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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 Gaussian process ： ウィキペディア英語版 Gaussian process In probability theory and statistics, Gaussian processes are a family of statistical distributions (not necessarily stochastic processes) in which time plays a role. In a Gaussian process, every point in some input space is associated with a normally distributed random variable. Moreover, every finite collection of those random variables has a multivariate normal distribution. The distribution of a Gaussian process is the joint distribution of all those (infinitely many) random variables, and as such, it is a distribution over functions. The concept of Gaussian processes is named after Carl Friedrich Gauss because it is based on the notion of the Gaussian distribution (normal distribution). Gaussian processes can be seen as an infinite-dimensional generalization of multivariate normal distributions. Gaussian processes are important in statistical modelling because of properties inherited from the normal. For example, if a random process is modeled as a Gaussian process, the distributions of various derived quantities can be obtained explicitly. Such quantities include the average value of the process over a range of times and the error in estimating the average using sample values at a small set of times. ==Definition== A Gaussian process is a statistical distribution ''X''''t'', ''t'' ∈ ''T'', for which any finite linear combination of samples has a joint Gaussian distribution. More accurately, any linear functional applied to the sample function ''X''''t'' will give a normally distributed result. Notation-wise, one can write ''X'' ~ GP(''m'',''K''), meaning the random function ''X'' is distributed as a GP with mean function ''m'' and covariance function ''K''. When the input vector ''t'' is two- or multi-dimensional, a Gaussian process might be also known as a ''Gaussian random field''. Some authors assume the random variables ''X''''t'' have mean zero; this greatly simplifies calculations without loss of generality and allows the mean square properties of the process to be ''entirely'' determined by the covariance function ''K''. 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「Gaussian process」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.