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Minkowski--Weyl Priors for Models With Parameter Constraints: An Analysis of the BioCycle Study

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

Abstract

We propose a general framework for performing full Bayesian analysis under linear inequality parameter constraints. The proposal is motivated by the BioCycle 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 BioCycle data using such a prior. We observe positive associations between estrogen and progesterone levels and F 2 -isoprostanes, a marker for oxidative stress. These findings are of particular interest to reproductive epidemiologists.

Suggested Citation

  • Michelle R. Danaher & Anindya Roy & Zhen Chen & Sunni L. Mumford & Enrique F. Schisterman, 2012. "Minkowski--Weyl Priors for Models With Parameter Constraints: An Analysis of the BioCycle Study," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(500), pages 1395-1409, December.
    • Handle: RePEc:taf:jnlasa:v:107:y:2012:i:500:p:1395-1409
    DOI: 10.1080/01621459.2012.712414
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    References listed on IDEAS

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    1. Zhen Chen & David B. Dunson, 2003. "Random Effects Selection in Linear Mixed Models," Biometrics, The International Biometric Society, vol. 59(4), pages 762-769, December.
    2. Geweke, John, 1986. "Exact Inference in the Inequality Constrained Normal Linear Regression Model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 1(2), pages 127-141, April.
    3. Hoffmann, K., 1993. "Generalized Bayes Stein-Type Estimators for Regression Parameters under Linear Constraints," Journal of Multivariate Analysis, Elsevier, vol. 46(1), pages 120-130, July.
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