Investigating agreement between different data sources using Bayesian state-space model: an application to estimating NE Atlantic mackerel catch and stock abundance

Bayesian Markov chain Monte Carlo methods are ideally suited to analyses of situations where there are a variety of data sources, particularly where the uncertainties differ markedly among the data and the estimated parameters can be correlated. The example of Northeast Atlantic (NEA) mackerel is used to evaluate the agreement between available data from egg surveys, tagging, and catch-at-age using multiple models within the Bayesian framework WINBUGS. The errors in each source of information are dealt with independently, and there is extensive exploration of potential sources of uncertainty in both the data and the model. Model options include variation by age and over time of both selectivity in the fishery and natural mortality, varying the precision and calculation method for spawning-stock biomass derived from an egg survey, and the extent of missing catches varying over time. The models are compared through deviance information criterion and Bayesian posterior predictive p-values. To reconcile mortality estimated from the different datasets the landings and discards reported would have to have been between 1.7 and 3.6 times higher than the recorded catches.