State-space likelihoods for nonlinear fisheries time-series

Abstract

State-space models are commonly used to incorporate process and observation errors in analysis of fisheries time series. A gap in analysis methods has been the lack of classical likelihood methods for nonlinear state-space models. We evaluate a method that uses weighted kernel density estimates of Bayesian posterior samples to estimate likelihoods (Monte Carlo Kernel Likelihoods, MCKL). Classical likelihoods require integration over the state-space, and we compare MCKL to the widely used errors-in-variables (EV) method, which estimates states jointly with parameters by maximizing a nonintegrated likelihood. For a simulated, linear, autoregressive model and a Schaefer model fit to cape hake (Merluccius capensis × M. paradoxus) data, classical likelihoods outperform EV likelihoods, which give asymptotically biased parameter estimates and inaccurate confidence regions. Our results on the importance of integrated state-space likelihoods also support the value of Bayesian analysis with Monte Carlo posterior integration. Both approaches provide valuable insights and can be used complementarily. Previously, Bayesian analysis was the only option for incorporating process and observation errors with complex nonlinear models. The MCKL method provides a classical approach for such models, so that choice of analysis approach need not depend on model complexity.