A Monte Carlo approach to quantifying discrepancies between intractable posterior distributions

• Published in: Journal of statistical computation and simulation 2017-05, Vol.87 (8), p.1666-1683
• Main Authors: Hepler, Staci A., Herbei, Radu
• Format: Article
• Language: English
• Subjects: Approximation; Bayesian analysis; Computation; Computer simulation; covariance tapering; Demand analysis; divergence; Inference; Kullback-Leibler; Mathematical analysis; Mathematical models; Model error; Monte Carlo methods; Monte Carlo simulation
• ISSN: 0094-9655; 1563-5163
• DOI: 10.1080/00949655.2017.1281277

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.