Statistics Seminars: Non-Stationary Extreme Value Mixture Modelling
17 October 2011 14:00 in CM221
Extreme value models are typically used to describe the distribution of rare events. An asymptotically motivated extreme value model is generally used to approximate the tail of some unknown population distribution. The fitted model is then used to extrapolate quantities of interest past the observed range of the sample data, i.e. estimating the 1 in 100 year rainfall event which may not have been observed in the historical data.
This seminar will discuss a semi-parametric modeling approach to determine the “threshold” beyond which the asymptotically motivated extreme value models provide a reliable approximation to the tail. Our semi-parametric mixture model incorporates the usual extreme value upper tail model, with the threshold as a parameter and the bulk distribution below the threshold captured by a flexible non-parametric kernel density estimator. This representation avoids the need to specify a-priori a particular parametric model for the bulk distribution, and only really requires the trivial assumption of a suitably smooth density. Bayesian inference is used to estimate the joint posterior for the threshold, extreme value tail model parameters and the kernel density bandwidth, allowing the uncertainty associated with all components to be accounted for in inferences.
The extension of this mixture model to describe the extremes of non-stationary processes, including automated (possibly non-constant) threshold estimation and uncertainty quantification is demonstrated. The results from simulations and application to a medical and air pollution problem will be presented.
(Joint work with MacDonald, A. and Lee, D.S.)
Contact Ian Jermyn