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Set-membership approach In statistics, a random vector ''x'' is classically represented by a probability density function. In a set-membership approach, ''x'' is represented by a set ''X'' to which ''x'' is assumed to belong. It means that the support of the probability distribution function of ''x'' is included inside ''X''. On the one hand, representing random vectors by sets makes it possible to provide less assumptions on the random variables (such as independence) and dealing with nonlinearities is easier. On the other hand, a probability distribution function provides a more accurate information than a set enclosing its support. ==Set-membership estimation== Set membership estimation (or ''set estimation'' for short) is an estimation approach which considers that measurements are represented by a set ''Y'' (most of the time a box of R''m'', where ''m'' is the number of measurements) of the measurement space. If ''p'' is the parameter vector and ''f'' is the model function, then the set of all feasible parameter vectors is , where ''P''0 is the prior set for the parameters. Characterizing ''P'' corresponds to a set-inversion problem .〔 〕 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「Set estimation」の詳細全文を読む スポンサード リンク
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