The effect of ambiguous prior knowledge on Bayesian model parameter inference and prediction

Environmental modeling often requires combining prior knowledge with information obtained from data. The robust Bayesian approach makes it possible to consider ambiguity in this prior knowledge. Describing such ambiguity using sets of probability distributions defined by the Density Ratio Class has important conceptual advantages over alternative robust formulations. Earlier studies showed that the Density Ratio Class is invariant under Bayesian inference and marginalization. We prove that (i) the Density Ratio Class is also invariant under propagation through deterministic models, whereas (ii) predictions of a stochastic model with parameters defined by a Density Ratio Class are embedded in a Density Ratio Class. These invariance properties make it possible to describe sequential learning and prediction under a unified framework. We developed numerical algorithms to minimize the additional computational burden relative to the use of single priors. Practical feasibility of these methods is demonstrated by their application to a simple ecological model. (C) 2014 Elsevier Ltd. All rights reserved.