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Bayesian Modeling of Footrace Finishing Times

Author

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  • Shotwell Matthew S

    (Medical University of South Carolina)

  • Slate Elizabeth H

    (Medical University of South Carolina)

Abstract

The 2007 Cooper River Bridge Run (CRBR) dataset has over 28,000 observations. The histogram of finishing times has a bimodal shape and varies in location and scale with the participants' gender and age. Four different mixture models are developed and assessed in terms of their ability to describe the features of this dataset. We discuss the "label switching" problem in the present context, review current solutions, and how they may be inadequate when covariates are present. The Bayes factor and the more modern deviance information criterion (DIC) are compared as devices for model selection. MCMC output is presented with plots of the model fits. We conclude with remarks on unanswered questions with regard to Bayesian mixture modeling, and the potential impact of this analysis for future Cooper River Bridge Runs. Raw data and BUGS programs corresponding to each model are available.

Suggested Citation

  • Shotwell Matthew S & Slate Elizabeth H, 2010. "Bayesian Modeling of Footrace Finishing Times," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 6(3), pages 1-21, July.
  • Handle: RePEc:bpj:jqsprt:v:6:y:2010:i:3:n:5
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    References listed on IDEAS

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    1. David J. Spiegelhalter & Nicola G. Best & Bradley P. Carlin & Angelika van der Linde, 2002. "Bayesian measures of model complexity and fit," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(4), pages 583-639.
    2. Matthew Stephens, 2000. "Dealing with label switching in mixture models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(4), pages 795-809.
    3. Francesco Bartolucci & Luisa Scaccia & Antonietta Mira, 2006. "Efficient Bayes factor estimation from the reversible jump output," Biometrika, Biometrika Trust, vol. 93(1), pages 41-52, March.
    4. Kim-Anh Do & Peter Müller & Feng Tang, 2005. "A Bayesian mixture model for differential gene expression," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 54(3), pages 627-644.
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