Robust sensing and perception in adverse weather conditions remain one of the biggest challenges for realizing reliable autonomous vehicle mobility services. Prior work has established that rainfall rate is a useful measure for the adversity of atmospheric weather conditions. This work presents a probabilistic hierarchical Bayesian model that infers rainfall rate from automotive lidar point cloud sequences with high accuracy and reliability. The model is a hierarchical mixture of experts model, or a probabilistic decision tree, with gating and expert nodes consisting of variational logistic and linear regression models. Experimental data used to train and evaluate the model is collected in a large-scale rainfall experiment facility from both stationary and moving vehicle platforms. The results show prediction accuracy comparable to the measurement resolution of a disdrometer, and the soundness and usefulness of the uncertainty estimation. The model achieves RMSE 2.42\,mm/h after filtering out uncertain predictions. The error is comparable to the mean rainfall rate change of 3.5\,mm/h between measurements. Model parameter studies show how predictive performance changes with tree depth, sampling duration, and crop box dimension. A second experiment demonstrates the predictability of higher rainfall above 300\,mm/h using a different lidar sensor, demonstrating sensor independence.