Joint Bayesian hierarchical inversion-classification and application in proteomics

In this paper, we combine inverse problem and classification for LC-MS data in a joint Bayesian context, given a set of biomarkers and the statistical characteristics of the biological classes. The data acquisition is modelled in a hierarchical way, including random decomposition of proteins into peptides and peptides into ions associated to peaks on the LC-MS measurement. A Bayesian global inversion, based on the hierarchical model for the direct problem, enables to take into account the biological and technological variabilities from those random processes and to estimate the parameters efficiently. We describe the statistical theoretical framework including the hierarchical direct model, the prior and posterior distributions and the estimators for the involved parameters. We resort to the MCMC algorithm and give preliminary results on a simulated data set.