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統計数学セミナー
過去の記録 ～04/19｜次回の予定｜今後の予定 04/20～
| 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. |
2009年04月22日(水)
15:00-16:10 数理科学研究科棟(駒場) 128号室
Arnaud DOUCET 氏 (統計数理研究所)
Interacting Markov chain Monte Carlo Methods for Solving Nonlinear Measure-Valued Equations
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2009/02.html
Arnaud DOUCET 氏 (統計数理研究所)
Interacting Markov chain Monte Carlo Methods for Solving Nonlinear Measure-Valued Equations
[ 講演概要 ]
We present a new class of interacting Markov chain Monte Carlo algorithms for solving numerically discrete-time measure-valued equations. The associated stochastic processes belong to the class of self-interacting Markov chains. In contrast to traditional Markov chains, their time evolution depend on the occupation measure of their past values. This general methodology allows us to provide a natural way to sample from a sequence of target probability measures of increasing complexity. We develop an original theoretical analysis to analyze the behaviour of these iterative algorithms. We establish a variety of convergence results including exponential estimates and a uniform convergence theorem with respect to the number of target distributions. We also illustrate these algorithms in the context of Feynman-Kac distribution flows.
(this is joint work with Professor Pierre Del Moral)
[ 参考URL ]We present a new class of interacting Markov chain Monte Carlo algorithms for solving numerically discrete-time measure-valued equations. The associated stochastic processes belong to the class of self-interacting Markov chains. In contrast to traditional Markov chains, their time evolution depend on the occupation measure of their past values. This general methodology allows us to provide a natural way to sample from a sequence of target probability measures of increasing complexity. We develop an original theoretical analysis to analyze the behaviour of these iterative algorithms. We establish a variety of convergence results including exponential estimates and a uniform convergence theorem with respect to the number of target distributions. We also illustrate these algorithms in the context of Feynman-Kac distribution flows.
(this is joint work with Professor Pierre Del Moral)
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2009/02.html
