Title: Data imputation of large observations via Bayesian inference for multivariate extremes
Authors: Isadora Antoniano-Villalobos - Ca' Foscari University of Venice (Italy) [presenting]
Simone Padoan - Bocconi University (Italy)
Abstract: Missing data is a known issue in statistics. In many environmental applications, the greatest interest is placed on large observations, e.g. of pollution levels, wind speed, precipitation or temperature, to name a few. In such contexts, usual data imputation methods may fail to reproduce the heavy tail behaviour of the quantities involved. Recent literature has proposed the use of multivariate extreme value theory to predict an unobserved component of a random vector given large observed values of the rest. This is achieved through the estimation of the angular measure controlling the dependence structure in the tail of the distribution. The idea can be used for effective data imputation at adequately large levels, provided that the model used for the angular measure is flexible enough to capture complex dependence structures. A Bayesian nonparametric model based on constrained Bernstein polynomials ensures such flexibility, while allowing for tractable inference. An additional advantage of this approach is the natural way in which uncertainty about the estimation is incorporated into the imputed values through the Bayesian paradigm.