Parameter estimation using randomized phases in an integrated assessment model for Antarctic krill.

An integrated model assessing the status and productivity of Antarctic krill (Euphausia superba, hereafter krill) was configured to estimate different subsets of 118 potentially estimable parameters in alternative configurations. We fixed the parameters that were not estimated in any given configuration at pre-specified values. The model was fitted to over forty years of fisheries and survey data for krill in Subarea 48.1, a statistical reporting area around the Antarctic Peninsula used by the Commission for the Conservation of Antarctic Marine Living Resources (CCAMLR). The number of estimated parameters was gradually increased across model configurations. Configurations that estimated more parameters fitted the data better, but the order in which the parameters were estimated became more important in finding the best fit. Twenty-two configurations estimating from 48 to 107 parameters were able to obtain an invertible Hessian matrix that was subsequently used to estimate parameter uncertainty. Parameter uncertainties calculated using asymptotic approximation around the maximum likelihood estimates were often larger than uncertainties based on Markov chain Monte Carlo sampling for the same parameters. Diagnostics applied to MCMC samples in the best model of each configuration that obtained an invertible Hessian indicated that the most highly parameterized configurations did not reach stationary distributions. A 96-parameter configuration was the best fitting model of those that passed the MCMC diagnostics. The ΔAIC and ΔBIC scores indicated essentially no support relative to the best model for the alternative models that also passed MCMC diagnostics. Simulated data using the configurations as operating models showed that while all configurations passed "self-tests" for spawning biomass and recruitment, there was a small negative bias due to model penalties in the fishing mortality estimates for years with the highest fishing mortalities. "Cross-tests" of configurations that estimated different parameters often differed from the operating model values.