Evaluating the impact of log-normal bias-correction on a state-space stock assessment model

In state-space stock assessment models, recruitment and numbers-at-age are typically modeled as log-normal random variables, with bias correction applied to ensure that their mean matches the expected mean of the random variable. However, it remains unclear whether estimation error in variance parameters, which influence bias correction, propagates to estimates of population quantities. We conducted simulation-estimation experiments to evaluate the effects of bias correction for log-normal random variables and observations. We found that applying bias correction on observations had minimal impact on estimated population quantities, whereas applying bias correction on the process had a significant effect, because estimation error in variance parameters created bias in population estimates. Specifically, when both recruitment deviations and numbers-at-age transitions were treated as random effects, substantial bias in estimated annual recruitments and SSB was found when bias correction was excluded in the operating model but applied in the estimation model. In contrast, not using bias correction had limited negative effects. Thus, we recommend avoiding bias correction for log-normal random variables in state-space models, especially when multiple random-effects processes are modeled simultaneously.