  The problem of selecting the most useful features from a great many (eg,
thousands) of candidates arises in many areas of modern sciences. An
interesting problem from genomic research is that, from thousands of genes that
are active (expressed) in certain tissue cells, we want to find the genes that
can be used to separate tissues of different classes (eg. cancer and normal).
In this paper, we report our empirical experiences of using Bayesian logistic
regression based on heavy-tailed priors with moderately small degree freedom
(such as 1) and very small scale, and using Hamiltonian Monte Carlo to do
computation. We discuss the advantages and limitations of this method, and
illustrate the difficulties that remain unsolved. The method is applied to a
real microarray data set related to prostate cancer. The method identifies only
3 non-redundant genes out of 6033 candidates but achieves better leave-one-out
cross-validated prediction accuracy than many other methods.
