Constructing partial prior specifications for models of complex physical systems

Abstract

Summary. Many large scale problems, particularly in the physical sciences, are solved using complex, high dimensional models whose outputs, for a given set of inputs, are expensive and time consuming to evaluate. The complexity of such problems forces us to focus attention on those limited aspects of uncertainty which are directly relevant to the tasks for which the model will be used. We discuss methods for constructing the relevant partial prior specifications for these uncertainties, based on the prior covariance structure. Our approach combines two sources of prior knowledge. First, we elicit both qualitative and quantitative prior information based on expert prior judgments, using computer-based elicitation tools for organizing the complex collection of assessments in a systematic way. Secondly, we test and refine these judgments using detailed experiments based on versions of the model which are cheaper to evaluate. Although the approach is quite general, we illustrate it in the context of matching hydrocarbon reservoir history.