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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.
This paper investigates the high-dimensional linear regression with highly correlated covariates. In this setup, the traditional sparsity assumption on the regression coefficients often fails to hold, and consequently many model selection procedures
We propose a novel approach to estimating the precision matrix of multivariate Gaussian data that relies on decomposing them into a low-rank and a diagonal component. Such decompositions are very popular for modeling large covariance matrices as they
We propose a new, flexible model for inference of the effect of a binary treatment on a continuous outcome observed over subsequent time periods. The model allows to seperate association due to endogeneity of treatment selection from additional longi
Its conceptual appeal and effectiveness has made latent factor modeling an indispensable tool for multivariate analysis. Despite its popularity across many fields, there are outstanding methodological challenges that have hampered practical deploymen
Factor models are a class of powerful statistical models that have been widely used to deal with dependent measurements that arise frequently from various applications from genomics and neuroscience to economics and finance. As data are collected at