On free energy barriers in Gaussian priors and failure of cold start MCMC for high-dimensional unimodal distributions
Open access
Date
2023-05-15Type
- Journal Article
Abstract
We exhibit examples of high-dimensional unimodal posterior distributions arising in nonlinear regression models with Gaussian process priors for which Markov chain Monte Carlo (MCMC) methods can take an exponential run-time to enter the regions where the bulk of the posterior measure concentrates. Our results apply to worst-case initialized ('cold start') algorithms that are local in the sense that their step sizes cannot be too large on average. The counter-examples hold for general MCMC schemes based on gradient or random walk steps, and the theory is illustrated for Metropolis-Hastings adjusted methods such as preconditioned Crank-Nicolson and Metropolis-adjusted Langevin algorithm. This article is part of the theme issue 'Bayesian inference: challenges, perspectives, and prospects'. Show more
Permanent link
https://doi.org/10.3929/ethz-b-000606200Publication status
publishedExternal links
Journal / series
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering SciencesVolume
Pages / Article No.
Publisher
Royal SocietySubject
MCMC; Bayesian inference; Gaussian processes; Computational hardnessOrganisational unit
09679 - Bandeira, Afonso / Bandeira, Afonso
02500 - Forschungsinstitut für Mathematik / Institute for Mathematical Research
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