Fluctuations, stability and instability of a distributed particle filter with local exchange
| Autor: | Kari Heine, Nick Whiteley |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2015 |
| Předmět: |
FOS: Computer and information sciences
Statistics and Probability Mathematical optimization 60F05 60F99 60G35 Central limit theorem 02 engineering and technology 01 natural sciences Stability (probability) Instability Methodology (stat.ME) 010104 statistics & probability Modelling and Simulation Local exchange 0202 electrical engineering electronic engineering information engineering 0101 mathematics Hidden Markov model Sequential Monte Carlo Statistics - Methodology Mathematics Markov chain Applied Mathematics Mathematical analysis Particle Filter 020206 networking & telecommunications Delta method Modeling and Simulation Benchmark (computing) Asymptotic variance Particle filter |
| Zdroj: | Heine, K & Whiteley, N 2017, ' Fluctuations, stability and instability of a distributed particle filter with local exchange ' Stochastic Processes and their Applications, vol 127, no. 8 . Heine, K & Whiteley, N P 2017, ' Fluctuations, stability and instability of a distributed particle filter with local exchange ', Stochastic Processes and their Applications, vol. 127, no. 8, pp. 2508-2541 . https://doi.org/10.1016/j.spa.2016.11.003 |
| DOI: | 10.1016/j.spa.2016.11.003 |
| Popis: | 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 $m\to\infty$. 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 $m^{-1/2}$. Comment: 49 pages, 7 figures |
| Databáze: | OpenAIRE |
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