Hierarchical models for uncertainty quantification: An overview

Abstract

Analyses of complex processes should account for the uncertainty in the data, the processes that generated the data, and the models that are used to represent the processes and data. Accounting for these uncertainties can be daunting in traditional statistical analyses. In recent years, hierarchical statistical models have provided a coherent probabilistic framework that can accommodate these multiple sources of quantifiable uncertainty. This overview describes a science-based hierarchical statistical modeling approach and the associated Bayesian inference. In addition, given that many complex processes involve the dynamical evolution of spatial processes, an overview of hierarchical dynamical spatio-temporal models is also presented. The hierarchical and spatio-temporal modeling frameworks are illustrated with a problem concerned with assimilating ocean vector wind observations from satellite and weather center analyses.