Physical mixture modeling with unknown number of components

Measured physical spectra often comprise an unknown number of components of known parametric family. A reversible jump Markov chain Monte Carlo (RJMCMC) technique is applied to the problem of estimating the number of components evident in the data jointly with the parameters of the components. The physical model consists of a mixture of components, an additive background, and a convolution with a blurring apparatus transfer function. The results were compared with the deconvolution of a form-free distribution. By calculating marginal posterior probability density distributions from the RJMCMC sample for the most probable number of components we estimated the parameters and their uncertainties, The method was applied to a benchmark test of Rutherford backscattering spectroscopy on a system consisting of a thin Cu film where we know that Cu consists of two isotopes.