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

Deukwoo Kwon, Maria Teresa Landi, Marina Vannucci, Haleem J. Issaq, Darue Prieto, Ruth M. Pfeiffer

Research output: Contribution to journalArticlepeer-review

14 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)2807-2818
Number of pages12
JournalComputational Statistics and Data Analysis
Volume55
Issue number10
DOIs
StatePublished - Oct 1 2011
Externally publishedYes

Keywords

  • Correlated predictors
  • Correlation-based search
  • Proteomic data

ASJC Scopus subject areas

  • Statistics and Probability
  • Computational Mathematics
  • Computational Theory and Mathematics
  • Applied Mathematics

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