We develop a nonparametric Bayesian analysis of regression discontinuity (RD) designs, allowing for covariates, in which we model and estimate the unknown functions of the forcing variable by basis expansion methods. In a departure from current methods, we use the entire data on the forcing variable, but we emphasize the data near the threshold by placing some knots at and near the threshold, a technique we refer to as soft-windowing. To handle the nonequally spaced knots that emerge from soft-windowing, we construct a prior on the spline coefficients, from a second-order Ornstein–Uhlenbeck process, which is hyperparameter light, and satisfies the Kullback–Leibler support property. In the fuzzy RD design, we explain the divergence between the treatment implied by the forcing variable, and the actual intake, by a discrete confounder variable, taking three values, complier, never-taker, and always-taker, and a model with four potential outcomes. Choice of the soft-window, and the number of knots, is determined by marginal likelihoods, computed by the method of Chib [Journal of the American Statistical Association, 1995, 90, 1313–1321] as a by-product of the Markov chain Monte Carlo (MCMC)-based estimation. Importantly, in each case, we allow for covariates, incorporated nonparametrically by additive natural cubic splines. The potential outcome error distributions are modeled as student-t, with an extension to Dirichlet process mixtures. We derive the large sample posterior consistency, and posterior contraction rate, of the RD average treatment effect (ATE) (in the sharp case) and RD ATE for compliers (in the fuzzy case), as the number of basis parameters increases with sample size. The excellent performance of the methods is documented in simulation experiments, and in an application to educational attainment of women from Meyersson [Econometrica, 2014, 82, 229–269].

我们开发了回归不连续性 (RD) 设计的非参数贝叶斯分析，允许协变量，其中我们通过基础扩展方法对强制变量的未知函数进行建模和估计。与当前方法不同的是，我们使用强制变量上的全部数据，但我们通过在阈值处和附近放置一些结来强调阈值附近的数据，我们将这种技术称为软窗口。为了处理从软窗口出现的非等间距结，我们从二阶 Ornstein-Uhlenbeck 过程构建样条系数的先验，该过程是超参数光，并满足 Kullback-Leibler 支持属性。在模糊 RD 设计中，我们通过离散混杂变量解释了强制变量隐含的治疗与实际摄入量之间的差异，采用三种价值观，顺从者、永不接受者和永远接受者，以及一个具有四种潜在结果的模型。软窗口的选择和结的数量由边际似然决定，边际似然由 Chib [Journal of the American Statistical Association , 1995, 90, 1313–1321] 作为基于马尔可夫链蒙特卡罗 (MCMC) 估计的副产品。重要的是，在每种情况下，我们都允许协变量，通过加性自然三次样条非参数地合并。潜在的结果误差分布被建模为学生t，并扩展到 Dirichlet 过程混合。随着基本参数的数量随着样本量的增加而增加，我们推导出 RD 平均治疗效果 (ATE)（在尖锐情况下）和编译器的 RD ATE（在模糊情况下）的大样本后验一致性和后验收缩率. 这些方法的出色性能在模拟实验中得到了证明，并且在 Meyersson 对女性教育程度的应用中得到了证明 [计量经济学, 2014, 82, 229–269]。