Matthew Moores

We propose a statistical model for narrowing line shapes in spectroscopy that are well approximated as linear combinations of Lorentzian or Voigt functions. We introduce a log-Gaussian Cox process to represent the peak locations thereby providing uncertainty quantification for the line narrowing. Bayesian formulation of the method allows for robust and explicit inclusion of prior information as probability distributions for parameters of the model. Estimation of the signal and its parameters is performed using a sequential Monte Carlo algorithm followed by an optimization step to determine the peak locations. Our method is validated using a simulation study and applied to a mineralogical Raman spectrum.

The potential for materials undergoing oxidation reactions to spontaneously combust when they are stored in large stockpiles is well known. We consider an application in which such self-heating is desirable and investigate the use of inert hotspots as a means to promote thermal runaway. The size and location of the hotspot are found to have the largest effects on self-heating. Less pronounced are effects due a periodic ambient temperature. The advection velocity through the stockpile can have large effects.

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, underlying Raman signal, 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 artefacts 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.

The inverse temperature parameter of the Potts model governs the strength of spatial cohesion and therefore has a major influence over the resulting model fit. A difficulty arises from the dependence of an intractable normalising constant on the value of this parameter and thus there is no closed-form solution for sampling from the posterior distribution directly. There is a variety of computational approaches for sampling from the posterior without evaluating the normalising constant, including the exchange algorithm and approximate Bayesian computation (ABC). A serious drawback of these algorithms is that they do not scale well for models with a large state space, such as images with a million or more pixels. We introduce a parametric surrogate model, which approximates the score function using an integral curve. Our surrogate model incorporates known properties of the likelihood, such as heteroskedasticity and critical temperature. We demonstrate this method using synthetic data as well as remotely-sensed imagery from the Landsat-8 satellite. We achieve up to a hundredfold improvement in the elapsed runtime, compared to the exchange algorithm or ABC. An open-source implementation of our algorithm is available in the R package bayesImageS.