Parameter estimation in modelling the dynamics of fish stock biomass: are currently used observation-error estimators reliable?

Production models are used in fisheries when only a time series of catch and abundance indices are available. Observation-error estimators are commonly used to fit the models to the data with a least squares type of objective function. An assumption associated with observation-error estimators is that errors occur only in the observed abundance index but not in the dynamics of stock and observed catch. This assumption is usually unrealistic. Because the least squares methods tend to be sensitive to error assumptions, results derived from these methods may be unreliable. In this study, we propose a robust observation-error estimator. We evaluate the performance of this method, together with the commonly used maximum likelihood method, under different error assumptions. When there was only observation error in the abundance index, maximum likelihood tended to perform better. However, with both observation and process errors, maximum likelihood yielded much larger estimation errors compared with the proposed method. This study suggests that the proposed method is robust to error assumptions. Because the magnitude and types of error cannot often be specified with confidence, the proposed method offers a potentially useful addition to methods used to fit production models to abundance index and catch data.