Bayesian Regression Discontinuity Design
Also known as: Bayesian RDD, Bayesian RD, Bayes RDD, Bayesian regression-discontinuity
Bayesian Regression Discontinuity Design (Bayesian RDD) embeds the classical RD framework — which estimates a local causal effect at a known assignment cutoff — within a Bayesian inferential engine. Prior distributions are placed on the regression functions on either side of the cutoff and on the treatment-effect parameter, yielding a full posterior distribution over the causal estimand rather than a single point estimate with a frequentist p-value.
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When to use it
Use Bayesian RDD when a sharp or fuzzy cutoff rule assigns treatment and you want principled uncertainty quantification — especially with small samples near the cutoff, where frequentist large-sample approximations are unreliable, or when you have prior subject-matter knowledge to encode. It is also preferable when the functional form of the regression on each side is uncertain and you want to average over that uncertainty rather than commit to a single bandwidth or polynomial degree. Do not use it when no true cutoff assignment rule exists; when the running variable is manipulated by units (density tests for manipulation should precede any RDD); when sample size is very large and frequentist RDD already provides reliable estimates with negligible gain from Bayesian overhead; or when computational resources are severely limited.
Strengths & limitations
- Produces a full posterior distribution over the treatment effect, enabling direct probability statements about the effect size.
- Propagates uncertainty about the regression functional form and bandwidth into inference, avoiding over-confidence from arbitrary specification choices.
- Handles small local samples near the cutoff better than frequentist asymptotic methods by borrowing information from the prior.
- Naturally extends to fuzzy designs, non-normal outcomes, and hierarchical or multilevel RD settings within a unified model.
- Credible intervals have a straightforward probabilistic interpretation that frequentist confidence intervals lack.
- Results can be sensitive to prior choices, particularly for the regression function; poorly chosen priors may dominate a sparse local sample.
- Computationally intensive: MCMC or variational inference is required, and convergence must be monitored carefully.
- Requires the same identifying assumption as frequentist RDD — no manipulation of the running variable at the cutoff — and Bayesian inference does not rescue this if the assumption fails.
- Software and expertise demands are higher than for standard frequentist RDD packages.
Frequently asked
What advantage does a Bayesian RDD have over standard RDD?
The primary advantage is full uncertainty quantification. Standard RDD yields a point estimate and a frequentist confidence interval whose width depends on bandwidth choice and asymptotic approximations. Bayesian RDD produces a posterior distribution over the causal effect that (a) averages over functional-form uncertainty, (b) is calibrated in small samples via the prior, and (c) supports direct probability statements such as the posterior probability that the effect exceeds a policy-relevant threshold.
Does the Bayesian approach remove the need for a bandwidth?
Not entirely. Gaussian-process priors encode smoothness and effectively perform continuous regularization, reducing sensitivity to explicit bandwidth choice, but the prior hyperparameters (e.g., length-scale) play an analogous role. Parametric Bayesian RDDs still require a window decision. Sensitivity of conclusions to these choices should always be reported.
Can Bayesian RDD handle fuzzy discontinuities?
Yes. In a fuzzy design, treatment uptake is a probabilistic function of crossing the cutoff rather than deterministic. Chib and Jacobi (2016) model this as a Bayesian two-stage (IV-type) system, placing priors on both the first-stage compliance and the second-stage outcome equation, and estimating the local average treatment effect (LATE) jointly.
How do I check whether the running variable is manipulated in a Bayesian RDD?
Manipulation tests (e.g., McCrary density test or its Bayesian extensions) are conducted before estimation, exactly as in frequentist RDD. The Bayesian inference engine does not protect against sorting around the cutoff; if manipulation is detected the causal reading is invalid regardless of the estimation approach.
What software can run Bayesian RDD?
Stan (via RStan or PyStan) allows users to write custom Bayesian RD models with Gaussian-process or polynomial priors and estimate them with HMC. JAGS and BUGS support parametric Bayesian RDDs. As of 2024, no single dominant R or Python package automates Bayesian RDD end-to-end the way rdrobust does for frequentist RDD, so custom Stan or brms code is the practical standard.
Sources
- Karabatsos, G., & Walker, S. G. (2004). Coherent inference in regression discontinuity designs with a Bayesian nonparametric approach. Journal of the American Statistical Association, 99(468), 1121-1131. link ↗
- Chib, S., & Jacobi, L. (2016). Bayesian fuzzy regression discontinuity analysis and returns to compulsory schooling. Journal of Applied Econometrics, 31(6), 1026-1047. DOI: 10.1002/jae.2481 ↗
How to cite this page
ScholarGate. (2026, June 3). Bayesian Regression Discontinuity Design. ScholarGate. https://scholargate.app/en/causal-inference/bayesian-regression-discontinuity-design
Which method?
Set this method beside its closest kin and read them side by side — the library lays the books on the table; the choice is yours.
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