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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
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    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.

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    File URL: http://hdl.handle.net/10.1080/01621459.2012.712414
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    Article provided by Taylor & Francis Journals in its journal Journal of the American Statistical Association.

    Volume (Year): 107 (2012)
    Issue (Month): 500 (December)
    Pages: 1395-1409

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    Handle: RePEc:taf:jnlasa:v:107:y:2012:i:500:p:1395-1409
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