An evaluation of estimability of parameters in the state-space non-linear logistic production model

Abstract

We evaluated the estimation of six free parameters in the state-space non-linear logistic production model, using two approaches: likelihood estimation and Bayesian posterior sampling. We simulated process and observation errors, and the biomass index (e.g., catch-per-unit-effort) data using actual data on fishery yields of Korean chub mackerel (Scomber japonicus), which fluctuated during 1976–2017. When estimating parameters and predicting random effects, we compared two contrasting cases: (i) without assumptions about parameters or priors (“wo”) and (ii) with extremely informative priors where the mode of the prior distribution for each parameter was set equal to the parameter’s true value, and very high precision (coefficient of variation, CV = 0.1, or 10%) was applied. As expected, the estimation performance was poor in the “wo” situation. However, the extremely informative priors did not reduce the bias of the estimates of precision although they reduced the bias of the point estimates. Informative priors with much lower precision (e.g., CV = 10, or 1000%) resulted in less bias of the estimates of precision than the extremely informative priors with the CV of 0.1. A sensitivity analysis demonstrated that estimation of all parameters was problematic unless accurate information about the uncertainties of the observation and process errors was incorporated even if extremely accurate information about the other parameters was available. When treating informative priors as penalized likelihoods, the differences were negligible in estimation between the likelihood and Bayesian approaches.