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

• Published in: Journal of the Royal Statistical Society. Series B, Statistical methodology Vol. 85; no. 2; pp. 497 - 522
• Main Authors: Cheung, Ying Kuen, Diaz, Keith M
• Format: Journal Article
• Language: English
• Published: England Oxford University Press 01.04.2023
• Subjects: Pipes; Probability; Response surface methodology; Simulation; Statistical analysis; Statistical methods; Clinical decision support tool; partial ordering; weighted posterior gain; sweep algorithm; posterior quantiles
• ISSN: 1369-7412; 1467-9868; 1467-9868
• DOI: 10.1093/jrsssb/qkad014

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.