Two examples of Bayesian analysis in fisheries: estimating the rate of change in total biomass of a fish stock and the decline of fish abundance by age over time
by
Manuela Azevedo
IPIMAR, Av. Brasília, 1449-006, Lisbon, Portugal

There are two main types of models to assess the sate of exploitation and determine the productivity of a fish stock, mainly depending on the detail of the basic data available: (i) production models that consider the stock globally and analyse the rate of variation of total biomass and (ii) the age-structured models that take into account the structure of the stock by age and analyse the evolution of the number of survivors of the different cohorts. The underlying mathematical models, basic assumptions and parameter vector are presented for each type of model. It is shown, using two important fisheries resources in Portuguese waters, the application of the Bayesian framework to infer about the values and uncertainty of the parameters of the model. The presentation focus on issues related to the choice of the likelihood function, the adoption of prior probability distributions that summarize the information on the parameters from all knowledge except that contained in the collected data and to the application of MCMC method, given the high dimensional integration required by the selected models, to obtain the posterior distributions for the parameters and derived quantities. The presentation is closed with remarks on sensitivity analysis to the choice of priors.

Date received: July 7, 2006