  In a state-space framework, temporal variations in fishery-dependent
processes can be modeled as random effects. This modeling flexibility makes
state-space models (SSMs) powerful tools for data-limited assessments. Though
SSMs enable the model-based inference of the unobserved processes, their
flexibility can lead to overfitting and non-identifiability issues. To address
these challenges, we developed a suite of state-space length-based
age-structured models and applied them to the Korean chub mackerel (Scomber
japonicus) stock. Our research demonstrated that incorporating temporal
variations in fishery-dependent processes can rectify model mis-specification
but may compromise robustness, which can be diagnosed through a series of model
checking processes. To tackle non-identifiability, we used a non-degenerate
estimator, implementing a gamma distribution as a penalty for the standard
deviation parameters of observation errors. This penalty function enabled the
simultaneous estimation of both process and observation error variances with
minimal bias, a notably challenging task in SSMs. These results highlight the
importance of model checking and the effectiveness of the penalized approach in
estimating SSMs. Additionally, we discussed novel assessment outcomes for the
mackerel stock.
