Page 392 - Special Topic Session (STS) - Volume 3

STS551 Stephen Wu et al.

Engineering applications of hierarchical Bayesian
modeling
3
2
1
Stephen Wu , Panagiotis Angelikopoulos , James L. Beck , Petros
Koumoutsakos
4
1 Institute of Statistical Mathematics, Research Organization of Information and Systems,
Tachikawa, Tokyo 190-8562, Japan
2 D.E. Shaw Research, New York, NY 10036, USA
3 California Institute of Technology, Pasadena, CA 91125, USA
4 Computational Science and Engineering Laboratory, ETH-Zurich, CH-8092, Switzerland

Abstract
Bayesian modelling and inference has become a very important method to
many modern engineering applications because it allows a unified framework
for uncertainty quantification and propagation to various problems, such as
model selection and robust prediction. A major trade-off comes from the
heavy computation demand, which prohibits the use of the full Bayesian
framework to complex simulation models. In particular, hierarchical Bayesian
model is a powerful modelling tool that offers great flexibility for uncertainty
quantification, yet classical Markov Chain Monte Carlo approach is usually
impractical for even a simple ordinary differential equation model. In my study,
I begin with a basic illustration of the power of hierarchical Bayesian model,
and then continue with a demonstration of its applications to engineering
problems by incorporating high performance computing and specifically
designed sampling methods. The applications, including pharmacokinetics
and molecular dynamics, involve fairly complicated models that classical
models used for Bayesian inference often lead to misleading results.

Keywords
Hierarchical Bayesian modeling; uncertainty quantification; importance
sampling; complex simulation

1. Introduction
Bayesian modelling and inference has become a very important method
to many modern engineering applications because it allows a unified
framework for uncertainty quantification and propagation to various
problems, such as model selection and robust prediction (Beck, 2010). A major
trade-off comes from the heavy computation demand, which prohibits the use
of the full Bayesian framework to complex simulation models, for example
finite element models of large civil structures and high-resolution fluid
dynamics simulations. Advanced Markov Chain Monte Carlo methods and
various Bayesian modeling techniques have extended the applications to a

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