Genomics is increasingly complemented by *metabonomics* – the quantitative measurement of the time-related multiparametric metabolic responses of multicellular systems to (patho)physiological stimuli or genetic modification [1]. Mass spectrometry and nuclear magnetic resonance (NMR) spectroscopy have become the two key technologies in the metabonomic field [2]. An appealing feature of NMR spectroscopy for metabonomic applications is its specific yet non-selective nature: proton (^{1}H) NMR can efficiently produce information on a large number of metabolites in biological samples like human serum. The abundance of protons and the inherently narrow as well as heterogeneous chemical shift range of ^{1}H NMR results in highly informative spectra that contain heavily overlapping resonances [3].

Recently, a call for applying ^{1}H NMR metabonomics to facilitate disease risk assessment and clinical diagnostics has emerged [1, 2, 4–8]. A key issue in bringing metabonomics for clinical use will be to bridge the gap between biochemistry – as revealed by ^{1}H NMR spectroscopy – and the relevant measures of current clinical practice. In a ^{1}H NMR spectrum, one metabolite can manifest several peaks, and the spectral intensities are both biochemically and (patho)physiologically related. Furthermore, the data sets are extensive but redundant: one measurement can yield tens of thousands of data points, but the effective dimensionality is much less due to a smaller number of NMR-visible compounds. Consequently, there are methodological challenges in trying to quantitatively associate ^{1}H NMR metabonomics data to relevant biochemical variables as well as to understand and visualise the underlying metabolic features that relate to various biomedical applications [8].

A key clinical application of ^{1}H NMR spectroscopy is to quantify lipoprotein lipids directly from plasma or serum samples [3, 7, 9–13]. One of the strategic reasons to use ^{1}H NMR to study lipoproteins is the avoidance of their tedious physical isolation from plasma via repetitive ultracentrifugations and thus the consequent potential to analyse extensive clinical data sets beyond current biochemical methodologies. Various ^{1}H NMR spectroscopy applications have focused on the main lipoprotein fractions, namely very low, intermediate, low and high density lipoproteins (VLDL, IDL, LDL and HDL, respectively), since these relate to general clinical guidelines to assess an individual's risk for atherosclerosis [3, 6, 12]. Interestingly, one of the advanced methods, already in clinical use, to determine plasma lipoproteins is a commercial ^{1}H NMR based assay named NMR LipoProfile^{®} by LipoScience Inc [13]. Thus, ^{1}H NMR spectroscopy and metabonomics of serum provides an extensively studied and demonstrative case of complex overlapping resonances with well-known biochemical rationale and spectral characteristics [3, 6, 7, 9–13].

Biomedical research relies heavily on the statistical analysis of empirical findings and extrapolation from limited sample sets to larger populations. Currently, hypothesis testing with pre-selected parametric formulations is the prevailing technique and statistical uncertainty is expressed indirectly by comparing the observations to a given null hypothesis. In multi-dimensional applications such as ^{1}H NMR metabonomics the null hypothesis is obtainable only for the simplest formulations, which are often inadequate to describe the data efficiently. In contrast, Bayesian theory [14, 15] explicitly incorporates uncertainty in the form of probability distributions, hence the null hypothesis is no longer required as the reference point. Furthermore, the parametric formulations need not be pre-selected heuristically, but can be included in the modelling process itself. Hence, the analysis becomes more dependent on the data and prior knowledge, and less dependent on arbitrary practical restrictions such as analytical tractability. However, applications of Bayesian methodology in NMR spectroscopy are sparse [16–18], perhaps due to the lack of computing power until recent years. A Bayesian spectral decomposition has produced promising results for metabonomic NMR data [19] but, to our knowledge, this is the first biomedical application of Bayesian inference on spectral quantification with special modelling emphasis on the metabolic rationale.

Thus, this work has two key objectives to establish. First, to quantify broad overlapping resonances from ^{1}H NMR spectra of serum using specific Bayesian models, and, second, to relate the resulting model kernels to the known biochemical characteristics of the spectra. This study focuses on a clinically significant application of ^{1}H NMR spectroscopy of serum for quantifying lipoprotein lipid concentrations used for the assessment of individuals' risk for coronary heart disease. A set of biochemically characterised serum samples, for which VLDL and IDL triglycerides (VLDL-TG and IDL-TG, respectively) as well as IDL, LDL and HDL cholesterol (IDL-C, LDL-C and HDL-C, respectively) concentrations are independently measured, is the origin for the ^{1}H NMR spectra. A Markov chain Monte Carlo (MCMC) in Bayesian inference is used to set up quantitative models based on these ^{1}H NMR spectra and to automatically define the number and locations of Gaussian kernels to indicate the spectral features corresponding to each biochemical variable.