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Langevin diffusions and the Metropolis-adjusted Langevin algorithm

Author

Listed:
  • Xifara, T.
  • Sherlock, C.
  • Livingstone, S.
  • Byrne, S.
  • Girolami, M.

Abstract

We describe a Langevin diffusion with a target stationary density with respect to Lebesgue measure, as opposed to the volume measure of a previously-proposed diffusion. The two are sometimes equivalent but in general distinct and lead to different Metropolis-adjusted Langevin algorithms, which we compare.

Suggested Citation

  • Xifara, T. & Sherlock, C. & Livingstone, S. & Byrne, S. & Girolami, M., 2014. "Langevin diffusions and the Metropolis-adjusted Langevin algorithm," Statistics & Probability Letters, Elsevier, vol. 91(C), pages 14-19.
    • Handle: RePEc:eee:stapro:v:91:y:2014:i:c:p:14-19
    DOI: 10.1016/j.spl.2014.04.002
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    References listed on IDEAS

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    1. Gareth O. Roberts & Jeffrey S. Rosenthal, 1998. "Optimal scaling of discrete approximations to Langevin diffusions," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 60(1), pages 255-268.
    2. J. O. Ramsay & G. Hooker & D. Campbell & J. Cao, 2007. "Parameter estimation for differential equations: a generalized smoothing approach," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(5), pages 741-796, November.
    3. Mark Girolami & Ben Calderhead, 2011. "Riemann manifold Langevin and Hamiltonian Monte Carlo methods," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 73(2), pages 123-214, March.
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    Cited by:

    1. Tore Selland Kleppe, 2016. "Adaptive Step Size Selection for Hessian-Based Manifold Langevin Samplers," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(3), pages 788-805, September.
    2. E. Zanini & E. Eastoe & M. J. Jones & D. Randell & P. Jonathan, 2020. "Flexible covariate representations for extremes," Environmetrics, John Wiley & Sons, Ltd., vol. 31(5), August.
    3. Arnak S. Dalalyan, 2017. "Theoretical guarantees for approximate sampling from smooth and log-concave densities," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(3), pages 651-676, June.
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    5. Samuel Livingstone, 2021. "Geometric Ergodicity of the Random Walk Metropolis with Position-Dependent Proposal Covariance," Mathematics, MDPI, vol. 9(4), pages 1-14, February.

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