Beyond Gaussian Processes: Flexible Bayesian Modeling and Inference for Geostatistical Processes

• Activity Number: 56 - Modern Bayesian Methods for Complex Spatial Data
• Type: Topic Contributed
• Date/Time: Sunday, August 7, 2022 : 4:00 PM to 5:50 PM
• Sponsor: International Society for Bayesian Analysis (ISBA)
• Author(s): Marcos Oliveira Prates* and Guilherme Aparecido Santos Aguilar and Flávio Bambirra Gonçalves
• Companies: Universidade Federal de Minas Gerais and Universidade Federal de Minas Gerais and Universidade Federal de Minas Gerais
• Keywords: Gaussian Process; Skewness; Spatial Statistics; Stochastic Process

Abstract

This work proposes a novel family of geostatistical models to account for structures that cannot be properly accommodated by traditional Gaussian processes, e.g., positiveness and/or asymmetry and/or heavy tails. This family is specified hierarchically, through an augmented process, and combines the infinite dimensional dynamics of Gaussian processes to that of any multivariate continuous distribution. Whilst processes defined by assigning arbitrary continuous distributions to be the finite-dimension distributions of the candidate process are typically not valid, the family proposed here may be arbitrarily similar to any of those (conceptual) processes and yet be valid. Formal results to establish the existence and other important properties of the proposed processes, such as their absolute continuity w.r.t. the Gaussian process measure, are provided. The authors would like to thank CAPES, CNPq and FAPEMIG for partial financial support.