Evaluating methods for estimating process and observation error variances in statistical catch-at-age analysis

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Statistical catch-at-age analysis (SCAA) allows analysts to explicitly account for process and observation errors in their stock assessment models. The variances associated with these errors are important because they weight the different data and error sources during the model fitting process. Misspecification of the error variances can lead to biased estimates of key management quantities. Values for the error variances commonly are obtained separately from SCAA and treated as known in the subsequent analysis. The advantages of estimating the error variances within SCAA include that all of the data available to the analysis can be synthesized to obtain the variance estimates and, with some methods, uncertainty surrounding the variance estimates can be quantified. We evaluated alternative approaches for estimating log catchability (process error) and log total catch (observation error) standard deviations within SCAA using Monte Carlo simulations: an ad hoc approach that tunes the model predicted log total catch standard deviation to match a prior value, and a Bayesian approach using either strongly or weakly informative priors for log catchability standard deviation. The Bayesian approach using strongly informative priors outperformed the other approaches in estimating the log total catch and log catchability standard deviations, as well as estimating biomass in the last year of analysis. The ad hoc approach produced misleading results which could indicate that total variance (i.e., process error variance plus observation error variance) was well estimated when, in fact, total variance was underestimated.