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

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

Journal of the American Statistical Association, 2012, vol. 107, issue 500, 1395-1409

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.

Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:taf:jnlasa:v:107:y:2012:i:500:p:1395-1409

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DOI: 10.1080/01621459.2012.712414

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