A Monte Carlo approach to quantifying discrepancies between intractable posterior distributions

作者：Hepler Staci A^*; Herbei Radu

来源：Journal of Statistical Computation and Simulation, 2017, 87(8): 1666-1683.

DOI：10.1080/00949655.2017.1281277

• Model error
• Kullback-Leibler
• divergence
• covariance tapering
• approximation

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.

• 出版日期2017