  Quasi-experimental research designs, such as regression discontinuity and
interrupted time series, allow for causal inference in the absence of a
randomized controlled trial, at the cost of additional assumptions. In this
paper, we provide a framework for discontinuity-based designs using Bayesian
model comparison and Gaussian process regression, which we refer to as
'Bayesian nonparametric discontinuity design', or BNDD for short. BNDD
addresses the two major shortcomings in most implementations of such designs:
overconfidence due to implicit conditioning on the alleged effect, and model
misspecification due to reliance on overly simplistic regression models. With
the appropriate Gaussian process covariance function, our approach can detect
discontinuities of any order, and in spectral features. We demonstrate the
usage of BNDD in simulations, and apply the framework to determine the effect
of running for political positions on longevity, of the effect of an alleged
historical phantom border in the Netherlands on Dutch voting behaviour, and of
Kundalini Yoga meditation on heart rate.
