Measuring uncertainty in fisheries stock assessment: the delta method, bootstrap, and MCMC


Arni Magnusson, Marine Research Institute, Skulagata 4, PO Box 1390, 121 Reykjavik, Iceland
Tel: +354 575 2000
Fax: +354 575 2001


Fisheries management depends on reliable quantification of uncertainty for decision-making. We evaluate which uncertainty method can be expected to perform best for fisheries stock assessment. The method should generate confidence intervals that are neither too narrow nor too wide, in order to cover the true value of estimated quantities with a probability matching the claimed confidence level. This simulation study compares the performance of the delta method, the bootstrap, and Markov chain Monte Carlo (MCMC). A statistical catch-at-age model is fitted to 1000 simulated datasets, with varying recruitment and observation noise. Six reference points are estimated, and confidence intervals are constructed across a range of significance levels. Overall, the delta method and MCMC performed considerably better than the bootstrap, and MCMC was the most reliable method in terms of worst-case performance, for our relatively data-rich scenario and catch-at-age model, which was not subject to substantial model misspecification. All three methods generated too narrow confidence intervals, underestimating the true uncertainty. Bias correction improved the bootstrap performance, but not enough to match the performance of the delta method and MCMC. We recommend using MCMC as the default method for quantifying uncertainty in fisheries stock assessment, although the delta method is the fastest to apply, and the bootstrap is useful to diagnose estimator bias.