  Most of previous works and applications of Bayesian factor model have assumed
the normal likelihood regardless of its validity. We propose a Bayesian factor
model for heavy-tailed high-dimensional data based on multivariate Student-$t$
likelihood to obtain better covariance estimation. We use multiplicative gamma
process shrinkage prior and factor number adaptation scheme proposed in
Bhattacharya & Dunson [Biometrika (2011) 291-306]. Since a naive Gibbs sampler
for the proposed model suffers from slow mixing, we propose a Markov Chain
Monte Carlo algorithm where fast mixing of Hamiltonian Monte Carlo is exploited
for some parameters in proposed model. Simulation results illustrate the gain
in performance of covariance estimation for heavy-tailed high-dimensional data.
We also provide a theoretical result that the posterior of the proposed model
is weakly consistent under reasonable conditions. We conclude the paper with
the application of proposed factor model on breast cancer metastasis prediction
given DNA signature data of cancer cell.
