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.
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