Thursday, January 17, 2013

XSPEC v12.8 - new statistics

XSPEC uses statistics for two purposes: 1) determining the best-fit parameter and its uncertainties; and 2) checking whether the model is a good fit to the data. In the past these have both been performed using the same statistic. There are two problems with this. Firstly, there are many goodness-of-fit statistical tests which do not use a statistic appropriate for parameter estimation. Secondly, using the same statistic for both parameter estimation and goodness of fit affects the properties of the statistic when used for the latter purpose.

XSPEC v12.8 now allows separate statistics to be defined for parameter estimation and goodness of fit. There are no changes to the statistic command for parameter estimation however to use a new goodness-of-fit statistic the command becomes statistic test whatever. At the end of a fit both statistic values are now written out. The goodness command now uses the test statistic. There is a new plot option to help visualizing the result of running the goodness command. The command plot goodness after running goodness generates a histogram plot of the test statistic values from the simulations as well as a line indicating the value for the actual data.

The new test statistics added include the familiar Kolmogorov-Smirnov along with the related Anderson-Darling and Cramer-von Mises. The runs statistic tests for runs of consecutive positive or negative residuals. Also added is the original Pearson chi-square statistic for Poisson data.

One new fit statistic has been added: the Whittle statistic for fitting power density spectra.

All these statistics are described in the manual in the extended appendix on statistics.

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