Bayesian model selection and parameter estimation of nuclear emission spectra using RJMCMC

This paper addresses the general problem of estimating parameters in nuclear spectroscopy. We present a unified Bayesian formulation to tackle the various aspects of this problem. This includes deconvolution and modelling of both the peaks and background. The peaks are modelled with Gaussian or Lorentz-type functions and the background with cubic B-splines. The Bayesian model allows us to define a posterior probability in the parameter space upon which all subsequent Bayesian inference is based. Direct evaluation of this distribution or its derived features such as the conditional expectation is, unfortunately, not possible on account of the need to evaluate high-dimension integrals. As such we resort to a stochastic numerical Bayesian technique, the reversible-jump Markov-chain Monte-Carlo method. We have carried out simulations on both artificial and real data. Our results on the 1995 IAEA γ-ray test spectra shows that our program performs better than those previously reported.