Chi2

class sherpa.stats.Chi2(name='chi2')

Bases: sherpa.stats.Stat

Chi Squared statistic.

The chi-square statistic is:

chi^2 = (sum)_i [ [ N(i,S) - B(i,x,pB) - S(i,x,pS) ]^2 / sigma(i)^2 ]

where N(i,S) is the total number of observed counts in bin i of the on-source region; B(i,x,pB) is the number of predicted background model counts in bin i of the on-source region (zero for background-subtracted data), rescaled from bin i of the off-source region, and computed as a function of the model argument x(i) (e.g., energy or time) and set of background model parameter values pB; S(i,x,pS) is the number of predicted source model counts in bin i, as a function of the model argument x(i) and set of source model parameter values pS; and sigma(i) is the error in bin i.

N(i,B) is the total number of observed counts in bin i of the off-source region; A(B) is the off-source “area”, which could be the size of the region from which the background is extracted, or the length of a background time segment, or a product of the two, etc.; and A(S) is the on-source “area”. These terms may be defined for a particular type of data: for example, PHA data sets A(B) to BACKSCAL * EXPOSURE from the background data set and A(S) to BACKSCAL * EXPOSURE from the source data set.

There are different ways of defining the sigma(i) terms, supported by the sub-classes.

Notes

It is assumed that there is a one-to-one mapping between a given background region bin and a given source region bin. For instance, in the analysis of PHA data, it is assumed that the input background counts spectrum is binned in exactly the same way as the input source counts spectrum, and any filter applied to the source spectrum automatically applied to the background spectrum. This means that the user cannot, for example, specify arbitrary background and source regions in two dimensions and get correct results. This limitation only applies to backgrounds included included as part of the data set - e.g. as with PHA files - and can be avoided by treating the background as a separate data set.

Methods Summary

calc_chisqr(data, model)	Return the chi-square value for each bin.
calc_stat(data, model)
calc_staterror(data)

Methods Documentation

calc_chisqr(data, model)

Return the chi-square value for each bin.

Parameters:

• data (a Data or DataSimulFit instance) – The data set, or sets, to use.
• model (a Model or SimulFitModel instance) – The model expression, or expressions. If a SimulFitModel is given then it must match the number of data sets in the data parameter.

Returns:

chisqr – The per-bin chi-square values.

Return type:

array of numbers

calc_stat(data, model)

static calc_staterror(data)