  As a principled dimension reduction technique, factor models have been widely
adopted in social science, economics, bioinformatics, and many other fields.
However, in high-dimensional settings, conducting a 'correct' Bayesianfactor
analysis can be subtle since it requires both a careful prescription of the
prior distribution and a suitable computational strategy. In particular, we
analyze the issues related to the attempt of being "noninformative" for
elements of the factor loading matrix, especially for sparse Bayesian factor
models in high dimensions, and propose solutions to them. We show here why
adopting the orthogonal factor assumption is appropriate and can result in a
consistent posterior inference of the loading matrix conditional on the true
idiosyncratic variance and the allocation of nonzero elements in the true
loading matrix. We also provide an efficient Gibbs sampler to conduct the full
posterior inference based on the prior setup from Rockova and George (2016)and
a uniform orthogonal factor assumption on the factor matrix.
