Analysis of Mixtures in Physical Spectra

Abstract: A reversible jump Markov chain Monte Carlo technique is applied to estimate the number and parameters of peaks in ubiquitous physical problems in the framework of Bayesian probability theory. For measured physical spectra often only the functional form of the structures is known but the number of the peaks and the parameters are unknown. The full joint posterior distribution for all parameters is sampled for estimating the number of components supported by the significant information in the noisy data and for estimating the unknown parameters for the most probable number of components. The method is applied to the classical Old Faithful density estimation problem and the physical problem of resolution enhancement and spectral decomposition of high-resolution electron energy loss data.