Parameter Estimation in X‐Ray Astronomy Revisited

The method of obtaining confidence intervals on a subset of the total numberof parameters (p) of a model used for fitting X-ray spectra is to perturb thebest-fitting model until, for each parameter, a range is found for which thechange in the fit statistic is equal to some critical value. This criticalvalue corresponds to the desired confidence level and is obtained from thechi-square distribution for q degrees of freedom, where q is the number ofinteresting parameters. With the advent of better energy-resolution detectors,such as those onboard ASCA it has become more common to fit complex models withnarrow features, comparable to the instrumental energy resolution. Toinvestigate whether this leads to significant non-Gaussian deviations betweendata and model, we use simulations based on ASCA data and we show that themethod is still valid in such cases. We also investigate the weak-source limitas well as the case of obtaining upper limits on equivalents widths of weakemission lines and find that for all practical purposes the method gives thecorrect confidence ranges. However, upper limits on emission-line equivalentwidths may be over-estimated in the extreme Poisson limit.Comment: 21 pages, 6 Figures. Latex with separate postscript figure files. Appears in ApJ. NOTE:replaces erroneous version sent out due to clerical erro