A Bayesian spatial hierarchical model for extreme precipitation in Great Britain

Intense precipitation events are commonly known to be associated with an increased risk of flooding. As a result of the societal and infrastructural risks linked with flooding, extremes of precipitation require careful modeling. Extreme value analysis is typically used to model large precipitation events, although an independent analysis of neighboring sites can produce very different estimates of risk. In reality, one would expect neighboring locations to exhibit similar extremal behavior. A common method of inducing spatial similarity of extremal behavior is to define a spatial structure on the parameters of a generalized Pareto distribution in a Bayesian hierarchical modeling framework. These methods are often implemented under the assumption of conditional independence in time and space, with the consequence that standard errors of parameter estimates are too small. We present an approach for accounting for spatial and temporal dependence when quantifying the uncertainty in Bayesian hierarchical models when the misspecification of conditional independence has been made. We also present comparisons of performance between this class of models and alternative approaches, applied to precipitation data in Great Britain.