Bayesian deconvolution in nuclear spectroscopy 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 Lorentzian type functions and the background with cubic B-splines. The number of peaks and spline knots are treated as unknowns and as such are also estimated together with the model parameters. The Bayesian model allows us to define a posterior probability on 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(RJMCMC) method.