A Monte Carlo Approach to Quantifying Model Error in Intractable Bayesian Hierarchical Models

• Activity Number: 302
• Type: Topic Contributed
• Date/Time: Tuesday, August 11, 2015 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistics and the Environment
• Author(s): Staci White* and Radu Herbei
• Companies: The Ohio State University and The Ohio State University
• Keywords: model error ; Bayesian estimation ; discrepancy ; tapering

Abstract

In intractable Bayesian hierarchical models, the posterior distribution of interest is often replaced by a computationally efficient approximation that is instead used for inference. In this work, we propose innovative statistical methodology that allows one to study the impact of such approximations by quantifying the model error, which we define to be the discrepancy between the two posterior distributions (target vs. approximation). This provides a structure to analyze model approximations with regard to the reliability of inference and computational efficiency. We illustrate our approach through a spatial analysis of global sea surface temperature where covariance tapering is used to alleviate the computational demand associated with inverting the full covariance matrix.