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An efficient stochastic search for Bayesian variable selection with high-dimensional correlated predictors

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Listed:
  • Kwon, Deukwoo
  • Landi, Maria Teresa
  • Vannucci, Marina
  • Issaq, Haleem J.
  • Prieto, DaRue
  • Pfeiffer, Ruth M.

Abstract

We present a Bayesian variable selection method for the setting in which the number of independent variables or predictors in a particular dataset is much larger than the available sample size. While most of the existing methods allow some degree of correlations among predictors but do not consider these correlations for variable selection, our method accounts for correlations among the predictors in variable selection. Our correlation-based stochastic search (CBS) method, the hybrid-CBS algorithm, extends a popular search algorithm for high-dimensional data, the stochastic search variable selection (SSVS) method. Similar to SSVS, we search the space of all possible models using variable addition, deletion or swap moves. However, our moves through the model space are designed to accommodate correlations among the variables. We describe our approach for continuous, binary, ordinal, and count outcome data. The impact of choices of prior distributions and hyperparameters is assessed in simulation studies. We also examined the performance of variable selection and prediction as the correlation structure of the predictors varies. We found that the hybrid-CBS resulted in lower prediction errors and identified better the true outcome associated predictors than SSVS when predictors were moderately to highly correlated. We illustrate the method on data from a proteomic profiling study of melanoma, a type of skin cancer.

Suggested Citation

  • Kwon, Deukwoo & Landi, Maria Teresa & Vannucci, Marina & Issaq, Haleem J. & Prieto, DaRue & Pfeiffer, Ruth M., 2011. "An efficient stochastic search for Bayesian variable selection with high-dimensional correlated predictors," Computational Statistics & Data Analysis, Elsevier, vol. 55(10), pages 2807-2818, October.
  • Handle: RePEc:eee:csdana:v:55:y:2011:i:10:p:2807-2818
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    References listed on IDEAS

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    2. Hans, Chris & Dobra, Adrian & West, Mike, 2007. "Shotgun Stochastic Search for," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 507-516, June.
    3. P. J. Brown & M. Vannucci & T. Fearn, 1998. "Multivariate Bayesian variable selection and prediction," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 60(3), pages 627-641.
    4. Liang, Feng & Paulo, Rui & Molina, German & Clyde, Merlise A. & Berger, Jim O., 2008. "Mixtures of g Priors for Bayesian Variable Selection," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 410-423, March.
    5. Casella, George & Moreno, Elias, 2006. "Objective Bayesian Variable Selection," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 157-167, March.
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    Cited by:

    1. Baragatti, M. & Pommeret, D., 2012. "A study of variable selection using g-prior distribution with ridge parameter," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1920-1934.

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