How robust are Bayesian posterior inferences based on a Ricker model with regards to measurement errors and prior assumptions about parameters?

• Published in: Canadian Journal of Fisheries and Aquatic Sciences
• Main Authors: Rivot, E, Prévost, E, Parent, E
• Format: Article in Journal/Newspaper
• Language: English
• Published: Canadian Science Publishing 2001
• Subjects: Aquatic Science; Ecology, Evolution, Behavior and Systematics; Atlantic salmon; Salmo salar
• Online Access: http://dx.doi.org/10.1139/f01-167; http://www.nrcresearchpress.com/doi/pdf/10.1139/f01-167

We present a Bayesian approach of a Ricker stock-recruitment (S/R) analysis accounting for measurement errors on S/R data. We assess the sensitivity of posterior inferences to (i) the choice of Ricker model parameterizations, with special regards to management-related ones, and (ii) prior parameter distributions. Closed forms for Ricker parameter posterior distributions exist given S/R data known without error. We use this property to develop a procedure based on the Rao–Blackwell formula. This procedure achieves integration of measurement errors by averaging these closed forms over possible S/R data sets sampled from distributions derived from a stochastic model relating field data to the S and R variables. High-quality Bayesian estimates are obtained. The analysis of the influence of different parameterizations and of the priors is made easier. We illustrate our methodological approach by a case study of Atlantic salmon (Salmo salar). Posterior distributions for S and R are computed from a mark–recapture stochastic model. Ignoring measurement errors underestimates parameter uncertainty and overestimates both stock productivity and density dependence. We warn against using management-related parameterizations because it makes the strong prior assumption of long-term sustainability of stocks. Posterior inferences are sensitive to the choice of prior. The use of informative priors as a remedy is discussed.