Locally Adaptive Bayesian Isotonic Regression using Half Shrinkage Priors

TL;DR

This paper introduces a Bayesian isotonic regression method using half shrinkage priors that adaptively handle local jumps in monotone functions, with efficient algorithms and theoretical guarantees.

Contribution

It proposes a novel Bayesian approach with half shrinkage priors for monotone function estimation, enhancing adaptivity and robustness over existing methods.

Findings

Method effectively detects local jumps in functions.

Theoretical proof of robustness to large differences.

Demonstrated superior performance in simulations and real data.

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.