Bayesian Inference for an Extreme Value Mixture Model

Extreme value theory is used to derive asymptotically motivated models for unusual or rare events, e.g. the upper or lower tails of a distribution. A new, flexible extreme value mixture model is proposed combining a nonparametric kernel density estimator with an appropriate tail model, which overcomes the key issue of determining the threshold which defines the distribution tail and accounts for uncertainty due to the threshold choice. Bayesian inference is used to account for all uncertainties and enables inclusion of expert prior information, potentially also overcoming the inherent sparsity of extremal data. An application to estimating the quantiles of daily FTSE log returns is used for demonstration.