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

2016/11/09 by Stephen Wu, Wu, Stephen, Panagiotis Angelikopoulos +5
Chemistry · Computer Science · #Analytical Chemistry and Chromatography #Applications (stat.AP) #Bayesian Methods and Mixture Models #Computational Drug Discovery Methods #FOS: Computer and information sciences

paper · pdf · doi:10.48550/arxiv.1611.02818

openalex publication_date 2016/11/09 · openalex created_date 2016/11/30 · openalex updated_date 2026/07/28

Abstract

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 examples - a Molecular Dynamics simulation for Krypton and a pharmacokinetic/pharmacodynamic model for cancer drug.

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