In 2022, Casal2 was endorsed by CCAMLR at Scientific Committee for use for integrated statistical catch-at-age toothfish stock assessments. As a part of the recommendations, the Scientific Committee encouraged further research on parameter transformations within the Casal2 stock assessment models to improve stability and Markov Chain Monte Carlo (MCMC) convergence.
Parameter transformations are to transform individual or combined parameters into a different “space” for estimation. These can help achieve more efficient model optimisation and model performance. In complex statistical models, such as stock assessment models, parameter transformations are useful for models that have highly correlated parameters or parameters with distributions that may be sub-optimal for mixing using the Metropolis-Hasting MCMC algorithm. In these cases, they can help reduce autocorrelation and confounding between parameters and improve the efficiency of both minimisation and MCMC algorithms.
We investigated the performance of the 2021 Ross Sea region stock assessment model with Casal2 v2023.05 (https://github.com/alistairdunn1/CASAL2) using the simplex method for constraining year class strengths (YCS) to have mean one versus the standard ‘Haist’ parameterisation and an associated vector average penalty. Log, square root, and inverse transformations on initial biomass (B0) and right-hand limb selectivity parameters were investigated to determine if these reduce correlations between parameters or improved the estimation of parameters with heavy tailed posterior distributions. Further, we compare the results using the ‘casal’ and ‘casal2’ compatibility options for tag release processes and tag recapture observations to evaluate the effect of the improved algorithms available in Casal2 and investigate the impacts of using catch in numbers rather than catch in biomass to model fishery removals. Model asserts are used to validate the outcomes between CASAL and Casal2, as well as validating updated versions of Casal2.
The results showed that the use of transformations helped improve MCMC chains without loss in the efficiency of estimation. Model estimates using transformations were almost identical to estimates obtained without transformation. The use of the simplex method for constraining YCS to average one improved the MCMC convergence diagnostics for the year class strength parameters and removed the requirement for an arbitrary penalty (called an additional prior in Casal2) on the average of the estimated parameters. Square root and log transformation on B0 showed little improvement (potentially as there were no strong correlations with a catchability coefficient in this model), but the use of the inverse transformation on selectivity right-hand limbs resulted in considerable improvements. The ‘casal2’ compatibility options had little effect and did not result in any changes in the model outcomes or conclusions. Use of catch in numbers rather than catch in biomass did not change the estimates of initial or current biomass, suggesting that the estimates of catch by number and biomass were consistent with each other and with the assumptions used for the age-length and the length-weight relationships.
We recommend that transformations be considered in assessments where improvements in diagnostics of MCMC convergence would be beneficial. For the Ross Sea region stock assessment, we recommend the use of the simplex method for estimating year class strengths and the inverse transformation for right-hand limb selectivity parameters, and the ‘casal2’ compatibility options.