Hierarchical Stochastic Model in Bayesian Inference for Engineering Applications: Theoretical Implications and Efficient Approximation
Publication: ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part B: Mechanical Engineering
Volume 5, Issue 1
Abstract
Hierarchical Bayesian models (HBMs) have been increasingly used for various engineering applications. We classify two types of HBM found in the literature as hierarchical prior model (HPM) and hierarchical stochastic model (HSM). Then, we focus on studying the theoretical implications of the HSM. Using examples of polynomial functions, we show that the HSM is capable of separating different types of uncertainties in a system and quantifying uncertainty of reduced order models under the Bayesian model class selection framework. To tackle the huge computational cost for analyzing HSM, we propose an efficient approximation scheme based on importance sampling (IS) and empirical interpolation method (EIM). We illustrate our method using two engineering examples—a molecular dynamics simulation for Krypton and a pharmacokinetic/pharmacodynamics (PKPD) model for cancer drug. This article is available in the ASME Digital Collection at https://doi.org/10.1115/1.4040571.
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Copyright © 2019 by ASME.
History
Received: Dec 21, 2017
Revision received: Jun 6, 2018
Published online: Aug 14, 2018
Published in print: Mar 1, 2019
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