Robust sparse Bayesian infinite factor models

Most of previous works and applications Bayesian factor model have assumed the normal likelihood regardless its validity. We propose a for heavy-tailed high-dimensional data based on multivariate Student-t to obtain better covariance estimation. use multiplicative gamma process shrinkage prior number adaptation scheme proposed in Bhattacharya Dunson [Biometrika 98(2):291–306, 2011]. Since naive Gibbs sampler suffers from slow mixing, we Markov Chain Monte Carlo algorithm where fast mixing Hamiltonian is exploited some parameters model. Simulation results illustrate gain performance estimation data. also provide theoretical result that posterior weakly consistent under reasonable conditions. conclude paper with application breast cancer metastasis prediction given DNA signature cells.