Construcción de distribuciones a priori no informativas y estimación de modelos de espacio de estados no linealesaplicación a la evaluación de recursos pesqueros mediante técnicas bayesianas

Abstract

Bayesian estimation of state-space models is an active area of research in the field of fisheries stock assessment. This field is characterized by the fact that fish stock is not observed but the Bayesian framework enables a formal approach to dynamic system analysis, including the uncertainty of the parameters and unknown variables. This work addresses the selection of non-informative prior distributions of the parameters in state-space models which are necessary to conduct a Bayesian analysis. Continuous time dynamic models of fishery resources are approximated in discrete time to provide a structure appropriated for the implementation of the aforementioned analysis. Additionally, methods aimed at determining non-informative prior distributions for finite data set are described concluding that Jeffreys (1967), based on Fisher (1922), Shannon's maximum entropy method, and Zellner (1971, 1977, 1995, 1996), based on the information measure of Shannon (1948); are the most appropriate. Bayesian techniques make feasible analyzing the stock-recruitment relations (Ricker, 1954; Berverton and Holt, 1957; and Cushing, 1971) together with human pressure on it caused by fishing industry (capture function). Both functions model the dynamics of fisheries resource. The non-informative prior distributions of these dynamic model parameters are determined in order to estimate them using Gibbs sampling (Geman y Geman, 1984),. The analysis described in previous paragraphs has been implemented using data on capture and fishing effort of Gulf of Cádiz fisheries from Garcia del Hoyo (2008) and González Galán (2004). In both cases there have been included parameters related with environmental conditions. The prior function associated to the parameters depends on their way to participate in the model. The location parameters follow uniform distributions, whereas the scaling parameters follow a log-uniform distribution. More differences have been obtained in the parameter q (catchability coefficient). If we choose Jeffreys' method, we conclude that it can be approximated to a triangular distribution. If we apply Zellner's method, we obtain a beta distribution (1/2, 1/2). Both distributions are linked to global behaviors of a population on which there is very little information. Therefore, they can be considered initial non-informative distributions. The two case studies, which have been developed using the information that was available on catch and effort, are characterized by fisheries whose evolution in time is subject to strong fluctuations which are linked to changes in environmental conditions. This behavior implies the need for adaptive techniques where the constant parameters of traditional models have little applicability. The possibility of introducing these environmental variables directly and allowing random changes in the parameters, makes fisheries modeling more real and, consequently, it allows us to improve the evaluation of resources and make coherent decisions.