Inferring Bayesian Priors with Limited Direct Data: Applications to Risk Analysis

Abstract

The usefulness of Bayesian analysis depends in great part on specifying appropriate prior distributions. In this article, we investigate three quantitative techniques for obtaining a prior distribution for steepness, a critical parameter in fisheries management. These techniques were developed in the context of a risk assessment of a power plant's impact on nine species of fish. All three techniques use mixed-effects models to estimate the parameters of the prior distributions, but they differ in the choice of the fish populations to include in the analysis. The first two methods use information from taxonomically similar and ecologically similar populations, respectively, to generate a prior distribution. The third method combines a mixed-effects model and a quantitative analysis of life history and environmental data to generate a prior distribution, using data from all available fish populations. These techniques represent an empirical Bayesian approach, which we preferred to a hierarchical Bayesian approach because it allowed us to rapidly explore numerous alternative model formulations.