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Adaptive methods for sequential importance sampling with application to state space models

Cornebise, Julien; Moulines, Éric and Olsson, Jimmy LU (2008) In Statistics and Computing 18(4). p.461-480
Abstract
In this paper we discuss new adaptive proposal strategies for sequential Monte Carlo algorithms—also known as particle filters—relying on criteria evaluating the quality of the proposed particles. The choice of the proposal distribution is a major concern and can dramatically influence the quality of the estimates. Thus, we show how the long-used coefficient of variation (suggested by Kong et al. in J. Am. Stat. Assoc. 89(278–288):590–599, 1994) of the weights can be used for estimating the chi-square distance between the target and instrumental distributions of the auxiliary particle filter. As a by-product of this analysis we obtain an auxiliary adjustment multiplier weight type for which this chi-square distance is minimal. Moreover, we... (More)
In this paper we discuss new adaptive proposal strategies for sequential Monte Carlo algorithms—also known as particle filters—relying on criteria evaluating the quality of the proposed particles. The choice of the proposal distribution is a major concern and can dramatically influence the quality of the estimates. Thus, we show how the long-used coefficient of variation (suggested by Kong et al. in J. Am. Stat. Assoc. 89(278–288):590–599, 1994) of the weights can be used for estimating the chi-square distance between the target and instrumental distributions of the auxiliary particle filter. As a by-product of this analysis we obtain an auxiliary adjustment multiplier weight type for which this chi-square distance is minimal. Moreover, we establish an empirical estimate of linear complexity of the Kullback-Leibler divergence between the involved distributions. Guided by these results, we discuss adaptive designing of the particle filter proposal distribution and illustrate the methods on a numerical example. (Less)
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Adaptive Monte Carlo, Auxiliary particle filter, Coefficient of variation, Kullback-Leibler divergence, Cross-entropy method, Sequential Monte Carlo, State space models
in
Statistics and Computing
volume
18
issue
4
pages
461 - 480
publisher
Springer
external identifiers
  • wos:000261607600009
  • scopus:57849133035
ISSN
0960-3174
DOI
10.1007/s11222-008-9089-4
language
English
LU publication?
yes
id
71dba19a-b52d-42d4-91d7-32b3692aab1c (old id 1271958)
date added to LUP
2009-05-11 14:46:48
date last changed
2017-10-08 03:51:20
@article{71dba19a-b52d-42d4-91d7-32b3692aab1c,
  abstract     = {In this paper we discuss new adaptive proposal strategies for sequential Monte Carlo algorithms—also known as particle filters—relying on criteria evaluating the quality of the proposed particles. The choice of the proposal distribution is a major concern and can dramatically influence the quality of the estimates. Thus, we show how the long-used coefficient of variation (suggested by Kong et al. in J. Am. Stat. Assoc. 89(278–288):590–599, 1994) of the weights can be used for estimating the chi-square distance between the target and instrumental distributions of the auxiliary particle filter. As a by-product of this analysis we obtain an auxiliary adjustment multiplier weight type for which this chi-square distance is minimal. Moreover, we establish an empirical estimate of linear complexity of the Kullback-Leibler divergence between the involved distributions. Guided by these results, we discuss adaptive designing of the particle filter proposal distribution and illustrate the methods on a numerical example.},
  author       = {Cornebise, Julien and Moulines, Éric and Olsson, Jimmy},
  issn         = {0960-3174},
  keyword      = {Adaptive Monte Carlo,Auxiliary particle filter,Coefficient of variation,Kullback-Leibler divergence,Cross-entropy method,Sequential Monte Carlo,State space models},
  language     = {eng},
  number       = {4},
  pages        = {461--480},
  publisher    = {Springer},
  series       = {Statistics and Computing},
  title        = {Adaptive methods for sequential importance sampling with application to state space models},
  url          = {http://dx.doi.org/10.1007/s11222-008-9089-4},
  volume       = {18},
  year         = {2008},
}