A Monte Carlo approach to quantifying discrepancies between intractable posterior distributions

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 comp...

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Bibliographic Details
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
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Summary: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.
ISSN:0094-9655
1563-5163
DOI:10.1080/00949655.2017.1281277