We propose nonparametric Bayesian estimators for causal inference exploiting Regression Discontinuity/Kink (RD/RK) under sharp and fuzzy designs. Our estimators are based on Gaussian Process (GP) regression and classification. The GP methods are powerful probabilistic machine learning approaches that are advantageous in terms of derivative estimation and uncertainty quantification, facilitating RK estimation and inference of RD/RK models. These estimators are extended to hierarchical GP models with an intermediate Bayesian neural network layer and can be characterized as hybrid deep learning models. Monte Carlo simulations show that our estimators perform comparably to and sometimes better than competing estimators in terms of precision, coverage and interval length. The hierarchical GP models considerably improve upon one-layer GP models. We apply the proposed methods to estimate the incumbency advantage of US house elections. Our estimations suggest a significant incumbency advantage in terms of both vote share and probability of winning in the next elections. Lastly we present an extension to accommodate covariate adjustment.