Monitoring changes of precipitation phase from space is important for understanding the mass balance of Earth's cryosphere in a changing climate. This paper examines a Bayesian nearest neighbor approach for prognostic detection of precipitation and its phase using passive microwave observations from the Global Precipitation Measurement (GPM) satellite. The method uses the weighted Euclidean distance metric to search through an a priori database populated with coincident GPM radiometer and radar observations as well as ancillary snow-cover data. The algorithm performance is evaluated using data from GPM official precipitation products, ground-based radars, and high-fidelity simulations from the Weather Research and Forecasting Model. Using the presented approach, we demonstrate that the hit probability of terrestrial precipitation detection can reach to 0.80, while the probability of false alarm remains below 0.11. The algorithm demonstrates higher skill in detecting snowfall than rainfall, on average by 10%. In particular, the probability of precipitation detection and its solid phase increases by 11% and 8%, over dry snow cover, when compared to other surface types. The main reason is found to be related to the ability of the algorithm in capturing the signal of increased liquid water content in snowy clouds over radiometrically cold snow-covered surfaces.