Bayesian methodology for model uncertainty using model performance data

A simple and useful characterization of many predictive models is in terms of model structure and model parameters. Accordingly, uncertainties in model predictions arise from uncertainties in the values assumed by the model parameters (parameter uncertainty) and the uncertainties and errors associated with the structure of the model (model uncertainty). When assessing uncertainty one is interested in identifying, at some level of confidence, the range of possible and then probable values of the unknown of interest. All sources of uncertainty and variability need to be considered. Although parameter uncertainty assessment has been extensively discussed in the literature, model uncertainty is a relatively new topic of discussion by the scientific community, despite being often the major contributor to the overall uncertainty. This article describes a Bayesian methodology for the assessment of model uncertainties, where models are treated as sources of information on the unknown of interest. The general framework is then specialized for the case where models provide point estimates about a single-valued unknown, and where information about models are available in form of homogeneous and nonhomogeneous performance data (pairs of experimental observations and model predictions). Several example applications for physical models used in fire risk analysis are also provided.