Mathematical foundation of an analytical approach to Bayesian-statistical Monte Carlo spectrum unfolding

The Bayesian-statistical Monte Carlo method of unfolding energy spectra of nuclear radiation particles offers a largely model-independent means of extracting the maximum information from the measurement data and the uncertainties associated with them. The uncertainty of the spectrum to be unfolded, including correlations, can also be obtained. The main shortcoming of the method is the huge number of calculations which must be carried out. The new analytical unfolding method described and mathematically founded here reduces this number by several orders of magnitude. The spectrum probability distribution, which according to Bayesian statistics and the principle of maximum entropy is most appropriate to the data, and which is required for the Monte Carlo method for drawing sample spectra from it at random, is replaced by a suitable exponential distribution from which an estimate of the desired spectrum can be analytically calculated. The associated uncertainty covariance matrix can also be obtained. A non-linear optimization problem for only a few parameters remains to be solved. The results are equivalent to those obtained by Monte Carlo unfolding in the limiting case of an infinite number of energy groups. This is mathematically proved in the present report. (orig.)22 refs.Available from TIB Hannover: RO 8345(24) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman