Bayesian Boundary Trend Filtering

Estimating support boundary curves have many applications such as economics, climate science, and medicine. In this paper, we develop a Bayesian trend filtering for estimating boundary trend. To this end, we introduce the truncated multivariate normal working likelihood and shrinkage priors based on scale mixtures of normal distribution. In particular, well-known horseshoe prior for difference leads to locally adaptive shrinkage estimation for boundary trend. However, the full conditional distributions of the Gibbs sampler involve high-dimensional truncated multivariate normal distribution. To overcome the difficulty of sampling, we employ an approximation of truncated multivariate normal distribution. Using the approximation, we propose an efficient Gibbs sampling algorithm via Polya-Gamma data augmentation. We also extend the proposed method by considering nearly isotonic constraint. The performance of the proposed method is illustrated through some numerical experiments and real data examples.