B1343
Title: Asymptotic theory for Bayesian inference and prediction: From the ordinary to a conditional peaks-over-threshold method
Authors: Simone Padoan - Bocconi University (Italy) [presenting]
Stefano Rizzelli - Catholic University - Milan (Italy)
Clement Dombry - Universite de Franche Comte (France)
Abstract: The peaks over threshold (POT) method is the most popular statistical method for the analysis of univariate extremes. Even though there is literature on Bayesian inference for the POT method, there is no asymptotic theory for such proposals. Even more importantly, the ambitious and challenging problem of predicting future extreme events according to a proper probabilistic forecasting approach has received no attention. The asymptotic theory is developed for the Bayesian inference based on the POT method. Such an asymptotic theory is extended to cover the Bayesian inference on the tail properties of the conditional distribution of a response random variable conditionally to a vector of random covariates. With the aim to make more accurate predictions of severe extreme events than those that occurred in the past, the posterior predictive distribution of a future unobservable excess variable is specified in the unconditional and conditional approach, and it is proven that Wasserstein is consistent and derives its contraction rates.
