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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Reversible-jump Markov chain Monte Carlo ： ウィキペディア英語版 Reversible-jump Markov chain Monte Carlo In computational statistics, reversible-jump Markov chain Monte Carlo is an extension to standard Markov chain Monte Carlo (MCMC) methodology that allows simulation of the posterior distribution on spaces of varying dimensions. Thus, the simulation is possible even if the number of parameters in the model is not known. Let :$n\_m\backslash in\; N\_m=\backslash \; \backslash ,$ be a model indicator and $M=\backslash bigcup\_^I\; \backslash R^$ the parameter space whose number of dimensions $d\_m$ depends on the model $n\_m$. The model indication need not be finite. The stationary distribution is the joint posterior distribution of $(M,N\_m)$ that takes the values $(m,n\_m)$. The proposal $m\text{'}$ can be constructed with a mapping $g\_$ of $m$ and $u$, where $u$ is drawn from a random component $U$ with density $q$ on $\backslash R^(m,u),n\_m\text{'})\; \backslash ,$ The function :$$ g_:=\Bigg((m,u)\mapsto \bigg((m',u')=\big(g_(m,u),g_(m,u)\big)\bigg)\Bigg) \, must be ''one to one'' and differentiable, and have a non-zero support: :$\backslash mathrm(g\_)\backslash ne\; \backslash varnothing\; \backslash ,$ so that there exists an inverse function :$g^\_=g\_\; \backslash ,$ that is differentiable. Therefore, the $(m,u)$ and $(m\text{'},u\text{'})$ must be of equal dimension, which is the case if the dimension criterion :$d\_m+d\_=d\_+d\_\; \backslash ,$ is met where $d\_$ is the dimension of $u$. This is known as ''dimension matching''. If $\backslash R^\backslash subset\; \backslash R^=d\_\; \backslash ,$ with :$(m,u)=g\_(m).\; \backslash ,$ The acceptance probability will be given by :$$ a(m,m')=\min\left(1, \fracf_(m')}(m,u)p_f_m(m)}\left|\det\left(\frac\right)\right|\right), where $|\backslash cdot\; |$ denotes the absolute value and $p\_mf\_m$ is the joint posterior probability :$$ p_mf_m=c^p(y|m,n_m)p(m|n_m)p(n_m), \, where $c$ is the normalising constant. == Software packages == There is an experimental RJ-MCMC tool available for the open source BUGS package. ==References== 〔 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「Reversible-jump Markov chain Monte Carlo」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.