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BAYESIAN INFERENCE FOR SURPLUS PRODUCTION MODEL WITH SCALE MIXTURE OF SKEW NORMAL ERRORS
Surplus production models (also known as biomass dynamic models) provide simple descriptions of
harvested populations, in terms of annual biomass levels (Bt), the intrinsic growth rate (r), the carrying capacity of the environment (K) and the efficiency of fishing gear. These models have a long history in fisheries science and have provided a key basis leading to the popularity of Maximum Sustainable Yield (MSY) and its associated biomass (BMSY) as biological reference points for fishing management. The surplus production can be modeled using the state-space approach with linear observation equation and nonlinear state equation. Normality is a standard assumption for state-space models, however in many practical situation this is not a good choice since this is not robust to outliers and may not accommodate asymmetric data. More flexible classes of distributions have been proposed in the literature to deal with the issues of asymmetry and outliers. In particular, the SMSN class of distribution has shown its utility in many applications where the assumption of normality must be relaxed. In this work, we show how Bayesian inference for nonlinear state-space model using elements of this family can be implemented. The methodology is applied to data from population of marine shrimp of the Chilean coast. The presentation will be partly based on Montenegro and Branco (2016) with some extensions that are being developed.
state-space model, scale mixture of skew normal , fishing management, biomass dynamic models.
Márcia D'Elia Branco, Carlos Patricio Montenegro, Rafael Oliveira Silva