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 journalArticle

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

Fingerprint

Linear Inequalities
Linear Constraints
Hormones
Inequality Constraints
Oxidative Stress
Cycle
Progesterone
Estrogen
Linear Mixed Model
Cohort Study
Bayesian Analysis
Parameter Space
Model
Decompose
Inequality constraints
Framework
Class

Keywords

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

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Cite this

Minkowski-Weyl priors for models with parameter constraints : An analysis of the BioCycle study. / Danaher, Michelle R.; Roy, Anindya; Chen, Zhen; Mumford, Sunni L.; Schisterman, Enrique F.

In: Journal of the American Statistical Association, Vol. 107, No. 500, 2012, p. 1395-1409.

Research output: Contribution to journalArticle

Danaher, Michelle R. ; Roy, Anindya ; Chen, Zhen ; Mumford, Sunni L. ; Schisterman, Enrique F. / Minkowski-Weyl priors for models with parameter constraints : An analysis of the BioCycle study. In: Journal of the American Statistical Association. 2012 ; Vol. 107, No. 500. pp. 1395-1409.
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