A Monte Carlo approach to quantifying discrepancies between intractable posterior distributions |
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Authors: | Staci A Hepler Radu Herbei |
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Institution: | 1. Department of Mathematics and Statistics, Wake Forest University, Winston-Salem, NC, USAheplersa@wfu.edu;3. Department of Statistics, The Ohio State University, Columbus, OH, USA |
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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. |
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Keywords: | Model error Kullback–Leibler divergence covariance tapering approximation |
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