Bayesian Infinite Factor Models with Non-Gaussian Factors

• Activity Number: 23 - Bayesian Methods and Approaches in Big Data Analysis
• Type: Topic-Contributed
• Date/Time: Sunday, August 8, 2021 : 1:30 PM to 3:20 PM
• Sponsor: International Society for Bayesian Analysis (ISBA)
• Author(s): Margarita Grushanina* and Sylvia Frühwirth-Schnatter
• Companies: Vienna University of Economics and Business and Vienna University of Economics and Business
• Keywords: factor analysis; multiplicative gamma process; adaptive Gibbs sampling; spike-and-slab prior; Laplace prior; non-Gaussian factors

Abstract

Bayesian factor models represent a very popular tool in the analysis of high-dimensional datasets. The cumbersome task of determining the number of factors has in recent years been addressed in literature by employing nonparametric models for the automatic inference on the number of factors. However, factors are usually assumed to be normally distributed. In reality, this assumption may prove to be too restrictive. Here, the factor model with automatic inference on the number of factors is extended to the non-Gaussian case. We relax the assumption of normality by employing a Laplace prior on factors. Two types of shrinkage priors are considered: the multiplicative gamma process prior and the cumulative shrinkage process, based on a sequence of spike-and-slab-distributions. An estimator of the covariance matrix, used to bound the prior on the idiosyncratic variances away from zero, is adapted to the non-Gaussian case. The models are tested both on simulated data sets as well as on a Eurozone countries’ inflation rates data set.