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'' 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.