Data-free inference of the joint distribution of uncertain model parameters

A critical problem in accurately estimating uncertainty in model predictions is the lack of details in the literature on the correlation (or full joint distribution) of uncertain model parameters. In this paper we describe a framework and a class of algorithms for analyzing such “missing data” probl...

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Bibliographic Details
Published in:Journal of computational physics 2012-03, Vol.231 (5), p.2180-2198
Main Authors: Berry, Robert D., Najm, Habib N., Debusschere, Bert J., Marzouk, Youssef M., Adalsteinsson, Helgi
Format: Article
Language:English
Subjects:
Algorithms
Bayesian analysis
Bayesian statistics
Computational techniques
Confidence intervals
Correlation
Exact sciences and technology
Mathematical methods in physics
Mathematical models
Missing data
Missing information
Physics
Statistics
Uncertainty
Uncertainty quantification
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Summary:A critical problem in accurately estimating uncertainty in model predictions is the lack of details in the literature on the correlation (or full joint distribution) of uncertain model parameters. In this paper we describe a framework and a class of algorithms for analyzing such “missing data” problems in the setting of Bayesian statistics. The analysis focuses on the family of posterior distributions consistent with given statistics (e.g. nominal values, confidence intervals). The combining of consistent distributions is addressed via techniques from the opinion pooling literature. The developed approach allows subsequent propagation of uncertainty in model inputs consistent with reported statistics, in the absence of data.
ISSN:0021-9991
1090-2716
DOI:10.1016/j.jcp.2011.10.031