Parameter estimation in X-ray astronomy

Abstract

The problems of model classification and parameter estimation are examined, with the objective of establishing the statistical reliability of inferences drawn from X-ray observations. For testing the validities of classes of models, the procedure based on minimizing the chi/sup 2/ statistic is recommended; it provides a rejection criterion at any desired significance level. Once a class of models has been accepted, a related procedure based on the increase of chi/sup 2/ gives a confidence region for the values of the model's adjustable parameters. The procedure allows the confidence level to be chosen exactly, even for highly nonlinear models. Numerical experiments confirm the validity of the prescribed technique.The chi/sup 2//sub min/+1 error estimation method is evaluated and found unsuitable when several parameter ranges are to be derived, because it substantially underestimates their joint errors. The ratio of variances method, while formally correct, gives parameter confidence regions which are more variable than necessary. (AIP)