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