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Proteomics promises to revolutionize cancer treatment and prevention by facilitating the discovery of molecular biomarkers. Progress has been impeded, however, by the small-sample, high-dimensional nature of proteomic data. We propose the application of a Bayesian approach to address this issue in classification of proteomic profiles generated by liquid chromatography–mass spectrometry (LC-MS). Our approach relies on a previously proposed model of the LC-MS experiment, as well as on the theory of the optimal Bayesian classifier (OBC). Computation of the OBC requires the combination of a likelihood-free methodology called approximate Bayesian computation (ABC) as well as Markov chain Monte Carlo (MCMC) sampling. Numerical experiments using synthetic LC-MS data based on an actual human proteome indicate that the proposed ABC-MCMC classification rule outperforms classical methods such as support vector machines, linear discriminant analysis, and 3-nearest neighbor classification rules in the case when sample size is small or the number of selected proteins used to classify is large.
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