  One of the most popular methodologies for estimating the average treatment
effect at the threshold in a regression discontinuity design is local linear
regression (LLR), which places larger weight on units closer to the threshold.
We propose a Gaussian process regression methodology that acts as a Bayesian
analog to LLR for regression discontinuity designs. Our methodology provides a
flexible fit for treatment and control responses by placing a general prior on
the mean response functions. Furthermore, unlike LLR, our methodology can
incorporate uncertainty in how units are weighted when estimating the treatment
effect. We prove our method is consistent in estimating the average treatment
effect at the threshold. Furthermore, we find via simulation that our method
exhibits promising coverage, interval length, and mean squared error properties
compared to standard LLR and state-of-the-art LLR methodologies. Finally, we
explore the performance of our method on a real-world example by studying the
impact of being a first-round draft pick on the performance and playing time of
basketball players in the National Basketball Association.
