翻訳と辞書 Words near each other ・ Coupletist ・ Coupling ・ Coupling (computer programming) ・ Coupling (disambiguation) ・ Coupling (electronics) ・ Coupling (Greek TV series) ・ Coupling (physics) ・ Coupling (piping) ・ Coupling (probability) ・ Coupling (U.S. TV series) ・ Coupling (UK TV series) ・ Coupling coefficient of resonators ・ Coupling Collection ・ Coupling constant ・ Coupling Facility ・ Coupling from the past ・ Coupling loss ・ Coupling nut ・ Coupling parameter ・ Coupling reaction ・ Coupling rod ・ Coupling, Energetics and Dynamics of Atmospheric Regions ・ Coupon ・ Coupon (bond) ・ Coupon (disambiguation) ・ Coupon (PWB) ・ Coupon Cabin ・ Coupon collector's problem ・ Coupon Craze ・ Coupon leverage Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Coupling from the past ： ウィキペディア英語版 Coupling from the past Among Markov chain Monte Carlo (MCMC) algorithms, coupling from the past is a method for sampling from the stationary distribution of a Markov chain. Contrary to many MCMC algorithms, coupling from the past gives in principle a perfect sample from the stationary distribution. It was invented by James Propp and David Wilson in 1996. ==The basic idea== Consider a finite state irreducible aperiodic Markov chain $M$ with state space $S$ and (unique) stationary distribution $\backslash pi$ ($\backslash pi$ is a probability vector). Suppose that we come up with a probability distribution $\backslash mu$ on the set of maps $f:S\backslash to\; S$ with the property that for every fixed $s\backslash in\; S$, its image $f(s)$ is distributed according to the transition probability of $M$ from state $s$. An example of such a probability distribution is the one where $f(s)$ is independent from $f(s\text{'})$ whenever $s\backslash ne\; s\text{'}$, but it is often worthwhile to consider other distributions. Now let $f\_j$ for $j\backslash in\backslash mathbb\; Z$ be independent samples from $\backslash mu$. Suppose that $x$ is chosen randomly according to $\backslash pi$ and is independent from the sequence $f\_j$. (We do not worry for now where this $x$ is coming from.) Then $f\_(x)$ is also distributed according to $\backslash pi$, because $\backslash pi$ is $M$-stationary and our assumption on the law of $f$. Define :$F\_j:=\; f\_\backslash circ\; f\_\backslash circ\backslash cdots\backslash circ\; f\_.$ Then it follows by induction that $F\_j(x)$ is also distributed according to $\backslash pi$ for every $j\backslash in\backslash mathbb\; N$. Now here is the main point. It may happen that for some $n\backslash in\backslash mathbb\; N$ the image of the map $F\_n$ is a single element of $S$. In other words, $F\_n(x)=F\_n(y)$ for each $y\backslash in\; S$. Therefore, we do not need to have access to $x$ in order to compute $F\_n(x)$. The algorithm then involves finding some $n\backslash in\; \backslash mathbb\; N$ such that $F\_n(S)$ is a singleton, and outputing the element of that singleton. The design of a good distribution $\backslash mu$ for which the task of finding such an $n$ and computing $F\_n$ is not too costly is not always obvious, but has been accomplished successfully in several important instances. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Coupling from the past」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.