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

On Posterior Consistency of Bayesian Factor Models in High Dimensions