Year
2014
Abstract
The problem of fitting a mathematical function to a set of correlated data using weighted linear least squares is a pervasive one in the field of radioanalytic measurements, arising in many applications. In practice this problem is often handled by simply ignoring the correlations, which can result in the underestimation of the uncertainties of parameter values obtained from the fit. To propagate fitting uncerta inties in a way that accurately incorporates such correlation effects requires both a generalization of the standard linear least squares fitting methodology and a careful analysis of the correlations that exist b e- tween input data points. While the general ized method for incorporating correlations in least squares fitting is well established, it is not widely known, and the evaluation of co r- relations between the data can be challenging. The method is demonstrated here in the context of fitting the detection efficiency as a function of energy for a gamma - ray spe c- troscopy system, where the correlations between the measured efficiency data used as i n- put to the fit arise from the use of multi - line nuclides and/or multi - nuclide gamma ray sources in the efficiency measurement. An analytic method is also demonstrated for eva l- uating the correlations between the efficiency data. Several examples of efficiency cal i- bration fits are shown, and the uncertainties obtained with and without considering the correlations for e ach example are compared.