Bayesian validation assessment of multivariate computational models

Xiaomo Jiang and Sankaran Mahadevan

Journal of Applied Statistics, 2008, vol. 35, issue 1, 49-65

Abstract: Multivariate model validation is a complex decision-making problem involving comparison of multiple correlated quantities, based upon the available information and prior knowledge. This paper presents a Bayesian risk-based decision method for validation assessment of multivariate predictive models under uncertainty. A generalized likelihood ratio is derived as a quantitative validation metric based on Bayes' theorem and Gaussian distribution assumption of errors between validation data and model prediction. The multivariate model is then assessed based on the comparison of the likelihood ratio with a Bayesian decision threshold, a function of the decision costs and prior of each hypothesis. The probability density function of the likelihood ratio is constructed using the statistics of multiple response quantities and Monte Carlo simulation. The proposed methodology is implemented in the validation of a transient heat conduction model, using a multivariate data set from experiments. The Bayesian methodology provides a quantitative approach to facilitate rational decisions in multivariate model assessment under uncertainty.

Keywords: Bayesian statistics; decision making; risk; reliability; model validation; multivariate statistics (search for similar items in EconPapers)
Date: 2008
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Citations: View citations in EconPapers (4)

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DOI: 10.1080/02664760701683577

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