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

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  • Mylène Bédard

    (Université de Montréal)

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

Suggested Citation

  • Mylène Bédard, 2025. "Non-stationary Phase of the Metropolis-adjusted Langevin Algorithm with Annealed Proposals," Methodology and Computing in Applied Probability, Springer, vol. 27(4), pages 1-40, December.
    • Handle: RePEc:spr:metcap:v:27:y:2025:i:4:d:10.1007_s11009-025-10206-1
    DOI: 10.1007/s11009-025-10206-1
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