Bayesian Density Regression With a Jump Discontinuity at a Given Threshold

Standard regression discontinuity design usually concentrates on the causal effects by assigning a threshold above or below which an intervention is assigned. By com- paring the real values of observations near the threshold, it is plausible to design some structures of discontinuity to capture the discontinuity information. Instead of looking at the observations, this paper develops a Bayesian density regression model whose parameters are related to covariates to achieve regression discontinuity design. The methodology is applied to simulated data first and then analyzing out- comes of yes/no votes to a large number of company proposals. During the process of Bayesian inference, we have adopted adaptive MCMC, importance sampling and Metropolis-adjusted Langevin algorithm to implement statistical inference. They to some extend make some sense in estimating the parameters and explain how the covariates affect the discontinuity magnitude.