The assimilation of cloudy and rainy microwave observations is under investigation at Météo-France with a method called “1D-Bay+3D/4D-Var”. This method comprises two steps: (i) a Bayesian inversion of microwave observations and (ii) the assimilation of the retrieved relative humidity profiles in a 3D/4D-Var framework. In this paper, two estimators for the Bayesian inversion are used: either a weighted average (WA) or the maximum likelihood (ML) of a kernel density function. Sensitivity studies over the first step of the method are conducted for different degrees of freedom: the observation error, the channel selection and the scattering properties of frozen hydrometeors in the observation operator. Observations over a 2 month period of the Global Precipitation Measurement (GPM) Microwave Imager (GMI) onboard the Global Precipitation Measurement Core Observatory satellite and forecasts of the convective scale model Application of Research to Operations at Mesoscale (AROME) have been chosen to conduct these studies. Two different meteorological situations are analyzed: those predicted cloudy in AROME but clear in the observations and, those predicted clear in AROME but cloudy in the observations. The main conclusions are as follows: First, low observational errors tend to be associated with the profiles with the highest consistency with the observations. Second, the validity of the retrieved profiles varies vertically with the set of channels used. Third, the radiative properties used in the radiative transfer simulations have a strong influence on the retrieved atmospheric profiles. Finally, the ML estimator has the advantage of being independent of the observation error but is less constrained than the WA estimator when few frequencies are considered. Although the presented sensitivities have been conducted to incorporate the scheme in a data assimilation system, the results may be generalized for geophysical retrieval purposes.