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

TL;DR

This paper explores the theoretical aspects of Hierarchical Stochastic Models in Bayesian inference, demonstrating their ability to distinguish uncertainties and proposing an efficient approximation method to reduce computational costs, validated on scientific examples.

Contribution

It provides a theoretical analysis of HSM, introduces an importance sampling-based approximation scheme, and applies it to complex scientific models.

Findings

HSM can effectively separate different uncertainties.

The proposed approximation reduces computational cost.

Validated on molecular dynamics and pharmacokinetic models.

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.