In modern clinical neuro-oncology, the diagnosis and classification of malignant gliomas remains problematic and effective therapies are still elusive. As patient prognosis and therapeutic decisions rely on accurate pathological grading or classification of tumor cells, extensive investigation is going on for accurately identifying the types of glioma cancer. Unfortunately, many malignant gliomas are diagnostically challenging; these non-classic lesions are difficult to classify by histological features, thereby resulting in considerable interobserver variability and limited diagnosis reproducibility. In recent years, there has been a move towards the use of cDNA microarrays for tumor classification. These high-throughput assays provide relative mRNA expression measurements simultaneously for thousands of genes. A key statistical task is to perform classification via different expression patterns. Gene expression profiles may offer more information than classical morphology and may provide a better alternative to the classical tumor diagnosis schemes. The classification becomes more difficult when there are more than two cancer types, as with glioma.

This talk 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 muliclass 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 the 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.