BAYESIAN METHODS IN EXTREME-VALUE MODELING - A REVIEW AND NEW DEVELOPMENTS

Extreme value problems are characterized by a scarcity of data and the requirement of modelling where the data are most sparse, This present s a dilemma when considering a Bayesian approach to inference: the val ue of additional prior information is likely to be substantial, but th e plausibility of formulating such prior knowledge for extremal behavi our is questionable, In this paper we review the literature linking th e themes of Bayesian and extreme value analysis, and use recent advanc es in Bayesian computational tools to assess the utility of a Bayesian extreme value analysis in three different situations: one where an ex pert is available to supply prior information; the second where maximu m likelihood fails; and the third where spatial information on related variables is used to formulate an empirical prior.