A Bayesian sieves model for the spectral measure characterizing the dependence structure of the tail of a bivariate distribution function will be presented. More precisely, as an alternative to parametric modelling of the spectral measure, we propose an infinite-dimensional model that is at the same time manageable and still dense within the class of spectral measures. Inference is done in a Bayesian framework using the censored-likelihood approach. In particular, we construct a prior distribution on the class of spectral measures and develop a trans-dimensional MCMC algorithm for numerical computations. The method provides a bivariate predictive density that can be used for predicting the extreme outcomes of a bivariate distribution. In a practical perspective, this is useful for computing rare event probabilities and extreme conditional quantiles.
Group for Research in Decision Analysis