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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 (), where is the set of possible observations, i.e. the sample space, and is a set of probability distributions on . 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 to represent a set (of distributions) which contains a distribution that adequately approximates the true distribution. Note that we do not require that 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 is almost always parameterized: . The set 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: . 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
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