Locally adaptive Bayesian isotonic regression using half shrinkage priors
提出一种新的贝叶斯方法，利用全局-局部收缩先验估计单调函数值，能自适应局部突变，并通过Gibbs抽样实现快速后验分析。
Abstract Isotonic regression or monotone function estimation is a problem of estimating function values under monotonicity constraints, which appears naturally in many scientific fields. This paper proposes a new Bayesian method with global–local shrinkage priors for estimating monotone function values. Specifically, we introduce half shrinkage priors for positive valued random variables and assign them for the first‐order differences of function values. We also develop fast and simple Gibbs sampling algorithms for full posterior analysis. By incorporating advanced shrinkage priors, the proposed method is adaptive to local abrupt changes or jumps in target functions. We show this adaptive property theoretically by proving that the posterior mean estimators are robust to large differences and that asymptotic risk for unchanged points can be improved. Finally, we demonstrate the proposed methods through simulations and applications to a real data set.