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Precision (statistics): Wikis

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In statistics, the term precision can mean a quantity defined in a specific way. this is in addition to its more general meaning in the context of accuracy and precision. "Precision" is used for in relation to a single quantity, while precision matrix or concentration matrix,[1] are used in relation to several quantities.

There can be differences in usage of the term for particaular statistical models but, in general statistical usage, the precision is defined to be the reciprical of the variance, while the precision matrix is the matrix inverse of the covariance matrix.[1]

One particular use of the precision matrix is in the context of Bayesian analysis of the multivariate normal distribution: for example, Bernardo & Smith[2] prefer to parameterise the multivariate normal distribution in terms of the precision matrix rather than the covariance matrix because of certain simplifiactions that then arise.

History

The term precision (“mensura praecisionis observationum”) first appeared in the works of Gauss (1809) “Theoria motus corporum coelestium in sectionibus conicis solem ambientium” (page 245). 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{h}{\surd\pi}\, e^{-hh\Delta\Delta} .

Later Whittaker & Robinson (1924) “Calculus of observations” called this quanitity the modulus, however nowadays this term dropped out of use.[3]

Definition

References

  1. ^ a b Dodge Y. (2003) The Oxford Dictionary of Statistical Terms, OUP. ISBN 0-19-920613-9
  2. ^ Bernardo, J. M. & Smith, A.F.M. (2000) Bayesian Theory, Wiley ISBN 0-471-49464-X
  3. ^ "Earliest known uses of some of the words in mathematics". http://jeff560.tripod.com/m.html.  

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