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In this paper, a Bayesian statistical approach for supervised classification and estimation of hydrometeors, using a C-band polarimetric radar, is presented and discussed. The Bayesian Radar Algorithm for Hydrometeor Classification at C-band (BRAHCC) is supervised by a backscattering microphysical model, aimed at representing ten different hydrometeor classes in water, ice, and mixed phase. The expected error budget is evaluated by means of contingency tables on the basis of C-band radar noisy and attenuated synthetic data. Its accuracy is better than that obtained from a previously developed fuzzy logic C-band classification algorithm. As a second step of the overall retrieval algorithm, a multivariate regression is adopted to derive water content statistical estimators, exploiting simulated polarimetric radar data for each hydrometeor class. The BRAHCC methodology is then applied to a convective hail event, observed by two C-band dual-polarized radars in a network configuration. The hydrometeor classification along the line of sight, connecting the two C-band radars, is performed using the BRAHCC applied to path-attenuation-corrected data. Qualitative results are consistent with those derived from the fuzzy logic algorithm. Hydrometeor water content temporal evolution is tracked along the radar line of sight. Hail vertical occurrence is derived and compared with an empirical hail detection index applied along the radar connection line during the whole event.