2015/05/10 by Kari Heine, Heine, Kari, Nick Whiteley +1
Computer Science · Mathematics · #60F05 #60F99 #60G35 #Bayesian Methods and Mixture Models #FOS: Computer and information sciences #Markov Chains and Monte Carlo Methods #Methodology (stat.ME) #Statistical Methods and Bayesian Inference #Target Tracking and Data Fusion in Sensor Networks
paper · pdf · doi:10.48550/arxiv.1505.02390
openalex publication_date 2015/05/10 · openalex created_date 2022/08/13 · openalex updated_date 2026/07/28
We study a distributed particle filter proposed by Boli 'c et al.~(2005).\nThis algorithm involves m groups of M particles, with interaction between\ngroups occurring through a "local exchange" mechanism. We establish a central\nlimit theorem in the regime where M is fixed and m\→\∞. A formula we\nobtain for the asymptotic variance can be interpreted in terms of colliding\nMarkov chains, enabling analytic and numerical evaluations of how the\nasymptotic variance behaves over time, with comparison to a benchmark algorithm\nconsisting of m independent particle filters. We prove that subject to\nregularity conditions, when m is fixed both algorithms converge\ntime-uniformly at rate M-1/2. Through use of our asymptotic variance\nformula we give counter-examples satisfying the same regularity conditions to\nshow that when M is fixed neither algorithm, in general, converges\ntime-uniformly at rate m-1/2.\n