Comparison of maximum likelihood estimation and chisquare statistics applied to counting experiments
Abstract
Five different statistics are compared with respect to parameter, error, and goodnessoffit estimation in the case of counting experiments. In particular, maximum likelihood approaches are opposed to chisquare techniques. It could be shown that the maximum likelihood estimation derived for Poisson distributed data (Poisson MLE) produces the best statistic in order to estimate parameters. If goodnessoffit estimations are to be done, Pearson's chisquare should be used. It is the only statistic that leads to the correct expectation value for chisquare. All the other statistics do not follow a chisquare distribution. It is discussed that the chisquare per degree of freedom is not well suited for judging the consistency of a model and the data. When estimating the mean of Poisson distributed data or the area under a peak, Poisson MLE was shown to be the only statistic that comes to consistent and unbiased results, two other statistics give asymptotically consistent results. The widely used Neyman's chisquare fails in all cases. Further, artificial Poisson distributed data have been created on the basis of known model functions. It is shown and discussed in which cases chisquare techniques fail to extract the correct parameter values and where they still can be used. Special emphasis is put on the evaluation of Dopplerbroadened gamma line shapes as they are measured in the CrystalGRID technique.
 Publication:

Nuclear Instruments and Methods in Physics Research A
 Pub Date:
 January 2001
 DOI:
 10.1016/S01689002(00)007567
 Bibcode:
 2001NIMPA.457..384H