Error estimation

From GOSIA

Error estimation in any physics field can sometimes be difficult and is often poorly understood. It is common for errors to be underestimated because of a failure to correlate error contributions from all significant (strongly coupled) fit parameters, and fallacies about error propagation abound. ==Diagonal errors versus correlated errors== The ''diagonal'' error is the error one obtains by varying only a single parameter "x" above and below it minimum [[chi-squared]] value to find the intersection of the chi-squared vs. with the line defined by chi-squared = minimum chi-squared + 1. The diagonal error is generally much smaller than the full correlated error, and the latter is the error that should be quoted. The ''correlated error'' is defined by the lower and upper limits of the parameter being measured of the (ideally elliptical) intersection of the [[reduced chi-squared]] surface with the plane defined by reduced-chi-squared + reduced-chi-squared_minimum + (reduced-chi-squared_minimum/N), where "N" is the number of [ degrees of freedom] in the fit. ==Proper treatment of correlated errors in the general case== Assuming that the errors in each measured parameter obey approximately a normal distribution, the correct derivation of the correlated error in each parameter is described in detail in <ref>D. Cline and P.M.S. Lesser, "Error estimation in non-linear least squares analysis of data," NIM '''82''' (1970) 291-293</ref> . This paper compares an incorrect procedure sometimes used with the correct treatment. ==Correlated errors calculated by Gosia's OP,ERRO function== ==Correlated errors using gosia2== Gosia2 fits parameters (matrix elements) for the nucleus being studied (the "investigated nucleus") by normalization of the Coulomb excitation gamma-ray yields of the investigated nucleus to those of the collision partner. However, it only correlates errors among the measured matrix element(s) of each collision partner individually, i.e., it does not do a complete correlated error calculation including both the beam nucleus and target nucleus free parameters. Hence, using the present version of gosia2, to get a complete correlated error analysis, some brute-force hand-calculations are necessary. Generally, gosia2 is used to measure only a few parameters for both collision partners, since the original Gosia can be used to self-normalize for large data sets. ===Brute force total correlated error estimation in gosia2 problems=== ==References== {{reflist}}

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