Hierarchical Stochastic Model in Bayesian Inference for Engineering Applications: Theoretical Implications and Efficient Approximation

[+] Author and Article Information
Stephen Wu

Postdoctoral, CSELab, ETH-Zurich, CH -8092, Switzerland

Panagiotis Angelikopoulos

Postdoctoral, CSELab, ETH-Zurich, CH -8092, Switzerland

James L. Beck

Professor, Department of Mechanical and Civil Engineering, California Institute of Technology, Pasadena, CA 91125, USA

Petros Koumoutsakos

Professor, CSELab, ETH-Zurich, CH -8092, Switzerland

1Corresponding author.

ASME doi:10.1115/1.4040571 History: Received December 21, 2017; Revised June 06, 2018


Hierarchical Bayesian models have been increasingly used for various engineering applications. We classify two types of Hierarchical Bayesian Model 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 and Empirical Interpolation Method. We illustrate our method using two engineering examples --- a Molecular Dynamics simulation for Krypton and a pharmacokinetic/pharmacodynamic model for cancer drug.

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