Bayesian Quantification for Coherent Anti-Stokes Raman Scattering Spectroscopy

Abstract

We propose a Bayesian statistical model for analyzing coherent anti-Stokes Raman scattering (CARS) spectra. Our quantitative analysis includes statistical estimation of constituent line-shape parameters, the underlying Raman signal, the error-corrected CARS spectrum, and the measured CARS spectrum. As such, this work enables extensive uncertainty quantification in the context of CARS spectroscopy. Furthermore, we present an unsupervised method for improving spectral resolution of Raman-like spectra requiring little to no a priori information. Finally, the recently proposed wavelet prism method for correcting the experimental artifacts in CARS is enhanced by using interpolation techniques for wavelets. The method is validated using CARS spectra of adenosine mono-, di-, and triphosphate in water, as well as equimolar aqueous solutions of d -fructose, d -glucose, and their disaccharide combination sucrose.

Infrared Spectroscopy of Chemically Diverse Carbon Clusters: A Data-Driven Approach

“…However, extracting the spectral features from a statistical sample seems also naturally suited to be tackled by machine learning (ML) techniques, a broad range of computational approaches that have become spectacularly popular in chemical physics and physical chemistry in the recent years. 15,16 Within the general context of relating properties to structure, several groups have recently shown the benefits of employing ML for vibrational spectroscopy [17][18][19] through a variety of approaches aiming to represent potential energy and electric dipole moment surfaces within perturbative frameworks, 20 to condense molecular information into topological descriptors, 21 or to numerically solve the quantum nuclear dynamics problem by better partitioning the various degrees of freedom. 22 In the present contribution, we explore several ML ideas to reconstruct the infrared spectrum of carbon clusters in a statistical sense, from a limited sample and using interpolation techniques in a multidimensional feature space, supervision being introduced through metric learning.…”

A Log-Gaussian Cox Process with Sequential Monte Carlo for Line Narrowing in Spectroscopy

“…In our previous work [10], we incorporated LOMEP as a pre-processing step for empirical Bayesian inference on the line shape parameters using a Sequential Monte Carlo (SMC) algorithm [5]. Here, we extend this approach to a fully-Bayesian statistical model that is capable of providing posterior distributions for the estimated line-narrowed spectrum, along with posterior distributions for the line width and impulse-response length.…”

“…Our SMC algorithm provides a scalable and parallelizable method of statistical inference for spectroscopic data. In addition to the primary interest of line narrowing, the posterior distributions for the line widths and peak locations have immediate applications in being incorporated as prior distributions for further statistical spectrum analysis techniques [10,19].…”

“…, π (T ) to ultimately obtain samples from the desired posterior distribution defined in Equation ( 9). We construct the distribution at step t of the tempering sequence as (10) where the superscript (t) denotes the iteration of the SMC algorithm and the tempering parameter κ (t) is chosen such that κ (t−1) < κ (t) < κ (t+1) < • • • ≤ 1 with κ (0) = 0. In Equation (10), the initial state of the particle distribution is equal to the joint prior for θ, M , and…”

“…At each subsequent iteration, the particles are updated so that the intermediate tempering distribution approaches the targeted posterior given in Equation ( 9). We determine the tempering schedule adaptively, as in [10,19], such that the relative decrease in effective sample size (ESS), defined as…”