Determining effective sample size in integrated age-structured assessment models

Effective sample size (ESS) is a quantity that allows for overdispersion of variance and is used commonly in integrated age-structured fishery assessment models to fit age-and-length-composition datasets. Owing to the sources of measurement, observation, process, and model-specification errors, the ESS is smaller than the actual sample size. In this study, methods to set a priori or to estimate the ESS when confronted with datasets that include these sources of error were investigated. In general, a number of methods previously proposed to incorporate the ESS resulted in accurate estimation of population quantities and parameters when different sources of error were included in the data on age and length compositions. Three objective methods to incorporate the ESS resulted in unbiased population quantities: (i) using sampling theory to derive the ESS from actual age and length compositions, (ii) iteratively estimating the ESS with the age-structured assessment model, and (iii) estimating the ESS as a parameter with the Dirichlet distribution.