Coupled conditional backward sampling particle filter
Autor: | Matti Vihola, Sumeetpal S. Singh, Anthony Lee |
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Přispěvatelé: | Apollo - University of Cambridge Repository |
Rok vydání: | 2020 |
Předmět: |
65C05
FOS: Computer and information sciences Statistics and Probability unbiased Markovin ketjut Time horizon Statistics - Computation 01 natural sciences Stability (probability) backward sampling 65C05 (Primary) 60J05 65C35 65C40 (secondary) 010104 statistics & probability convergence rate FOS: Mathematics Applied mathematics 0101 mathematics coupling Hidden Markov model 65C35 Computation (stat.CO) Mathematics stokastiset prosessit Backward sampling Series (mathematics) Probability (math.PR) Sampling (statistics) conditional particle filter Monte Carlo -menetelmät Rate of convergence 65C60 65C40 numeerinen analyysi Statistics Probability and Uncertainty Particle filter Mathematics - Probability Smoothing |
Zdroj: | Ann. Statist. 48, no. 5 (2020), 3066-3089 |
Popis: | The conditional particle filter (CPF) is a promising algorithm for general hidden Markov model smoothing. Empirical evidence suggests that the variant of CPF with backward sampling (CBPF) performs well even with long time series. Previous theoretical results have not been able to demonstrate the improvement brought by backward sampling, whereas we provide rates showing that CBPF can remain effective with a fixed number of particles independent of the time horizon. Our result is based on analysis of a new coupling of two CBPFs, the coupled conditional backward sampling particle filter (CCBPF). We show that CCBPF has good stability properties in the sense that with fixed number of particles, the coupling time in terms of iterations increases only linearly with respect to the time horizon under a general (strong mixing) condition. The CCBPF is useful not only as a theoretical tool, but also as a practical method that allows for unbiased estimation of smoothing expectations, following the recent developments by Jacob et al. (to appear). Unbiased estimation has many advantages, such as enabling the construction of asymptotically exact confidence intervals and straightforward parallelisation. 24 pages, 5 figures |
Databáze: | OpenAIRE |
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