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Calibrated Bayes Factors in Assessing Genetic Association Models

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  • J. G. Liao
  • Duanping Liao
  • Arthur Berg

Abstract

Three competing genetic models—additive, dominant, and recessive—are often considered in genetic association analysis. We propose and develop a calibrated Bayes approach for comparing these competing models that has the desired property of giving equal support to the three models when no genetic association is present. The naïve approach with noncalibrated priors is shown to produce misleading Bayes factors. The method is fully developed with simulation studies, real data analyses, and an efficient algorithm based on an asymptotic approximation. An illuminating connection to the Kullback–Leibler divergence is also established. The proposed calibrated prior can serve as a reference prior for a genetic association study or as a common baseline prior for comparing Bayes analyses of different datasets.

Suggested Citation

  • J. G. Liao & Duanping Liao & Arthur Berg, 2016. "Calibrated Bayes Factors in Assessing Genetic Association Models," The American Statistician, Taylor & Francis Journals, vol. 70(3), pages 250-256, July.
    • Handle: RePEc:taf:amstat:v:70:y:2016:i:3:p:250-256
    DOI: 10.1080/00031305.2015.1109548
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    References listed on IDEAS

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    1. Little, Roderick J., 2006. "Calibrated Bayes: A Bayes/Frequentist Roadmap," The American Statistician, American Statistical Association, vol. 60, pages 213-223, August.
    2. J. G. Liao, 1999. "A Hierarchical Bayesian Model for Combining Multiple 2 × 2 Tables Using Conditional Likelihoods," Biometrics, The International Biometric Society, vol. 55(1), pages 268-272, March.
    3. Sinharay S. & Stern H.S., 2002. "On the Sensitivity of Bayes Factors to the Prior Distributions," The American Statistician, American Statistical Association, vol. 56, pages 196-201, August.
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