Sankhya: The Indian Journal of Statistics

2007, Volume 69, Pt. 3, 514--547

Gene Expression-Based Glioma Classification Using Hierarchical Bayesian Vector Machines

Sounak Chakraborty, University of Missouri, Columbia, USA
Bani K. Mallick, Texas A & M University, College Station, USA
Debashis Ghosh, University of Michigan, Ann Arbor, USA
Malay Ghosh, University of Florida, Gainesville, USA
Edward Dougherty Texas A & M University, College Station, USA

SUMMARY. This paper considers several Bayesian classification methods for the analysis of the glioma cancer with microarray data based on reproducing kernel Hilbert space under the multiclass setup. We consider the multinomial logit likelihood as well as the likelihood related to the multiclass Support Vector Machine (SVM) model. It is shown that our proposed Bayesian classification models with multiple shrinkage parameters can produce more accurate classification scheme for the glioma cancer compared to several existing classical methods. We have also proposed a Bayesian variable selection scheme for selecting the differentially expressed genes integrated with our model. This integrated approach improves classifier design by yielding simultaneous gene selection.

AMS (2000) subject classification. Primary 62G08, 62H30, 68T05, 68T10.

Key words and phrases. Gibbs sampling, Markov chain Monte Carlo, Metropolis- Hastings algorithm, microarrays, reproducing kernel Hilbert space, shrinkage parameters, support vector machines.

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