Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5130045 | Stochastic Processes and their Applications | 2017 | 34 Pages |
We study a distributed particle filter proposed by BoliÄ et al. (2005). This algorithm involves m groups of M particles, with interaction between groups occurring through a “local exchange” mechanism. We establish a central limit theorem in the regime where M is fixed and mââ. A formula we obtain for the asymptotic variance can be interpreted in terms of colliding Markov chains, enabling analytic and numerical evaluations of how the asymptotic variance behaves over time, with comparison to a benchmark algorithm consisting of m independent particle filters. We prove that subject to regularity conditions, when m is fixed both algorithms converge time-uniformly at rate Mâ1/2. Through use of our asymptotic variance formula we give counter-examples satisfying the same regularity conditions to show that when M is fixed neither algorithm, in general, converges time-uniformly at rate mâ1/2.