Computational Challenges to Bayesian Density Discontinuity Regression

Many policies subject an underlying continuous variable to an artificial cutoff. Agents may regulate the magnitude of the variable to stay on the preferred side of a known cutoff, which results in the form of a jump discontinuity of the distribution of the variable at the cutoff value. In this paper, we present a statistical method to estimate the presence and magnitude of such jump discontinuities as functions of measured covariates.

For the posterior computation of our model, we use a Gibbs sampling scheme as the overall structure. For each iteration, we have two layers of data augmentation. We first adopt the rejection history strategy to remove the intractable integral and then generate Pólya-Gamma latent variables to ease the computation. We implement algorithms including adaptive Metropolis, ensemble MCMC, and independent Metropolis for each parameter within the Gibbs sampler. We justify our method based on the simulation study.

As for the real data, we focus on a study of corporate proposal voting, where we encounter several computational challenges. We discuss the multimodality issue from two aspects. In an effort to solve this problem, we borrow the idea from parallel tempering. We build an adaptive parallel tempered version of our sampler. The result shows that introducing the tempering method indeed improves the performance of our original sampler.