On the role of interaction in sequential Monte Carlo algorithms
| Autor: | Nick Whiteley, Anthony Lee, Kari Heine |
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| Rok vydání: | 2016 |
| Předmět: |
FOS: Computer and information sciences
Statistics and Probability convergence Degree (graph theory) particle filters Parameterized complexity 020206 networking & telecommunications 02 engineering and technology Statistics - Computation 01 natural sciences 010104 statistics & probability hidden Markov mode Resampling hidden Convergence (routing) 0202 electrical engineering electronic engineering information engineering Standard algorithms 0101 mathematics Hidden Markov model Degeneracy (mathematics) Particle filter hidden Markov model Algorithm Computation (stat.CO) Mathematics |
| Zdroj: | Bernoulli 22, no. 1 (2016), 494-529 Whiteley, N, Lee, A & Heine, K 2016, ' On the role of interaction in sequential Monte Carlo algorithms ', Bernoulli, vol. 22, no. 1, pp. 494-529 . https://doi.org/10.3150/14-BEJ666 |
| ISSN: | 1350-7265 |
| DOI: | 10.3150/14-bej666 |
| Popis: | We introduce a general form of sequential Monte Carlo algorithm defined in terms of a parameterized resampling mechanism. We find that a suitably generalized notion of the Effective Sample Size (ESS), widely used to monitor algorithm degeneracy, appears naturally in a study of its convergence properties. We are then able to phrase sufficient conditions for time-uniform convergence in terms of algorithmic control of the ESS, in turn achievable by adaptively modulating the interaction between particles. This leads us to suggest novel algorithms which are, in senses to be made precise, provably stable and yet designed to avoid the degree of interaction which hinders parallelization of standard algorithms. As a byproduct, we prove time-uniform convergence of the popular adaptive resampling particle filter. Published at http://dx.doi.org/10.3150/14-BEJ666 in the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm) |
| Databáze: | OpenAIRE |
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