Dimension‐free mixing for high‐dimensional Bayesian variable selection

Quan Zhou, Jun Yang, Dootika Vats, Gareth O. Roberts and Jeffrey S. Rosenthal

Journal of the Royal Statistical Society Series B, 2022, vol. 84, issue 5, 1751-1784

Abstract: Yang et al. proved that the symmetric random walk Metropolis–Hastings algorithm for Bayesian variable selection is rapidly mixing under mild high‐dimensional assumptions. We propose a novel Markov chain Monte Carlo (MCMC) sampler using an informed proposal scheme, which we prove achieves a much faster mixing time that is independent of the number of covariates, under the assumptions of Yang et al. To the best of our knowledge, this is the first high‐dimensional result which rigorously shows that the mixing rate of informed MCMC methods can be fast enough to offset the computational cost of local posterior evaluation. Motivated by the theoretical analysis of our sampler, we further propose a new approach called ‘two‐stage drift condition’ to studying convergence rates of Markov chains on general state spaces, which can be useful for obtaining tight complexity bounds in high‐dimensional settings. The practical advantages of our algorithm are illustrated by both simulation studies and real data analysis.

Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
https://doi.org/10.1111/rssb.12546

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:bla:jorssb:v:84:y:2022:i:5:p:1751-1784

Ordering information: This journal article can be ordered from
http://ordering.onli ... 1111/(ISSN)1467-9868

Access Statistics for this article

Journal of the Royal Statistical Society Series B is currently edited by P. Fryzlewicz and I. Van Keilegom

More articles in Journal of the Royal Statistical Society Series B from Royal Statistical Society Contact information at EDIRC.
Bibliographic data for series maintained by Wiley Content Delivery ().