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

Abstract

This paper presents a Bayesian approach to fisheries stock assessment using the delay difference model to describe nonlinear population dynamics. Given a time series of annual catch and effort data, models in the Deriso-Schnute 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 biomass dynamics equations and the observations. Because the biomass dynamics are nonlinear, the common Kalman filter is generally not applicable for parameter estimation. However, it is demonstrated that the Bayesian approach can handle any form of nonlinear relationship in the state and observation equations as well as realistic distributional assumptions. Difficulties with posterior calculations are overcome by the Gibbs sampler in conjunction with the adaptive rejection Metropolis sampling algorithm.