return levels, advocating the posterior predictive distribution as being most representative of the information required by engineers interested in design level specifications.


Bayesian inference Extremal index MCMC Clusters Extreme values

AMS 2000 Subject Classification