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    Bayesian Methods for Metabolomics

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    Metabolomics, the large-scale study of small molecules, enables the underlying biochemical activity and state of cells or tissues to be directly captured. Nuclear Magnetic Resonance (NMR) Spectroscopy is one of the major data capturing tech- niques for metabolomics, as it provides highly reproducible, quantitative informa- tion on a wide variety of metabolites. This work presents possible solutions for three problems involved to aid the development of better algorithms for NMR data analy- sis. After reviewing relevant concepts and literature, we first utilise observed NMR chemical shift titration data for a range of urinary metabolites and develop a the- oretical model of chemical shift using a Bayesian statistical framework and model selection procedures to estimate the number of protonation sites, a key parameter to model the relationship between chemical shift variation and pH and usually un- known in uncatalogued metabolites. Secondly, with the aim of obtaining explicit concentration estimates for metabolites from NMR spectra, we discuss a Monte Carlo Co-ordinate Ascent Variational Inference (MC-CAVI) algorithm that com- bines Markov chain Monte Carlo (MCMC) methods with Co-ordinate Ascent VI (CAVI), demonstrate MC-CAVI’s suitability for models with hard constraints and compare MC-CAVI’s performance with that of MCMC in an important complex model used in NMR spectroscopy data analysis. The third distribution seeks to im- prove metabolite identification, one of the biggest bottlenecks in metabolomics and severely hindered by resonance overlapping in one-dimensional NMR spectroscopy. In particular, we present a novel Bayesian method for widely used two-dimensional (2D) 1H J-resolved (JRES) NMR spectroscopy, which has considerable potential to accurately identify and quantify metabolites within complex biological samples, through combining B-spline tight wavelet frames with theoretical templates. We then demonstrate the effectiveness of our approach via analyses of JRES datasets from serum and urine
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