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A physically oriented inversion algorithm to retrieve precipitation from satellite-based passive microwave measurements named the Bayesian algorithm for microwave-based precipitation retrieval (BAMPR) is proposed. First, we illustrate the procedure that BAMPR follows to produce precipitation estimates from observed multichannel brightness temperatures. Retrieval products are the surface rain rates, columnar equivalent water contents, and hydrometeor content profiles, together with the associated estimation uncertainties. Numerical tests performed on simulated measurements show that retrieval errors are reduced when a rain type and pattern classification procedure is employed, and that estimates are quite sensitive to the adopted error model. Finally, for different tropical storms that were observed by the Tropical Rainfall Measuring Mission (TRMM) Microwave Imager (TMI), we compare the rain retrieved from BAMPR relative to those retrieved from the Goddard Profiling (Gprof) algorithm and the Precipitation Radar-adjusted TMI estimation of rainfall (PATER) algorithm. Despite a similar inversion approach, the algorithms exhibit different performances that can be mainly related to different training databases and retrieval constraints such as cloud classification.