Evaluating uncertainty in harvest control law catches using Bayesian Markov chain Monte Carlo virtual population analysis with adaptive rejection sampling and including structural uncertainty

Abstract

A new method is developed for calculating Bayes posterior distributions of future catches that conform to a specified harvest control law while incorporating uncertainty in biological reference points, natural mortality, and some aspects of model structure in addition to the usual stochastic noise. A Markov chain Monte Carlo approach is used to calculate Bayesian posterior distributions for critical parameters of a Norwegian spring-spawning herring (Clupea harengus) stock assessment using an assessment model that incorporates catch-at-age, survey, and tag release and recapture observations. Exceptionally, the approach allows prior uncertainty in model structure (e.g., whether survey observation errors should be treated as normal, lognormal, or gamma variates; whether Ricker or Beverton-Holt forms are used to model recruitment). This modelling approach is a useful tool that allows management advice to be provided that takes into account uncertainty in model structures and in some parameters that, by conventional methods, need to be specified as arbitrary "best" choices. The method is also used to quantify uncertainty in some biological reference points and to calculate a probability distribution for a future catch with respect to a specified harvest control law. This has the advantage of a consistent treatment of uncertainty throughout the process of stock modelling, reference point estimation, and concomitant catch forecasting.