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Conference Season

June 2, 2018

I’ll be attending the final i-Like workshop in Newcastle-upon-Tyne, then heading to ABC in Edinburgh and the ISBA World Meeting before returning to Warwick for BAYSM (the Bayesian Young Statisticians’ Meeting). I’ll also be presenting a talk about bayesImageS at the UseR! conference in Brisbane. Titles and abstracts for my talks are below.

This will be my farewell tour of the UK, as I’ll be relocating back to Australia after an amazing four years as a postdoc at the University of Warwick. After UseR!, I’ll be taking up a lectureship in the School of Mathematics and Statistics and the National Institute for Applied Statistics Research Australia (NIASRA) at the University of Wollongong.

Parametric Functional Approximate Bayesian (PFAB) Algorithm for the Potts Model

ABC in Edinburgh, Sunday June 24

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 are 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’.

Moores, Pettitt & Mengersen (2015; v2 2018) “Scalable Bayesian inference for the inverse temperature of a hidden Potts model” arXiv:1503.08066 [stat.CO]

Sequential Monte Carlo for Multivariate Calibration in Chemometrics

ISBA World Meeting, University of Edinburgh, Monday June 25

Raman spectroscopy can be used to identify molecules by the characteristic scattering of light from a laser. Each Raman-active dye label has a unique spectral signature, comprised by the locations and amplitudes of the peaks. The presence of a large, non-uniform background presents a major challenge to analysis of these spectra. We introduce a sequential Monte Carlo (SMC) algorithm to separate the observed spectrum into a series of peaks plus a smoothly-varying baseline, corrupted by additive white noise. The peaks are modelled as Lorentzian, Gaussian, or pseudo-Voigt functions, while the baseline is estimated using a penalised cubic spline. Our model-based approach accounts for differences in resolution and experimental conditions. We incorporate prior information to improve identifiability and regularise the solution. By utilising this representation in a Bayesian functional regression, we can quantify the relationship between molecular concentration and peak intensity, resulting in an improved estimate of the limit of detection. The posterior distribution can be incrementally updated as more data becomes available, resulting in a scalable algorithm that is robust to local maxima. These methods have been implemented as an R package, using RcppEigen and OpenMP.

Moores, Gracie, Carson, Faulds, Graham & Girolami (2016; v2 2018) “Bayesian modelling and quantification of Raman spectroscopy” arXiv:1604.07299 [stat.AP]

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