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

2024/03/13 by Federica Milinanni, Milinanni, Federica, Pierre Nyquist +1 · 1 voice
Mathematics · Economics, Econometrics and Finance · #Markov Chains and Monte Carlo Methods #Stochastic processes and statistical mechanics #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2403.08691

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.

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