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統計数学セミナー
過去の記録 ～04/24｜次回の予定｜今後の予定 04/25～
| 担当者 | 吉田朋広、荻原哲平、小池祐太 |
|---|---|
| セミナーURL | http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/ |
| 目的 | 確率統計学およびその関連領域に関する研究発表, 研究紹介を行う. |
2016年07月26日(火)
13:00-14:30 数理科学研究科棟(駒場) 052号室
本講演は大阪大学で行い，東京大学へWeb配信いたします.
Ajay Jasra 氏 (National University of Singapore)
Multilevel Particle Filters
本講演は大阪大学で行い，東京大学へWeb配信いたします.
Ajay Jasra 氏 (National University of Singapore)
Multilevel Particle Filters
[ 講演概要 ]
In this talk the filtering of partially observed diffusions,
with discrete-time observations, is considered.
It is assumed that only biased approximations of the diffusion can be
obtained, for choice of an accuracy parameter indexed by $l$.
A multilevel estimator is proposed, consisting of a telescopic sum of
increment estimators associated to the successive levels.
The work associated to $\cO(\varepsilon^2)$ mean-square error between
the multilevel estimator and average with respect to the filtering
distribution is shown to scale optimally, for example as
$\cO(\varepsilon^{-2})$ for optimal rates of convergence of the
underlying diffusion approximation.
The method is illustrated on several examples.
In this talk the filtering of partially observed diffusions,
with discrete-time observations, is considered.
It is assumed that only biased approximations of the diffusion can be
obtained, for choice of an accuracy parameter indexed by $l$.
A multilevel estimator is proposed, consisting of a telescopic sum of
increment estimators associated to the successive levels.
The work associated to $\cO(\varepsilon^2)$ mean-square error between
the multilevel estimator and average with respect to the filtering
distribution is shown to scale optimally, for example as
$\cO(\varepsilon^{-2})$ for optimal rates of convergence of the
underlying diffusion approximation.
The method is illustrated on several examples.
