  A wide class of Bayesian models involve unidentifiable random matrices that
display rotational ambiguity, with the Gaussian factor model being a typical
example. A rich variety of Markov chain Monte Carlo (MCMC) algorithms have been
proposed for sampling the parameters of these models. However, without
identifiability constraints, reliable posterior summaries of the parameters
cannot be obtained directly from the MCMC output. As an alternative, we propose
a computationally efficient post-processing algorithm that allows inference on
non-identifiable parameters. We first orthogonalize the posterior samples using
Varimax and then tackle label and sign switching with a greedy matching
algorithm. We compare the performance and computational complexity with other
methods using a simulation study and chemical exposures data. The algorithm
implementation is available in the infinitefactor R package on CRAN.
