English

Large deviations for Independent Metropolis Hastings and Metropolis-adjusted Langevin algorithm

Probability 2026-02-23 v4 Statistics Theory Statistics Theory

Abstract

In this paper, we prove large deviation principles for the empirical measures associated with the Independent Metropolis Hastings (IMH) sampler and the Metropolis-adjusted Langevin Algorithm (MALA). These are the first large deviation results for empirical measures of Markov chains arising from specific Metropolis-Hastings methods on a continuous state space. Moreover, we show that the existing large deviation framework, that we developed in a previous work (Milinanni and Nyquist, 2024), does not cover the Random Walk Metropolis sampler, even in cases when the underlying Markov chain is geometrically ergodic.

Keywords

Cite

@article{arxiv.2403.08691,
  title  = {Large deviations for Independent Metropolis Hastings and Metropolis-adjusted Langevin algorithm},
  author = {Federica Milinanni and Pierre Nyquist},
  journal= {arXiv preprint arXiv:2403.08691},
  year   = {2026}
}

Comments

30 pages, 0 figures, 1 table

R2 v1 2026-06-28T15:18:58.721Z