Why do Bayesian and maximum likelihood assessments of the Bering-Chukchi-Beaufort Seas stock of bowhead whales differ?

Abstract

An approach to baleen whale stock assessment based on maximum likelihood estimation is outlined. This approach is able to consider uncertainty in all of the parameters of the BALEEN II population dynamics model used for the assessment of the Bering-Chukchi-Beaufort (B-C-B) Seas stock of bowhead whales. It replaces the prior distributions used in the Bayesian analyses to incorporate indirect information by bounds (only) on model quantities. The results from this approach are notably different from Bayesian analyses based on the same data/assumptions. These differences result from two factors: the specific shapes chosen for the priors for biological parameters needed for the Bayesian approach, and the updating of these priors, together with the covariance introduced between them, by the exclusion process which ensures consistency of parameter sets generated from these priors with the population model, before the data are taken into account in the assessment. The second of these factors is shown to be much more important in accounting for the difference between the results. However, it is unclear whether this exclusion process is defensibly accorded the probabilistic interpretation that the Bayesian approach assumes of it. Until this question is satisfactorily settled, the bounded maximum likelihood method introduced in this paper may provide a more defensible basis for assessment of the B-C-B bowhead population, even though it may be unable to take account of some information which could be incorporated in a Bayesian approach.