Error estimation
From GOSIA
(still in progress) |
(added plot example) |
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# Iterate this procedure, stepping <math>x=\langle f\| ML\| i\rangle</math> through values below and above the best value from the gosia2 fit and recording the points <math>x,\chi^2</math>. | # Iterate this procedure, stepping <math>x=\langle f\| ML\| i\rangle</math> through values below and above the best value from the gosia2 fit and recording the points <math>x,\chi^2</math>. | ||
| - | Using the procedure above, a plot of <math>\chi^2</math> vs. <math>x</math> can be generated, which should look similar to the sketch shown | + | Using the procedure above, a plot of <math>\chi^2</math> vs. <math>x</math> can be generated, which should look similar to the sketch [[File:Gosia2_correlated_error_sketch.png|thumb|right|A sketch of a plot used to estimate correlated errors. A parabolic fit to the chi-squared points is shown in black. The green line indicates the new chi-squared minimum from the correlated error calculation, while the dashed red line indicates the min chi^2 + 1 criterion. The vertical lines indicate the correlated error on the matrix element.]] This may give a slightly improved best value of the matrix element as well. |
The correlated error for this matrix element <math>\langle f\| ML\| i\rangle</math> is then given by matrix element values where a fit to the points (a parabolic fit is usually sufficient) intersects the line defined by <math>\chi^2=\chi^2_{\rm min} + 1</math>. As in the sections above, this criterion is derived 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> | The correlated error for this matrix element <math>\langle f\| ML\| i\rangle</math> is then given by matrix element values where a fit to the points (a parabolic fit is usually sufficient) intersects the line defined by <math>\chi^2=\chi^2_{\rm min} + 1</math>. As in the sections above, this criterion is derived 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> | ||
