Bayesian inference method for model validation and confidence extrapolation

Abstract

This paper presents a Bayesian-hypothesis-testing-based methodology for model validation and confidence extrapolation under uncertainty, using limited test data. An explicit expression of the Bayes factor is derived for the interval hypothesis testing. The interval method is compared with the Bayesian point null hypothesis testing approach. The Bayesian network with Markov Chain Monte Carlo simulation and Gibbs sampling is explored for extrapolating the inference from the validated domain at the component level to the untested domain at the system level. The effect of the number of experiments on the confidence in the model validation decision is investigated. The probabilities of Type I and Type II errors in decision-making during the model validation and confidence extrapolation are quantified. The proposed methodologies are applied to a structural mechanics problem. Numerical results demonstrate that the Bayesian methodology provides a quantitative approach to facilitate rational decisions in model validation and confidence extrapolation under uncertainty.

Keywords:

• Bayesian statistics
• Bayes factor
• hypothesis testing
• model validation
• extrapolation

Acknowledgements

The research was supported by funds from Sandia National Laboratories, Albuquerque, New Mexico (contract no. BG-7732, project monitors: Dr Thomas L. Paez, Dr Laura P. Swiler, and Dr Martin Pilch). The support is gratefully acknowledged.