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In probability theory and statistics, covariance is a measure of how much two variables change together, and the covariance function, or kernel, describes the spatial covariance of a random variable process or field. For a random field or stochastic process ''Z''(''x'') on a domain ''D'', a covariance function ''C''(''x'', ''y'') gives the covariance of the values of the random field at the two locations ''x'' and ''y'': : The same ''C''(''x'', ''y'') is called the autocovariance function in two instances: in time series (to denote exactly the same concept except that ''x'' and ''y'' refer to locations in time rather than in space), and in multivariate random fields (to refer to the covariance of a variable with itself, as opposed to the cross covariance between two different variables at different locations, ''Cov''(''Z''(''x''1), ''Y''(''x''2))). == Admissibility == For locations ''x''1, ''x''2, …, ''x''''N'' ∈ ''D'' the variance of every linear combination : can be computed as : A function is a valid covariance function if and only if this variance is non-negative for all possible choices of ''N'' and weights ''w''1, …, ''w''''N''. A function with this property is called positive definite. 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「covariance function」の詳細全文を読む スポンサード リンク
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