Variability, Tuning, and Simulation for the Doubleday–DerisoCatch-at-Age Model

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Abstract
This paper presents a method for estimating the variances of biomass estimates made using the nonlinear least squares catch-at-age model. The estimates begin with the standard covariance matrix of parameters estimated using nonlinear least squares and is therefore an extension of usual methods. In this paper the catch-at-age model is tuned to independent survey estimates of biomass. If the variances of these survey estimates are known, it is possible to estimate an optimal value for the weighting variable λ in the nonlinear least squares. The methods are applied to the walleye pollock (Theragra chalcogramma) fishery in the Eastern Bering Sea. Results from this study generally support the theoretical interpretation of λ as a ratio of variances. When the model is constrained to recent survey biomass estimates, estimates of the coefficient of variation of biomasses in earlier years are large. Also, the results largely depend on what constraints on selectivities are assumed. A simulation was performed assuming catches-at-age are distributed as lognormal random variables and that selectivities are all estimated. Results from the simulation indicate that modelled biomass estimates for early years are questionable, and probably seriously biased. However, the simulation generally validated the analytic estimates of the variance of modelled biomass estimates.

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