Monotone response surface of multi-factor condition: estimation and Bayes classifiers

• 成果类型: Article
• 署名作者: Cheung, Ying Kuen; Diaz, Keith M.
• 署名单位: Columbia University; Columbia University
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1093/jrsssb/qkad014
• 发表日期: 2023
• 页码: 497-522
• 关键词: models

摘要

We formulate the estimation of monotone response surface of multiple factors as the inverse of an iteration of partially ordered classifier ensembles. Each ensemble (called product-of-independent-probability-escalation (PIPE)-classifiers) is a projection of Bayes classifiers on the constrained space. We prove that the inverse of PIPE-classifiers (iPIPE) exists, and propose algorithms to efficiently compute iPIPE by reducing the space over which optimisation is conducted. The methods are applied in analysis and simulation settings where the surface dimension is higher than what the isotonic regression literature typically considers. Simulation shows that iPIPE-based credible intervals achieve nominal coverage probability and are more precise compared to unconstrained estimation.