SUPRA-BAYESIAN POOLING OF PRIORS LINKED BY A DETERMINISTIC SIMULATION MODEL

Abstract

Deterministic simulation models are used to guide decision-making and enhance understanding of complex systems such as disease transmission, population dynamics, and tree plantation growth. Bayesian inference about parameters in deterministic simulation models can require the pooling of expert opinion. One class of approaches to pooling expert opinion in this context is supra-Bayesian pooling, in which expert opinion is treated as data for an ultimate decision maker. This article details and compares two supra-Bayesian approaches—“event updating” and “parameter updating.” The suitability of each approach in the context of deterministic simulation models is assessed based on theoretical properties, performance on examples, and the selection and sensitivity of required hyperparameters. In general, we favor a parameter updating approach because it uses more intuitive hyperparameters, it performs sensibly on examples, and because the alternative event updating approach fails to exhibit a desirable property (relative propensity consistency) in all cases. Inference in deterministic simulation models is an increasingly important statistical and practical problem, and supra-Bayesian methods represent one viable option for achieving a sensible pooling of expert opinion.

Keywords:

• Bayesian inference
• Expert opinion
• External Bayesianity
• Prior aggregation
• Relative propensity consistency

ACKNOWLEDGMENTS

This research was supported by the North Slope Borough (Alaska), the State of Alaska (through the Alaska Department of Community and Regional Affairs), and the National Oceanic and Atmospheric Administration (through the National Marine Mammal Laboratory to the Alaska Eskimo Whaling Commission); and by NSF grant #SBR-9875508.