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Quantifying Model Error in Bayesian Parameter Estimation

White, Staci A
http://orcid.org/0000-0002-2940-088X
http://rave.ohiolink.edu/etdc/view?acc_num=osu1433771825

Abstract Details

2015, Doctor of Philosophy, Ohio State University, Statistics.
As technological power increases, statistical models are becoming increasing complex. In a Bayesian analysis, performing parametric inference typically requires exploring the posterior distribution using Markov chain Monte Carlo methods. Unfortunately, these methods are impractical when the computational demand associated with the posterior distribution is large. In these intractable Bayesian hierarchical models, the posterior distribution of interest is often replaced by a computationally efficient approximation that is instead used for inference. However, the error that is introduced by this intentional model misspecification typically goes unaccounted for in the resulting inference. In this dissertation, I propose an approach to quantify the model error, which I define to be the discrepancy between a computationally intractable target posterior distribution and its approximation. The discrepancy between probability models is summarized using the φ-divergence. I develop a strongly consistent estimator for the φ-divergence that alleviates known computational difficulties with estimating normalizing constants. This approach provides a structure to analyze model approximations with regard to the reliability of inference and computational efficiency. The methodology was applied to an oceanographic tracer inversion problem where evaluation of the likelihood function requires the analytically intractable solution to a partial differential equation. The suggested approach to estimating the φ-divergence requires numerous evaluations of the unnormalized target density. This can be accomplished in many settings using parallel computing. However, I propose an extension of the previous research to accommodate situations where the computational demand associated with the target model is extreme. This work utilizes Gaussian process prediction to eliminate the need to compute the unnormalized target density for a large number of parameter values. I illustrate this extension through a spatial analysis of global sea surface temperature where covariance tapering is used to alleviate the computational demand associated with inverting the full covariance matrix. In addition, I develop a framework to performing model selection when the goal of a Bayesian analysis is parameter estimation. I use the Kullback-Leibler distance as the basis of a criterion for determining the "best" from a class of approximations to the target posterior distribution. This approach is more efficient than estimating the φ-divergence for each approximation under consideration as is required for the previous work. As more intricate statistical models become accessible with the increase in computing power, it becomes increasingly important to consider the impact that modeling choices have on posterior inference. This dissertation introduces a formal means to study the effect of model approximations when the target posterior distribution is computationally intractable. By continuing to pursue this research direction, I can provide the Bayesian modeling community with tools to better understand the consequences of using approximations in complex Bayesian hierarchical models.
Radu Herbei, Ph.D. (Advisor)
Mark Berliner, Ph.D. (Committee Member)
Peter Craigmile, Ph.D. (Committee Member)
187 p.
Statistics
Model Error; Bayesian Estimation; Hierarchical Model; Approximation; Kullback-Leibler; divergence

Recommended Citations

Citations

  • White, S. A. (2015). Quantifying Model Error in Bayesian Parameter Estimation [Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1433771825

    APA Style (7th edition)

  • White, Staci. Quantifying Model Error in Bayesian Parameter Estimation. 2015. Ohio State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1433771825.

    MLA Style (8th edition)

  • White, Staci. "Quantifying Model Error in Bayesian Parameter Estimation." Doctoral dissertation, Ohio State University, 2015. http://rave.ohiolink.edu/etdc/view?acc_num=osu1433771825

    Chicago Manual of Style (17th edition)

osu1433771825
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This open access ETD is published by The Ohio State University and OhioLINK.