2020/04/30 by Panagiotis Papastamoulis, Ioannis Ntzoufras
Computer Science · Mathematics · #Algorithm #Applied mathematics #Artificial intelligence #Bayesian Methods and Mixture Models #Bayesian inference #Bayesian probability #Blind Source Separation Techniques #Computer science #Identifiability #Markov chain Monte Carlo #Mathematics #Posterior probability #Statistical Methods and Bayesian Inference #Statistics #stat.CO #stat.ME
paper · pdf · doi:10.1007/s11222-022-10084-4
published as Statistics and Computing 32, Article number: 23 (2022) · to appear in STCO
arxiv created 2022/01/24 · openalex publication_date 2022/02/27 · arxiv updated 2022/03/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
A well known identifiability issue in factor analytic models is the invariance with respect to orthogonal transformations. This problem burdens the inference under a Bayesian setup, where Markov chain Monte Carlo (MCMC) methods are used to generate samples from the posterior distribution. We introduce a post-processing scheme in order to deal with rotation, sign and permutation invariance of the MCMC sample. The exact version of the contributed algorithm requires to solve 2q assignment problems per (retained) MCMC iteration, where q denotes the number of factors of the fitted model. For large numbers of factors two approximate schemes based on simulated annealing are also discussed. We demonstrate that the proposed method leads to interpretable posterior distributions using synthetic and publicly available data from typical factor analytic models as well as mixtures of factor analyzers. An R package is available online at CRAN web-page.