A LOG-GAUSSIAN COX PROCESS WITH SEQUENTIAL MONTE CARLO FOR LINE NARROWING IN SPECTROSCOPY

We propose a statistical model for narrowing line shapes in spec-troscopy that are well approximated as linear combinations of Lorentzian or Voigt functions. We introduce a log-Gaussian Cox process to represent the peak locations thereby providing uncertainty quantification for the line narrowing. Bayesian formulation of the method allows for robust and explicit inclusion of prior information as probability distributions for parameters of the model. Estimation of the signal and its parameters is performed using a sequential Monte Carlo algorithm followed by an optimization step to determine the peak locations. Our method is validated using a simulation study and applied to a mineralogical Raman spectrum.

Automated summary

We propose a statistical model for narrowing line shapes in spectroscopy. Our model uses linear combinations of Lorentzian or Voigt functions to approximate the line shapes. We introduce a log-Gaussian Cox process to represent the peak locations, providing uncertainty quantification for the line narrowing. Our Bayesian formulation allows for robust and explicit inclusion of prior information as probability distributions for model parameters. We validate our method using simulation study and apply it to a mineralogical Raman spectrum.