Bayesian extreme value models: Asymptotic behavior, hierarchical convergence, and predictive robustness

The efficacy of Bayesian extreme value models is examined, with a focus on their ability to analyze tail behavior and their predictive accuracy. The hierarchical structure in Bayesian extreme value models helps model heterogeneity by borrowing strength across groups. The theoretical results indicate that the Kullback-Leibler divergence between posteriors drawn from various priors is bounded, reinforcing the stability of Bayesian extreme value models against prior selections. As the sample size grows, the influence of priors diminishes. In addition, the results establish that the hyperposterior distribution converges to a specific distribution as group size increases. This robustness is restricted to prior assumptions and integrates into its hierarchical structure. Another finding confirms the convergence of predictive distributions, especially for big data analyses. The advantage of hierarchical modeling over non-hierarchical counterparts is underscored as the variance component of the predictive loss function diminishes in hierarchical Bayesian extreme value models.