A comparison of stock assessment uncertainty estimates using maximum likelihood and Bayesian methods implemented with the same model framework

Many fisheries stock assessment models are implemented specifically for likelihood-based estimation or for Bayesian inference (via full integration of the joint posterior distributions), but not all have appropriate structure for both statistical approaches. Bias correction of recruitment deviations, in particular, must be adjusted to achieve consistency in each case. Fisheries management often uses the two types of results similarly, setting future catch quotas based on expected values or posterior medians depending on which is available given time constraints. Using two recent examples from the U.S. west coast, Pacific hake and sablefish, both implemented in Stock Synthesis, we find that likelihood-based estimates of key management quantities, such as spawning biomass, corresponded well with posterior modes, but tend to be lower (on an absolute scale) than posterior median values and that the asymptotic approximation for uncertainty intervals based on the Hessian matrix tends to overestimate the likelihood of smaller stock sizes and underestimate that of larger stock sizes. This pattern may be caused by a basic asymmetry in most fisheries data-sets: the necessity of a minimum stock size to have generated the observed catch/time-series, but little information regarding the plausibility among much larger stock sizes. Where only one type of inference is available, this asymmetry may be important for management decision-making. Even if management takes explicit account of uncertainty, in some cases adding a precautionary buffer that scales with the relative uncertainty in point estimates, the differences in catch advice may turn out to be important and the relative reductions non-linear.