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September 2022 On Posterior Consistency of Bayesian Factor Models in High Dimensions
Yucong Ma, Jun S. Liu
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Bayesian Anal. 17(3): 901-929 (September 2022). DOI: 10.1214/21-BA1281


As a principled dimension reduction technique, factor models have been widely adopted in applications. However, conducting a proper Bayesian factor analysis can be subtle in high-dimensional settings since it requires both a careful prescription of the prior distribution and a suitable computational strategy. We analyze issues of posterior inconsistency and sensitivity under different priors for high-dimensional sparse normal factor models, and show why adopting the n-orthonormal factor assumption can resolve these issues and lead to a more robust and efficient Bayesian analysis. We also provide an efficient Gibbs sampler to conduct the required computation, and show that it can be orders of magnitude more efficient than compared existing algorithms.

Funding Statement

This research is supported in part by the National Science Foundation of USA Grants DMS-1613035, DMS-1712714 and DMS-1903139.


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Yucong Ma. Jun S. Liu. "On Posterior Consistency of Bayesian Factor Models in High Dimensions." Bayesian Anal. 17 (3) 901 - 929, September 2022.


Published: September 2022
First available in Project Euclid: 28 July 2021

Digital Object Identifier: 10.1214/21-BA1281

Keywords: factor analysis , Gibbs sampling , high dimensional data , orthogonality , posterior consistency


Vol.17 • No. 3 • September 2022
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