A Monte Carlo approach to quantifying discrepancies between intractable posterior distributions. Issue 8 (24th May 2017)

• Record Type: Journal Article
• Authors: Hepler, Staci A.; Herbei, Radu
• Is Part Of: Journal of statistical computation and simulation. Volume 87:Issue 8(2017)
• Page Start: 1666
• Page End: 1683
• Publication Date: 2017-05-24
• Subjects: Model error -- Kullback–Leibler -- divergence -- covariance tapering -- approximation; 62; Mathematical statistics -- Data processing -- Periodicals; Digital computer simulation -- Periodicals; 519.5028505
• DOI: 10.1080/00949655.2017.1281277
• Languages: English
• ISSNs: 0094-9655

Abstract

ABSTRACT: The computational demand required to perform inference using Markov chain Monte Carlo methods often obstructs a Bayesian analysis. This may be a result of large datasets, complex dependence structures, or expensive computer models. In these instances, the posterior distribution is replaced by a computationally tractable approximation, and inference is based on this working model. However, the error that is introduced by this practice is not well studied. In this paper, we propose a methodology that allows one to examine the impact on statistical inference by quantifying the discrepancy between the intractable and working posterior distributions. This work provides a structure to analyse model approximations with regard to the reliability of inference and computational efficiency. We illustrate our approach through a spatial analysis of yearly total precipitation anomalies where covariance tapering approximations are used to alleviate the computational demand associated with inverting a large, dense covariance matrix.