Using sequential particle methods and non-parametric distributions in bayesian evaluations of abundance and catch at age time series

Abstract

We describe an approach to analyzing time series for two variables connected through the state model with abundance and catch data sets and cohort and catch equations as an example. First, we create a deterministic model with parameters that maximizes the closeness of given data and data generated by a model. Then, we obtain cohort stochastic models using the difference between initial and modeled data. They are represented as hidden Bayesian models with abundances as states and catches as observations. Using these models, one can evaluate posterior densities and calculate averages, deviations, etc. As a general matter, the recursive equations met by posterior densities have no analytic solutions. We describe several particle methods that may be used for density approximations and following calculations of their statistical quantities. All generated sample densities are smoothed with non-parametric kernel density estimation. The Fishmetica package was extended with functions for generating samples and weights for filtering, predicting and smoothing densities. Numerical simulations were conducted for a test data set. Several extensions of the approach are proposed including an additional option for comparing the basic models with the use of a likelihood function.