An analytical approach to Monte Carlo spectrum unfolding

Abstract

The Monte Carlo spectrum unfolding method offers model-independent means for extracting the maximum information from the measurement data together with their uncertainties. The uncertainty of the unfolded spectrum, including correlations, can also be obtained. Its main shortcoming is the huge number of calculations which must be carried out. The analytical unfolding method proposed reduces the amount of calculations by orders of magnitude. It essentially consists in replacing the most appropriate a priori probability distribution required for drawing sample spectra from it at random for the Monte Carlo statistics with a certain exponential distribution from which the desired spectrum and its uncertainty covariance matrix can be analytically calculated. By taking into account the principle of maximum entropy, only a few-parameter, non-linear optimization problem remains to be solved. The results are equivalent to those obtained by the Monte Carlo unfolding in the limiting case of an infinite number of energy groups.