Locally adaptive Bayesian isotonic regression using half shrinkage priors

Ryo Okano, Yasuyuki Hamura, Kaoru Irie, Shonosuke Sugasawa

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
Pages (from-to)109-141
Number of pages33
JournalScandinavian Journal of Statistics
Volume51
Issue number1
DOIs
Publication statusPublished - 2024 Mar

Keywords

  • horseshoe prior
  • isotonic regression
  • monotone curve estimation
  • tail robustness

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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