翻訳と辞書 Words near each other ・ Nestor Hammarlund ・ Nestor Ignat ・ Nestor Iskander's Tale on the Taking of Tsargrad ・ Nestor Ivanovich Novozhilov ・ Nestor J. Zaluzec ・ Nestor Jacono ・ Nestor Khergiani ・ Nestor Kotlyarevsky ・ Nestor Kukolnik ・ Nestor L'Hôte ・ Nestor Lakoba ・ Nestor Leynes ・ Nestor Léon Marchand ・ Nestor Makhno ・ Nestor Mata ・ Nested sampling algorithm ・ Nested set model ・ Nested SQL ・ Nested stack automaton ・ Nested transaction ・ Nested triangles graph ・ Nested word ・ Nestedness ・ NestEgg ・ Nestegis ・ Nestegis apetala ・ Nestegis cunninghamii ・ Nestegis lanceolata ・ Nestegis montana ・ Nestegis sandwicensis 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 Nested sampling algorithm ： ウィキペディア英語版 Nested sampling algorithm The nested sampling algorithm is a computational approach to the problem of comparing models in Bayesian statistics, developed in 2004 by physicist John Skilling. ==Background== Bayes' theorem can be applied to a pair of competing models $M1$ and $M2$ for data $D$, one of which may be true (though which one is not known) but which both cannot simultaneously be true. The posterior probability for $M1$ may be calculated as follows: : $$ \begin P(M1|D) & \\ & \\ & \frac } \end Given no a priori information in favor of $M1$ or $M2$, it is reasonable to assign prior probabilities $P(M1)=P(M2)=1/2$, so that $P(M2)/P(M1)=1$. The remaining Bayes factor$P(D|M2)/P(D|M1)$ is not so easy to evaluate since in general it requires marginalization of nuisance parameters. Generally, $M1$ has a collection of parameters that can be lumped together and called $\backslash theta$, and $M2$ has its own vector of parameters that may be of different dimensionality but is still referred to as $\backslash theta$. The marginalization for $M1$ is : $P(D|M1)\; =\; \backslash int\; d\; \backslash theta\; P(D|\backslash theta,M1)\; P(\backslash theta|M1)$ and likewise for $M2$. This integral is often analytically intractable, and in these cases it is necessary to employ a numerical algorithm to find an approximation. The nested sampling algorithm was developed by John Skilling specifically to approximate these marginalization integrals, and it has the added benefit of generating samples from the posterior distribution $P(\backslash theta|D,M1)$. It is an alternative to methods from the Bayesian literature such as bridge sampling and defensive importance sampling. Here is a simple version of the nested sampling algorithm, followed by a description of how it computes the marginal probability density $Z=P(D|M)$ where $M$ is $M1$ or $M2$: Start with $N$ points $\backslash theta\_1,...,\backslash theta\_N$ sampled from prior. for $i=1$ to $j$ do % The number of iterations j is chosen by guesswork. $L\_i\; :=\; \backslash min($current likelihood values of the points$)$; $X\_i\; :=\; \backslash exp(-i/N);$ $w\_i\; :=\; X\_\; -\; X\_i$ $Z\; :=\; Z\; +\; L\_i$ *w_i; Save the point with least likelihood as a sample point with weight $w\_i$. Update the point with least likelihood with some Markov Chain Monte Carlo steps according to the prior, accepting only steps that keep the likelihood above $L\_i$. end return $Z$; At each iteration, $X\_i$ is an estimate of the amount of prior mass covered by the hypervolume in parameter space of all points with likelihood greater than $\backslash theta\_i$. The weight factor $w\_i$ is an estimate of the amount of prior mass that lies between two nested hypersurfaces $\backslash$ and $\backslash$. The update step $Z\; :=\; Z+L\_i$ *w_i computes the sum over $i$ of $L\_i$ *w_i to numerically approximate the integral : $$ \begin P(D|M) &=& \int P(D|\theta,M) P(\theta|M) d \theta \\ &=& \int P(D|\theta,M) dP(\theta|M)\\ \end The idea is to chop up the range of $f(\backslash theta)\; =\; P(D|\backslash theta,M)$ and estimate, for each interval $(f(\backslash theta\_i))$, how likely it is a priori that a randomly chosen $\backslash theta$ would map to this interval. This can be thought of as a Bayesian's way to numerically implement Lebesgue integration. 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「Nested sampling algorithm」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.