Posterior Integration in Dynamic Models

The analysis of general dynamic models involves a sequence of posterior distributions corresponding to the subsequent stages of the dynamic model. In the absence of normal/linear structure numerical integration schemes are required to estimate features of these posterior distributions. This paper reviews some previously suggested Monte Carlo based algorithms and suggests a new scheme which makes use of a Metropolis type algorithm to propagate a Monte Carlo sample simulated from the initial prior distribution through all stages of the dynamic model. For each of the posterior distributions in the dynamic model, the algorithm makes a Monte Carlo sample available which allows then to estimate posterior integrals as desired. Before proceeding to the analysis at time t, the algorithm requires reconstruction of the posterior distribution corresponding to period t ? 1. This is solved by an implementation of a mixture of Dirichlet process model, making use of the already available Monte Carlo sample.