With the arrival of gene expression microarrays a new challenge has opened up for
identification or classification of cancer tissues. Due to the large number of genes providing
valuable information simultaneously compared to very few available tissue samples the
cancer staging or classification becomes very tricky.
In this paper we introduce a hierarchical Bayesian probit model for two class cancer
classification. Instead of assuming a linear structure for the function that relates the gene
expressions with the cancer types we only assume that the relationship is explained by
an unknown function which belongs to an abstract functional space like the reproducing
kernel Hilbert space. Our formulation automatically reduces the dimension of the problem
from the large number of covariates or genes to a small sample size. We incorporate a
Bayesian gene selection scheme with the automatic dimension reduction to adaptively
select important genes and classify cancer types under an unified model. Our model is
highly flexible in terms of explaining the relationship between the cancer types and gene
expression measurements and picking up the differentially expressed genes. The proposed
model is successfully tested on three simulated data sets and three publicly available
leukemia cancer, colon cancer, and prostate cancer real life data sets.