Logarithmic Pooling of Priors Linked by a Deterministic Simulation Model

Abstract

We consider Bayesian inference when priors and likelihoods are both available for inputs and outputs of a deterministic simulation model. This problem is fundamentally related to the issue of aggregating (i.e., pooling) expert opinion. We survey alternative strategies for aggregation, then describe computational approaches for implementing pooled inference for simulation models. Our approach (1) numerically transforms all priors to the same space; (2) uses log pooling to combine priors; and (3) then draws standard Bayesian inference. We use importance sampling methods, including an iterative, adaptive approach that is more flexible and has less bias in some instances than a simpler alternative. Our exploratory examples are the first steps toward extension of the approach for highly complex and even noninvertible models.