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Sequential Monte Carlo for Bayesian Analysis of Spectroscopy

Banff International Research Station for Mathematical Innovation and Discovery

The spectral signature of a molecule can be predicted using a quantum-mechanical model, such as time-dependent density functional theory (TD-DFT). However, there are no uncertainty estimates associated with these predictions, and matching with peaks in observed spectra is often performed by eye. This talk introduces a model-based approach for baseline estimation and peak fitting, using TD-DFT predictions as an informative prior. The peaks are modelled as a mixture of Lorentzian, Gaussian, or pseudo-Voigt broadening functions, while the baseline is represented as a penalised cubic spline. We fit this model using a sequential Monte Carlo (SMC) algorithm, which is robust to local maxima and enables the posterior distribution to be incrementally updated as more data becomes available. We apply our method to multivariate calibration of Raman-active dye molecules, enabling us to estimate the limit of detection (LOD) of each peak. This is joint work with Mark Girolami & Jake Carson (U. Warwick), and Karen Faulds, Duncan Graham & Kirsten Gracie (U. Strathclyde)

Mathematics; Statistics; Statistical mechanics, structure of matter; Statistical mechanics

video/mp4

Author affiliation: University of Wollongong

2019-05-13

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/70149

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/