IDEAS home Printed from https://ideas.repec.org/a/spr/metcap/v8y2006i2d10.1007_s11009-006-8550-0.html
   My bibliography  Save this article

An Adaptive Version for the Metropolis Adjusted Langevin Algorithm with a Truncated Drift

Author

Listed:
  • Yves F. Atchadé

    (University of Ottawa)

Abstract

This paper extends some adaptive schemes that have been developed for the Random Walk Metropolis algorithm to more general versions of the Metropolis-Hastings (MH) algorithm, particularly to the Metropolis Adjusted Langevin algorithm of Roberts and Tweedie (1996). Our simulations show that the adaptation drastically improves the performance of such MH algorithms. We study the convergence of the algorithm. Our proves are based on a new approach to the analysis of stochastic approximation algorithms based on mixingales theory.

Suggested Citation

  • Yves F. Atchadé, 2006. "An Adaptive Version for the Metropolis Adjusted Langevin Algorithm with a Truncated Drift," Methodology and Computing in Applied Probability, Springer, vol. 8(2), pages 235-254, June.
  • Handle: RePEc:spr:metcap:v:8:y:2006:i:2:d:10.1007_s11009-006-8550-0
    DOI: 10.1007/s11009-006-8550-0
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11009-006-8550-0
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.

    File URL: https://libkey.io/10.1007/s11009-006-8550-0?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. Jarner, Søren Fiig & Hansen, Ernst, 2000. "Geometric ergodicity of Metropolis algorithms," Stochastic Processes and their Applications, Elsevier, vol. 85(2), pages 341-361, February.
    2. James Davidson & Robert de Jong, 1997. "Strong laws of large numbers for dependent heterogeneous processes: a synthesis of recent and new results," Econometric Reviews, Taylor & Francis Journals, vol. 16(3), pages 251-279.
    3. O. Stramer & R. L. Tweedie, 1999. "Langevin-Type Models II: Self-Targeting Candidates for MCMC Algorithms," Methodology and Computing in Applied Probability, Springer, vol. 1(3), pages 307-328, October.
    4. Pelletier, Mariane, 1998. "On the almost sure asymptotic behaviour of stochastic algorithms," Stochastic Processes and their Applications, Elsevier, vol. 78(2), pages 217-244, 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. Julio López & Sebastián Maldonado & Ricardo Montoya, 2017. "Simultaneous preference estimation and heterogeneity control for choice-based conjoint via support vector machines," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 68(11), pages 1323-1334, November.
    2. Param Vir Singh & Nachiketa Sahoo & Tridas Mukhopadhyay, 2014. "How to Attract and Retain Readers in Enterprise Blogging?," Information Systems Research, INFORMS, vol. 25(1), pages 35-52, March.
    3. Pierrette Chagneau & Frédéric Mortier & Nicolas Picard & Jean-Noël Bacro, 2011. "A Hierarchical Bayesian Model for Spatial Prediction of Multivariate Non-Gaussian Random Fields," Biometrics, The International Biometric Society, vol. 67(1), pages 97-105, March.
    4. Tridas Mukhopadhyay & ParamVir Singh & Seung Hyun Kim, 2011. "Learning Curves of Agents with Diverse Skills in Information Technology-Enabled Physician Referral Systems," Information Systems Research, INFORMS, vol. 22(3), pages 586-605, September.
    5. Param Vir Singh & Corey Phelps, 2013. "Networks, Social Influence, and the Choice Among Competing Innovations: Insights from Open Source Software Licenses," Information Systems Research, INFORMS, vol. 24(3), pages 539-560, September.
    6. Yingda Lu & Kinshuk Jerath & Param Vir Singh, 2013. "The Emergence of Opinion Leaders in a Networked Online Community: A Dyadic Model with Time Dynamics and a Heuristic for Fast Estimation," Management Science, INFORMS, vol. 59(8), pages 1783-1799, August.
    7. Samuel Livingstone & Giacomo Zanella, 2022. "The Barker proposal: Combining robustness and efficiency in gradient‐based MCMC," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(2), pages 496-523, April.

    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. Dalalyan, Arnak S. & Karagulyan, Avetik, 2019. "User-friendly guarantees for the Langevin Monte Carlo with inaccurate gradient," Stochastic Processes and their Applications, Elsevier, vol. 129(12), pages 5278-5311.
    2. Allassonnière, Stéphanie & Kuhn, Estelle, 2015. "Convergent stochastic Expectation Maximization algorithm with efficient sampling in high dimension. Application to deformable template model estimation," Computational Statistics & Data Analysis, Elsevier, vol. 91(C), pages 4-19.
    3. O. F. Christensen & J. Møller & R. P. Waagepetersen, 2001. "Geometric Ergodicity of Metropolis-Hastings Algorithms for Conditional Simulation in Generalized Linear Mixed Models," Methodology and Computing in Applied Probability, Springer, vol. 3(3), pages 309-327, September.
    4. Yves Atchade, 2005. "An Adaptive Version for the Metropolis Adjusted Langevin Algorithm with a Truncated Drift," RePAd Working Paper Series LRSP-WP1, Département des sciences administratives, UQO.
    5. Pelletier, Mariane, 1999. "An Almost Sure Central Limit Theorem for Stochastic Approximation Algorithms," Journal of Multivariate Analysis, Elsevier, vol. 71(1), pages 76-93, October.
    6. Junming Li & Xiulan Han & Xiao Li & Jianping Yang & Xuejiao Li, 2018. "Spatiotemporal Patterns of Ground Monitored PM 2.5 Concentrations in China in Recent Years," IJERPH, MDPI, vol. 15(1), pages 1-15, January.
    7. Fort, G. & Moulines, E., 2003. "Polynomial ergodicity of Markov transition kernels," Stochastic Processes and their Applications, Elsevier, vol. 103(1), pages 57-99, January.
    8. Chris Sherlock & Anthony Lee, 2022. "Variance Bounding of Delayed-Acceptance Kernels," Methodology and Computing in Applied Probability, Springer, vol. 24(3), pages 2237-2260, September.
    9. 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.
    10. Kanaya, Shin, 2017. "Convergence Rates Of Sums Of Α-Mixing Triangular Arrays: With An Application To Nonparametric Drift Function Estimation Of Continuous-Time Processes," Econometric Theory, Cambridge University Press, vol. 33(5), pages 1121-1153, October.
    11. O. Stramer & R. L. Tweedie, 1999. "Langevin-Type Models I: Diffusions with Given Stationary Distributions and their Discretizations," Methodology and Computing in Applied Probability, Springer, vol. 1(3), pages 283-306, October.
    12. Lacour, Claire, 2008. "Nonparametric estimation of the stationary density and the transition density of a Markov chain," Stochastic Processes and their Applications, Elsevier, vol. 118(2), pages 232-260, February.
    13. Giovanni Cerulli, 2012. "Are R&D Subsidies Provided Optimally? Evidence from a Simulated Agency-Firm Stochastic Dynamic Game," Journal of Artificial Societies and Social Simulation, Journal of Artificial Societies and Social Simulation, vol. 15(1), pages 1-7.
    14. Fort, Gersende & Moulines, Eric, 2000. "V-Subgeometric ergodicity for a Hastings-Metropolis algorithm," Statistics & Probability Letters, Elsevier, vol. 49(4), pages 401-410, October.
    15. David A. Spade, 2020. "Geometric ergodicity of a Metropolis-Hastings algorithm for Bayesian inference of phylogenetic branch lengths," Computational Statistics, Springer, vol. 35(4), pages 2043-2076, December.
    16. Samuel Livingstone & Giacomo Zanella, 2022. "The Barker proposal: Combining robustness and efficiency in gradient‐based MCMC," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(2), pages 496-523, April.
    17. Casella, Bruno & Roberts, Gareth O. & Stramer, Osnat, 2011. "Stability of Partially Implicit Langevin Schemes and Their MCMC Variants," MPRA Paper 95220, University Library of Munich, Germany.
    18. Kamatani, Kengo, 2020. "Random walk Metropolis algorithm in high dimension with non-Gaussian target distributions," Stochastic Processes and their Applications, Elsevier, vol. 130(1), pages 297-327.
    19. Cizek, P., 2004. "Asymptotics of Least Trimmed Squares Regression," Other publications TiSEM dab5d551-aca6-40bf-b92e-c, Tilburg University, School of Economics and Management.
    20. Kanaya, Shin, 2017. "Convergence Rates Of Sums Of Α-Mixing Triangular Arrays: With An Application To Nonparametric Drift Function Estimation Of Continuous-Time Processes," Econometric Theory, Cambridge University Press, vol. 33(5), pages 1121-1153, October.

    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:spr:metcap:v:8:y:2006:i:2:d:10.1007_s11009-006-8550-0. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.