Non-stationary Phase of the Metropolis-adjusted Langevin Algorithm with Annealed Proposals

Mylène Bédard ()
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Mylène Bédard: Université de Montréal

Methodology and Computing in Applied Probability, 2025, vol. 27, issue 4, 1-40

Abstract: Abstract The Metropolis-adjusted Langevin algorithm (MALA) is an informed MCMC method that is used to sample from a target distribution of interest. Its proposal distribution makes use of the gradient of the target’s log-density in order to generate suitable candidates for the chain. This sampler is quite efficient in the stationary phase, but displays a notoriously erratic behaviour out of stationarity. The Metropolis-adjusted Langevin algorithm with annealed proposals (aMALA) is a generalization of the usual MALA that features two tuning parameters: the usual step size $$\delta$$ and a parameter $$\gamma$$ that may be adjusted to accommodate N, the dimension of the target distribution (with $$\gamma =1$$ corresponding to MALA). It has been established in Boisvert-Beaudry and Bédard (Stat Comput 32(1):5, 2022) that aMALA with $$1

Keywords: Markov chain Monte Carlo; Metropolis-adjusted Langevin algorithm; Diffusion limit; Optimal scaling; Transience; Primary 60J22; Secondary 62F15 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s11009-025-10206-1

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