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Precision (statistics) : ウィキペディア英語版
Precision (statistics)
In statistics, the dual term variability is preferred to the use of ''precision''. Variability is the amount of imprecision.
There can be differences in usage of the term for particular statistical models but, in common statistical usage, the precision is defined to be the reciprocal of the variance, while the precision matrix is the matrix inverse of the covariance matrix.〔Dodge Y. (2003) ''The Oxford Dictionary of Statistical Terms'', OUP. ISBN 0-19-920613-9〕
One particular use of the precision matrix is in the context of Bayesian analysis of the multivariate normal distribution: for example, Bernardo & Smith〔Bernardo, J. M. & Smith, A.F.M. (2000) ''Bayesian Theory'', Wiley ISBN 0-471-49464-X〕 prefer to parameterise the multivariate normal distribution in terms of the precision matrix rather than the covariance matrix because of certain simplifications that then arise.
==History==
The term ''precision'' in this sense (“mensura praecisionis observationum”) first appeared in the works of Gauss (1809) “''Theoria motus corporum coelestium in sectionibus conicis solem ambientium''” (page 212). Gauss’s definition differs from the modern one by a factor of \scriptstyle\sqrt2. He writes, for the density function of a normal random variable with precision ''h'',
:
\varphi\Delta = \tfrac\, e^ .

Later Whittaker & Robinson (1924) “''Calculus of observations''” called this quantity ''the modulus'', but this term has dropped out of use.

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