Video of my talk in Oaxaca
I was very lucky to be invited to attend a 5 day workshop at the Casa Matemática Oaxaca (CMO-BIRS), “Computational Statistics and Molecular Simulation: A Practical Cross-Fertilization” where I presented my work on the Rao-Blackwellized particle filter for Bayesian modelling of Raman spectroscopy. A link to the video is here and the abstract for my talk is below. See also commentary on selected talks by one of the organisers, Prof. Xi’an.
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.
