  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.
