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.

翻译：估计支持边界曲线在经济学、气候科学和医学等领域具有广泛应用。本文提出一种用于估计边界趋势的贝叶斯趋势滤波方法。为此，我们引入截断多元正态工作似然函数以及基于正态分布尺度混合的收缩先验。特别地，针对差分项采用著名的马蹄形先验，可实现边界趋势的局部自适应收缩估计。然而，吉布斯采样的全条件分布涉及高维截断多元正态分布。为克服采样困难，我们采用截断多元正态分布的近似方法。基于该近似，我们通过Polya-Gamma数据增广提出一种高效吉布斯采样算法。此外，我们通过考虑近单调约束扩展了所提方法。数值实验和实际数据示例验证了所提方法的有效性。