IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v91y2014icp14-19.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715214001333
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spl.2014.04.002?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.
    4. Bédard, Mylène, 2017. "Hierarchical models: Local proposal variances for RWM-within-Gibbs and MALA-within-Gibbs," Computational Statistics & Data Analysis, Elsevier, vol. 109(C), pages 231-246.
    5. Vandecasteele, Hannes & Samaey, Giovanni, 2024. "Computational efficiency study of a micro-macro Markov chain Monte Carlo method for molecular dynamics," Applied Mathematics and Computation, Elsevier, vol. 474(C).
    6. Samuel Livingstone, 2021. "Geometric Ergodicity of the Random Walk Metropolis with Position-Dependent Proposal Covariance," Mathematics, MDPI, vol. 9(4), pages 1-14, February.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Burda Martin & Maheu John M., 2013. "Bayesian adaptively updated Hamiltonian Monte Carlo with an application to high-dimensional BEKK GARCH models," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 17(4), pages 345-372, September.
    3. Dang, Khue-Dung & Quiroz, Matias & Kohn, Robert & Tran, Minh-Ngoc & Villani, Mattias, 2019. "Hamiltonian Monte Carlo with Energy Conserving Subsampling," Working Paper Series 372, Sveriges Riksbank (Central Bank of Sweden).
    4. Beskos, A. & Pinski, F.J. & Sanz-Serna, J.M. & Stuart, A.M., 2011. "Hybrid Monte Carlo on Hilbert spaces," Stochastic Processes and their Applications, Elsevier, vol. 121(10), pages 2201-2230, October.
    5. Van Kinh Nguyen & Frank Klawonn & Rafael Mikolajczyk & Esteban A Hernandez-Vargas, 2016. "Analysis of Practical Identifiability of a Viral Infection Model," PLOS ONE, Public Library of Science, vol. 11(12), pages 1-16, December.
    6. Mike Tsionas & Marwan Izzeldin & Lorenzo Trapani, 2019. "Bayesian estimation of large dimensional time varying VARs using copulas," Papers 1912.12527, arXiv.org.
    7. M Ludkin & C Sherlock, 2023. "Hug and hop: a discrete-time, nonreversible Markov chain Monte Carlo algorithm," Biometrika, Biometrika Trust, vol. 110(2), pages 301-318.
    8. González Javier & Vujačić Ivan & Wit Ernst, 2013. "Inferring latent gene regulatory network kinetics," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 12(1), pages 109-127, March.
    9. Golchi, Shirin & Campbell, David A., 2016. "Sequentially Constrained Monte Carlo," Computational Statistics & Data Analysis, Elsevier, vol. 97(C), pages 98-113.
    10. Martin Burda & John Maheu, 2011. "Bayesian Adaptive Hamiltonian Monte Carlo with an Application to High-Dimensional BEKK GARCH Models," Working Papers tecipa-438, University of Toronto, Department of Economics.
    11. Tsionas, Mike G. & Izzeldin, Marwan & Trapani, Lorenzo, 2022. "Estimation of large dimensional time varying VARs using copulas," European Economic Review, Elsevier, vol. 141(C).
    12. Bédard, Mylène, 2017. "Hierarchical models: Local proposal variances for RWM-within-Gibbs and MALA-within-Gibbs," Computational Statistics & Data Analysis, Elsevier, vol. 109(C), pages 231-246.
    13. Hanwen Huang & Andreas Handel & Xiao Song, 2020. "A Bayesian approach to estimate parameters of ordinary differential equation," Computational Statistics, Springer, vol. 35(3), pages 1481-1499, September.
    14. Atkinson, Scott E. & Tsionas, Mike G., 2021. "Generalized estimation of productivity with multiple bad outputs: The importance of materials balance constraints," European Journal of Operational Research, Elsevier, vol. 292(3), pages 1165-1186.
    15. Qianwen Tan & Subhashis Ghosal, 2021. "Bayesian Analysis of Mixed-effect Regression Models Driven by Ordinary Differential Equations," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(1), pages 3-29, May.
    16. Jaeger, Jonathan & Lambert, Philippe, 2012. "Bayesian penalized smoothing approaches in models specified using affine differential equations with unknown error distributions," LIDAM Discussion Papers ISBA 2012017, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    17. Jia Liu & John M. Maheu & Yong Song, 2024. "Identification and forecasting of bull and bear markets using multivariate returns," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 39(5), pages 723-745, August.
    18. Dimitrakopoulos, Stefanos & Tsionas, Mike, 2019. "Ordinal-response GARCH models for transaction data: A forecasting exercise," International Journal of Forecasting, Elsevier, vol. 35(4), pages 1273-1287.
    19. Vanhatalo, Jarno & Veneranta, Lari & Hudd, Richard, 2012. "Species distribution modeling with Gaussian processes: A case study with the youngest stages of sea spawning whitefish (Coregonus lavaretus L. s.l.) larvae," Ecological Modelling, Elsevier, vol. 228(C), pages 49-58.
    20. Will Penny & Biswa Sengupta, 2016. "Annealed Importance Sampling for Neural Mass Models," PLOS Computational Biology, Public Library of Science, vol. 12(3), pages 1-25, March.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:stapro:v:91:y:2014:i:c:p:14-19. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.