Simultaneous Estimation of Noise Variance and Number of Peaks in Bayesian Spectral Deconvolution

TL;DR

This paper introduces a Bayesian inference framework for accurately estimating noise variance and the number of peaks in complex spectra, improving physical interpretation and avoiding overfitting.

Contribution

It presents a novel two-step Bayesian approach with advanced sampling techniques to simultaneously estimate noise and peak count in spectral data.

Findings

Efficiently estimates noise variance and peak number.

Reduces overfitting and misinterpretation of spectral data.

Demonstrates effectiveness through simulation results.

Abstract

The heuristic identification of peaks from noisy complex spectra often leads to misunderstanding of the physical and chemical properties of matter. In this paper, we propose a framework based on Bayesian inference, which enables us to separate multipeak spectra into single peaks statistically and consists of two steps. The first step is estimating both the noise variance and the number of peaks as hyperparameters based on Bayes free energy, which generally is not analytically tractable. The second step is fitting the parameters of each peak function to the given spectrum by calculating the posterior density, which has a problem of local minima and saddles since multipeak models are nonlinear and hierarchical. Our framework enables the escape from local minima or saddles by using the exchange Monte Carlo method and calculates Bayes free energy via the multiple histogram method. We discuss a simulation demonstrating how efficient our framework is and show that estimating both the noise variance and the number of peaks prevents overfitting, overpenalizing, and misunderstanding the precision of parameter estimation.