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See also: Additive smoothing (Laplace smoothing) a method of smoothing of a statistical estimator In mathematics, Laplace's method, named after Pierre-Simon Laplace, is a technique used to approximate integrals of the form : where ''ƒ''(''x'') is some twice-differentiable function, ''M'' is a large number, and the integral endpoints ''a'' and ''b'' could possibly be infinite. This technique was originally presented in Laplace (1774, pp. 366–367). ==The idea of Laplace's method== Assume that the function ''ƒ''(''x'') has a unique global maximum at ''x''0. Then, the value ''ƒ''(''x''0) will be larger than other values ''ƒ''(''x''). If we multiply this function by a large number ''M'', the ratio between ''Mƒ''(''x''0) and ''Mƒ''(''x'') will stay the same (since ''Mƒ''(''x''0)/''Mƒ''(''x'') = ''ƒ''(''x''0)/''ƒ''(''x'')), but it will grow exponentially in the function (see figure) : Thus, significant contributions to the integral of this function will come only from points ''x'' in a neighborhood of ''x''0, which can then be estimated. 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「Laplace's method」の詳細全文を読む スポンサード リンク
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