Impacts of outliers and mis-specification of priors on Bayesian fisheries-stock assessment

Abstract

Bayesian inference is increasingly used in estimating model parameters for fish-stock assessment, because of its ability to incorporate uncertainty and prior knowledge and to provide information for risk analyses in evaluating alternative management strategies. Normal distributions are commonly used in formulating likelihood functions and informative prior distributions; these are sensitive to data outliers and mis-specification of prior distributions, both common problems in fisheries-stock assessment. Using a length-structured stock-assessment model for a New Zealand abalone fishery as an example, we evaluate the robustness of three likelihood functions and two prior-distribution functions, with respect to outliers and mis-specification of priors, in 48 different combinations. The two robust likelihood estimators performed slightly less well when no data outliers were present and much better when data outliers were present. Similarly, the Cauchy distribution was less sensitive to prior mis-specification than the normal distribution. We conclude that replacing the normal distribution with "fat-tailed" distributions for likelihoods and priors can improve Bayesian assessments when there are data outliers and mis-specification of priors, with relatively minor costs when there are none.