A discussion of 'Sparse Bayesian factor analysis when the number of factors is unknown' by Sylvia Fruhwirth-Schnatter, Darjus Hosszejni and Hedibert Freitas Lopes

Conditional on knowing the number of factors, r, analysis in static and dynamic factor models is straightforward for the Bayesian. However, inference on r is challenging. A Bayesian could use marginal likelihoods to select the number of factors (see Geweke, 1996). But in the standard big data setups nowadays (which involve a large number of variables/measurements m), this is computationally cumbersome, requiring the estimation of a large set of models that vary in r
(≤ m).