Performance evaluation of information criteria for estimating a shape parameter in a Bayesian state-space biomass dynamics model

Estimating a shape parameter in a Bayesian state-space biomass dynamics model is an essential task in fisheries stock assessments because it is strongly associated with the status of the stock. However, it is frequently difficult to estimate the shape parameter accurately. If it is possible to statistically select the best model, which is closer to the true model, using information criteria, it will enable us to determine the shape parameter with high accuracy. To accomplish this goal, we evaluated the performance of five information criteria: widely applicable information criteria with conditional and marginal likelihoods (WAICc, WAICm), deviance information criteria with conditional and marginal likelihoods (DICc, DICm), and a widely applicable Bayesian information criterion (WBIC) using a numerical simulation for various scenarios. We also demonstrated an application of the methods to real-world fisheries stock assessment. We found five main results: (1) the performances of WAICm, DICm and WBIC were better than the conditional information criteria, (2) the relative performance of WAICm was unaffected by the magnitude of both observation and process errors, (3) the relative performance of WBIC and DICm was unaffected by the magnitude of process error, (4) WBIC was the most promising information criterion for selecting the shape parameter in the case study, and (5) the best model enhanced accuracy of the stock assessment.