Convergence of unfolded spectrum with response function for single radiation based on Bayes' theorem

Abstract

A Bayesian unfolding method has previously been proposed to infer the source spectrum from measured pulse height distribution data. In contrast to the conventional unfolding methods using the Bayes' theory, the pulse height response function for a single radiation is used as the likelihood function. In the present work, the convergence of the unfolded to the source spectrum by this method is proven analytically from the viewpoint of the Kullback–Leibler divergence when a flat-type spectrum is assigned to the initial prior spectrum. In addition, the unfolding capability of this method is demonstrated using a numerical simulation for the ideal case where the statistical error in the measured pulse height distribution can be neglected.