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A key challenge for analyzing fisheries time-series data has been to incorporate sources of uncertainty such as process error, observation error, and model-structure uncertainty. Recent years have seen promising advances in methods for handling the first two together in a state-space
framework, but likelihood calculations for state-space models require high-dimensional integrals, which make their use computationally challenging. The first section of this paper reviews model-fitting methods that use a state-space model structure, including errors-in-variables methods, Bayesian
methods that do and do not use the state-space likelihood, and the possibility of classical likelihood analysis with nonlinear, non-Gaussian state-space models. It also discusses the relationship between true likelihood calculations and errors-in-variables likelihoods, as well as the role
of Monte Carlo methods in implementing Bayesian and/or state-space model analyses. The second section introduces a numerical method for calculating state-space likelihoods without Monte Carlo methods and gives examples in a classical maximum-likelihood framework. The method is applicable when
the dimension of the state space at each time step is low. Although recent advances in model-fitting and analysis methods are promising, inferences from noisy data and complex processes will continue to be variable and uncertain.
The Bulletin of Marine Science is dedicated to the dissemination of high quality research from the world's oceans. All aspects of marine science are treated by the Bulletin of Marine Science, including papers in marine biology, biological oceanography, fisheries, marine affairs, applied marine physics, marine geology and geophysics, marine and atmospheric chemistry, and meteorology and physical oceanography.