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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 Statistical model ： ウィキペディア英語版 Statistical model A statistical model embodies a set of assumptions concerning the generation of the observed data, and similar data from a larger population. A model represents, often in considerably idealized form, the data-generating process. The model assumptions describe a set of probability distributions, some of which are assumed to adequately approximate the distribution from which a particular data set is sampled. A model is usually specified by mathematical equations that relate one or more random variables and possibly other non-random variables. As such, "a model is a formal representation of a theory" (Herman Adèr quoting Kenneth Bollen). All statistical hypothesis tests and all statistical estimators are derived from statistical models. More generally, statistical models are part of the foundation of statistical inference. ==Formal definition== In mathematical terms, a statistical model is usually thought of as a pair ($S,\; \backslash mathcal$), where $S$ is the set of possible observations, i.e. the sample space, and $\backslash mathcal$ is a set of probability distributions on $S$. The intuition behind this definition is as follows. It is assumed that there is a "true" probability distribution that generates the observed data. We choose $\backslash mathcal$ to represent a set (of distributions) which contains a distribution that adequately approximates the true distribution. Note that we do not require that $\backslash mathcal$ contains the true distribution, and in practice that is rarely the case. Indeed, as Burnham & Anderson state, "A model is a simplification or approximation of reality and hence will not reflect all of reality"—whence the saying "all models are wrong". The set $\backslash mathcal$ is almost always parameterized: $\backslash mathcal=\backslash$. The set $\backslash Theta$ defines the ''parameters'' of the model. A parameterization is generally required to have distinct parameter values give rise to distinct distributions, i.e. to meet this condition: $P\_\; =\; P\_\; \backslash Rightarrow\; \backslash theta\_1\; =\; \backslash theta\_2$. A parameterization that meets the condition is said to be ''identifiable''.〔 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「Statistical model」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.