Error estimation
From GOSIA
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==Diagonal errors versus correlated errors== | ==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 ''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. | + | 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== | ==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 Cline and Lesser, "Error estimation in non-linear least squares analysis of data," NIM '''82''' | + | 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 calculated by Gosia's OP,ERRO function== | ||
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===Brute force total correlated error estimation in gosia2 problems=== | ===Brute force total correlated error estimation in gosia2 problems=== | ||
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| + | ==References== | ||
| + | {{reflist}} | ||
