Combined Parameter and State Estimation in Simulation-Based Filtering
Much of the recent and current interest in simulation-based methods of sequential Bayesian analysis of dynamic models has been focused on improved methods of filtering for time-varying state vectors. We now have quite effective algorithms for time-varying states, as represented throughout this volume. Variants of the auxiliary particle filtering algorithm (Pitt and Shephard 1999b), in particular, are of proven applied efficacy in quite elaborate models. However, the need for more general algorithms that deal simultaneously with both fixed model parameters and state variables is especially pressing. We simply do not have access to efficient and effective methods of treating this problem, especially in models with realistically large numbers of fixed model parameters. It is a very challenging problem.
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