Decomposition of a Chemical Spectrum using a Marked Point Process and a Constant Dimension Model

We consider the problem of estimating the peak parameters in a spectroscopic signal, i.e. their locations, amplitudes and form parameters. A marked point process provides a suitable representation for this phenomenon: it consists in modeling the spectrum as a noisy sum of points lying in the observation space and characterized by their locations and some marks (amplitude and widths). A non-supervised Bayesian approach coupled with MCMC methods is retained to solve the problem. But the peak number is unknown. Rather than using a method for model uncertainty (such as RJMCMC) we propose an approach in which the dimension model is constant: consequently, the Gibbs sampler appears possible and natural. The idea consists in considering an upper bound for peak number and modelling the peak occurrence by a Bernoulli distribution. At last, a label switching method adapted to the approach is also proposed. The method is illustrated by an application on a real spectrum.