Hierarchical Modelling in Bayesian Factor Analysis

Bayesian factor models are a popular tool for factor analysis. Current state-of-the-art Bayesian factor analysis approaches leverage the beta-Bernoulli process prior to characterise the factors and do not require prior knowledge about the factor dimensionality. This prior, however, ignores the potential hierarchical structure within the factor values, a key aspect for a principled interpretation of the analysis. In this presentation, we introduce a new framework based on a new class of nonparametric priors termed beta-NRMI processes that overcome this limitation. This class of priors allows the development of an innovative hierarchical modelling methodology for Bayesian factor analysis. We present numerical implementations based on simulated and real-world datasets to illustrate the usefulness of our hierarchical modelling methodology.