Abstract
We study a distributed particle filter proposed by Boli\'c 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 m→∞. 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 M−1/2. 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 m−1/2.
Original language | English |
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Pages (from-to) | 2508-2541 |
Number of pages | 34 |
Journal | Stochastic Processes and their Applications |
Volume | 127 |
Issue number | 8 |
Early online date | 9 Dec 2016 |
DOIs | |
Publication status | Published - Aug 2017 |
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Professor Nick Whiteley
- School of Mathematics - Heilbronn Chair in Data Science
- Statistical Science
Person: Member, Academic , Member