This thesis has been prepared at the CEA Léti, Minatec Campus, (Grenoble, France) and the IMS (Bordeaux, France) in the field of information and signal processing of proteomic data. The aim is to reconstruct the proteomic profile from the data provided by complex analytical workflow combining a spectrometer and a chromatograph. The signals are measurements of peptide traces which have low amplitude within a complex and noisy background. Therefore, adapted statistical signal processing methods are required. The uncertainty can be of technical nature (instruments, measurements) or of biological nature (individuals, "patients"). A hierarchical model, describing the forward problem of data acquisition, allows the explicit inclusion of those sources of variability within the probabilistic model. The use of the inverse problem methodology, finally, leads us to the estimation of the parameters of interest. In this thesis, we have studied three types of inverse problems for the following applications: 1) quantification of targeted proteins, seen as estimation of the protein concentration, 2) supervised training from a labelled cohort, seen as estimation of distribution parameters for each class, 3) classification given the knowledge about the classes, seen as estimation of the class a biological sample belongs to. We solve these inverse problems within a Bayesian framework, resorting to stochastic sampling methods (Monte Carlo Markov Chain) for computation.
