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Calibration (statistics) : ウィキペディア英語版
Calibration (statistics)
There are two main uses of the term calibration in statistics that denote special types of statistical inference problems. Thus "calibration" can mean
:
*A reverse process to regression, where instead of a future dependent variable being predicted from known explanatory variables, a known observation of the dependent variables is used to predict a corresponding explanatory variable.〔Upton, G, Cook, I. (2006) ''Oxford Dictionary of Statistics'', OUP. ISBN 978-0-19-954145-4〕
:
*Procedures in statistical classification to determine class membership probabilities which assess the uncertainty of a given new observation belonging to each of the already established classes.
In addition, "calibration" is used in statistics with the usual general meaning of calibration. For example, model calibration can be also used to refer to Bayesian inference about the value of a model's parameters, given some data set, or more generally to any type of fitting of a statistical model.
==In regression==
The ''calibration problem'' in regression is the use of known data on the observed relationship between a dependent variable and an independent variable to make estimates of other values of the independent variable from new observations of the dependent variable.〔Brown, P.J. (1994) ''Measurement, Regression and Calibration'', OUP. ISBN 0-19-852245-2〕〔Ng, K. H., Pooi, A. H. (2008) "Calibration Intervals in Linear Regression Models", ''Communications in Statistics - Theory and Methods'', 37 (11), 1688–1696. ()〕〔Hardin, J. W., Schmiediche, H., Carroll, R. J. (2003) "The regression-calibration method for fitting generalized linear models with additive measurement error", ''Stata Journal'', 3 (4), 361–372. (link ), (pdf )〕 This can be known as "inverse regression":〔Draper, N.L., Smith, H. (1998) ''Applied Regression analysis, 3rd Edition'', Wiley. ISBN 0-471-17082-8〕 see also sliced inverse regression.
One example is that of dating objects, using observable evidence such as tree rings for dendrochronology or carbon-14 for radiometric dating. The observation is caused by the age of the object being dated, rather than the reverse, and the aim is to use the method for estimating dates based on new observations. The problem is whether the model used for relating known ages with observations should aim to minimise the error in the observation, or minimise the error in the date. The two approaches will produce different results, and the difference will increase if the model is then used for extrapolation at some distance from the known results.

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