B0675
Title: Where do extremes come from? Dependent mixtures for block maxima
Authors: Viviana Carcaiso - University of Padova (Italy) [presenting]
Isadora Antoniano-Villalobos - Ca' Foscari University of Venice (Italy)
Ilaria Prosdocimi - Ca Foscari University of Venice (Italy)
Abstract: In the block maxima approach for extreme value analysis, maximum values are commonly assumed to be derived from large samples of a stationary process. However, this assumption may not hold in many applications. For instance, when analyzing annual rainfall maxima, extremes can be associated with different weather patterns within a given year. In such scenarios, finite mixture models can be useful. The focus is on two-component mixtures of Gumbel distributions, with observations labelled based on the specific physical processes that generated them. However, the distinction between the two groups identified by known labels may not effectively separate the tails. To address this, the proposed model avoids deterministic allocation of data points to mixture components and instead uses labels and additional variables to probabilistically inform the allocation. A Bayesian hierarchical approach is used to enable the borrowing of information between the groups for the estimation of model parameters and to directly quantify the uncertainty associated with the component allocation. To evaluate and compare different models, proper scoring rules are employed as measures of predictive performance. By considering these rules, the aim is to determine when a mixture model aligned with physical characteristics is preferable to relying solely on a single distribution.
