Bayesian stock assessment using a state-space implementation of the delay difference model

This paper presents a Bayesian approach to fisheries stock assessment using the delay difference model to describe nonlinear population dynamics. Give n a time series of annual catch and effort data, models in the Deriso-Schnu te family predict exploitable biomass in the following year from biomass in the current and previous year and from past spawning stock, A state-space model is used, as it allows incorporation of random errors in both the biom ass dynamics equations and the observations. Because the biomass dynamics a re nonlinear, the common Kalman filter is generally not applicable for para meter estimation. However, it is demonstrated that the Bayesian approach ca n handle any form of nonlinear relationship in the state and observation eq uations as well as realistic distributional assumptions. Difficulties with posterior calculations are overcome by the Gibbs sampler in conjunction wit h the adaptive rejection Metropolis sampling algorithm.