Chi-square statistic with Primini variance function.
The chi-square statistic is a biased
estimator of model parameters (unlike the likelihood functions). In
an attempt to remove this bias, Kearns, Primini, & Alexander
(1995, ADASS IV, 331) use a scheme dubbed `Iterative Weighting' (IW;
see Wheaton et al. 1995, ApJ 438, 322), in which
sigma(i)^2 = S[i,x(i),pS^(j-1)] + [A(N)/A(B)]^2 B_off[i,x(i),pB^(j-1)] ,
where j is the number of iterations that have
been carried out in the fitting process, B_off is the background model amplitude in bin i of the off-source region, and pS^(j-1) and pB^(j-1) are the set of source and background
model parameter values derived during the iteration previous to the
current one.
In addition to reducing parameter estimate bias, it can be used even
when the number of counts in each bin is small (< 5), although the
user should proceed with caution.
The background should not be subtracted from the data when this
statistic is used. CHI PRIMINI
underestimates the variance when fitting background-subtracted data.
See
CHISQUARE for more information, including
definitions of the quantities shown above.
Specify the fitting statistic and then confirm it has been set.
sherpa> STATISTIC CHI PRIMINI
WARNING: with CHI PRIMINI, displayed error bars will only be
correct after a fit is performed with the current filter.
sherpa> SHOW STATISTIC
Statistic: Chi-Squared Primini
- sherpa
-
bayes,
cash,
chicvar,
chidvar,
chigehrels,
chimvar,
chisquare,
cstat,
get_stat_expr,
statistic,
truncate,
userstat
|
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