Flexible Bayesian analysis of the von Bertalanffy growth function with the use of a log-skew-t distribution

Abstract

The von Bertalanffy growth function is the model most widely applied to describe growth in fish populations. Parameters describing this function usually are estimated from observed lengths at different ages by using maximum likelihood and by assuming Gaussian distributed errors. In harvested populations, observed length at age usually involves a high level of skewness and extreme values because of the size-selective sampling process. Some approaches, based on the maximum-likelihood method for making inferences, have been developed to resolve such issues. We propose a Bayesian framework for estimating growth parameters for nonlinear regression models—a framework that is based on the family of log-skew-t distributions and which provides an approach that is flexible enough for modeling the presence of asymmetries and heavy tails. This framework based on a method in which 1) the error accounts for both skewness and heavy-tailed distributions of a log-skew-t model, and 2) the observed length at each age has a heteroscedastic error distribution. The proposed method was applied and compared with the methods of previous models by using observed length-at-age data for the southern blue whiting (Micromesistius australis), an important fish species harvested in the southeast Pacific. Comparisons indicated that the proposed model is the best for describing data on southern blue whiting.