Minkowski-Weyl priors for models with parameter constraints: An analysis of the BioCycle study

Michelle R. Danaher, Anindya Roy, Zhen Chen, Sunni L. Mumford, Enrique F. Schisterman

Research output: Contribution to journalArticlepeer-review

Abstract

We propose a general framework for performing full Bayesian analysis under linear inequality parameter constraints. The proposal is motivated by the Bio Cycle Study, a large cohort study of hormone levels of healthy women where certain well-established linear inequality constraints on the log-hormone levels should be accounted for in the statistical inferential procedure. Based on the Minkowski-Weyl decomposition of polyhedral regions, we propose a class of priors that are fully supported on the parameter space with linear inequality constraints, and we fit a Bayesian linear mixed model to the Bio Cycle data using such a prior. We observe positive associations between estrogen and progesterone levels and F2-isoprostanes, a marker for oxidative stress. These findings are of particular interest to reproductive epidemiologists.

Original languageEnglish (US)
Pages (from-to)1395-1409
Number of pages15
JournalJournal of the American Statistical Association
Volume107
Issue number500
DOIs
StatePublished - 2012
Externally publishedYes

Keywords

  • Bayesian inference
  • Extreme directions
  • Extreme points
  • Parameter restriction
  • Polyhedral region

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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