Sequential Monte Carlo methods for static parameter estimation in random set models

Bayesian inferencing for applications where the dimension of the parameter is also unknown requires modeling the parameter as an (ordered or unordered) random finite set. In most practical estimation problems, Monte Carlo methods is the standard tool. In particular the transdimensional Markov chain Monte Carlo (MCMC) method has been used to simulate from the posterior density of the random finite set. However the MCMC approach involves accessing the entire sequence of data for each iteration, and becomes computationally infeasible for massive data sets. This paper presents two sequential Monte Carlo strategies to reduce the number full accesses to the data. The first combines sequential importance sampling with MCMC to sequentially sample from the posterior. The second introduces artificial dynamics in the parameter to cast the problem as a Bayesian filtering problem so that particle techniques can be applied.