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Optimal estimation
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Optimal estimation : ウィキペディア英語版
Optimal estimation
In applied statistics, optimal estimation is a regularized matrix inverse method based on Bayes theorem.
It is used very commonly in the geosciences, particularly for atmospheric sounding.
A matrix inverse problem looks like this:
:
\mathbf \vec x = \vec y

The essential concept is to transform the matrix, A, into a conditional probability and the variables, \vec x and \vec y into probability distributions by assuming Gaussian statistics and using empirically-determined covariance matrices.
==Derivation==

Typically, one expects the statistics of most measurements to be Gaussian. So for example for P(\vec y|\vec x), we can write:
:
P(\vec y|\vec x) = \frac |}

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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