Abstract
We would like to congratulate the authors on their valuable contribution to the Bayesian factor analysis framework. The paper combines different ideas, simultaneously addressing identifiability issues and performing estimation and inference on the number of factors r. Moreover, the proposed approach builds nicely on the sparse Bayesian factor analysis literature, with a clever elicitation of suitable shrinkage priors paired with a tailored MCMC estimation procedure. We wish to raise a few discussion points and hear the authors perspectives on them.