COMBINED PARAMETER AND STATE ESTIMATION IN SIMULATION-BASED FILTERING
Jane Liu and Mike West
We discuss simulation-based sequential analysis -- or particle filtering -- in dynamic models, with a primary focus on sequential Bayesian learning about time-varying state vectors and fixed model parameters simultaneously. We discuss a general approach that combines old ideas of smoothing using kernel methods with newer ideas of auxilliary particle filtering. It is shown here that our specific smoothing approaches can interpret and suggest modifications to techniques that add "artificial evolution noise" to fixed model parameters at each time point to address problems of sample attrition and prior:data conflict. Our new approach permits smoothing and regeneration of sample points of model parameters without the "loss of historical information" inherent in earlier methods; this is achieved using shrinkage modifications of kernel smoothing, as introduced by the second author in the early 1990s. Following some theoretical development, discussion and a small simulated example to demonstrate its efficacy, we report some experiences in using the method in a challenging application in multivariate dynamic factor models for financial time series, as recently studied using straight MCMC methods by the second author and other collaborators. Some summary comments and comparisons with MCMC methods are given in this applied context.
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