Uncertainty estimation and model selection in stock assessment models with non-parametric effects on fishing mortality

Abstract

Uncertainty coming from assessment models leads to risk in decision making and ignoring or misestimating it can result in an erroneous management action. Some parameters, such as selectivity or survey catchabilities, can present a wide range of shapes and the introduction of smooth functions, which up to now have not been widely used in assessment models, allows for more flexibility to capture underlying nonlinear structures. In this work a simulation study emulating a sardine population is carried out to compare three different methods for uncertainty estimation: multivariate normal distribution, bootstrap (without and with relative bias correction) and Markov chain Monte Carlo (MCMC). In order to study their performance depending on the model complexity, five different scenarios are defined depending on the shape of the smooth function of the fishing mortality. From 100 simulated datasets, performance is measured in terms of point estimation, coefficients of variation, bias, skewness, coverage probabilities, and correlation. In all approaches model fitting is carried out using the a4a framework. All three methods result in very similar performance. The main differences are found for observation variance parameters where the bootstrap and the multivariate normal approach result in underestimation of these parameters. In general, MCMC is considered to have better performance, being able to detect skewness, showing small relative bias and reaching expected coverage probabilities. It is also more efficient in terms of time consumption in comparison with bootstrapping.