Fast Bayesian Deconvolution using Simple Reversible Jump Moves

TL;DR

This paper introduces a Bayesian deconvolution method that efficiently estimates the number of spectral peaks and their parameters using reversible jump moves and replica exchange Monte Carlo, outperforming traditional sweep simulations.

Contribution

The paper presents a novel MCMC-based deconvolution technique that automatically determines the number of peaks in spectral data, improving model selection efficiency.

Findings

Demonstrates superior performance over sweep simulations in synthetic data.

Successfully applied to real spectral data, matching previous mineralogical results.

Efficiently estimates the number and parameters of spectral peaks.

Abstract

We propose a Markov chain Monte Carlo-based deconvolution method designed to estimate the number of peaks in spectral data, along with the optimal parameters of each radial basis function. Assuming cases where the number of peaks is unknown, and a sweep simulation on all candidate models is computationally unrealistic, the proposed method efficiently searches over the probable candidates via trans-dimensional moves assisted by annealing effects from replica exchange Monte Carlo moves. Through simulation using synthetic data, the proposed method demonstrates its advantages over conventional sweep simulations, particularly in model selection problems. Application to a set of olivine reflectance spectral data with varying forsterite and fayalite mixture ratios reproduced results obtained from previous mineralogical research, indicating that our method is applicable to deconvolution on real data sets.