Editing Calibration (statistics) (section)

==In regression==
{{Cleanup|reason = unclear what it does|date=September 2023}}
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.<ref>Brown, P.J. (1994) ''Measurement, Regression and Calibration'', OUP. {{ISBN|0-19-852245-2}}</ref><ref>Ng, K. H., Pooi, A. H. (2008) "Calibration Intervals in Linear Regression Models", ''Communications in Statistics - Theory and Methods'', 37 (11), 1688–1696. [http://www.informaworld.com/10.1080/03610920701826120]</ref><ref>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&ndash;372. [http://www.stata-journal.com/article.html?article=st0050 link], [http://www.stata-journal.com/sjpdf.html?article=st0050 pdf]</ref> This can be known as "inverse regression";<ref>Draper, N.L., Smith, H. (1998) ''Applied Regression analysis, 3rd Edition'', Wiley. {{ISBN|0-471-17082-8}}</ref> there is also [[sliced inverse regression]]. The following multivariate calibration methods exist for transforming classifier scores into [[class membership probabilities]] in the case with classes count greater than two:
* Reduction to binary tasks and subsequent pairwise coupling, see Hastie and Tibshirani (1998)<ref>T. Hastie and R. Tibshirani, "[http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.46.6032]," Classification by pairwise coupling. In: M. I. Jordan, M. J. Kearns and [[Sara Solla|S. A. Solla]] (eds.), Advances in Neural Information Processing Systems, volume 10, Cambridge, MIT Press, 1998.</ref>
* Dirichlet calibration, see Gebel (2009)<ref name="Gebel2009" />

=== Example ===
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 [[causality|cause]]d 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 [[Operational definition|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.