IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v83y2015icp101-115.html
   My bibliography  Save this article

Adaptive Metropolis algorithm using variational Bayesian adaptive Kalman filter

Author

Listed:
  • Mbalawata, Isambi S.
  • Särkkä, Simo
  • Vihola, Matti
  • Haario, Heikki

Abstract

Markov chain Monte Carlo (MCMC) methods are powerful computational tools for analysis of complex statistical problems. However, their computational efficiency is highly dependent on the chosen proposal distribution, which is generally difficult to find. One way to solve this problem is to use adaptive MCMC algorithms which automatically tune the statistics of a proposal distribution during the MCMC run. A new adaptive MCMC algorithm, called the variational Bayesian adaptive Metropolis (VBAM) algorithm, is developed. The VBAM algorithm updates the proposal covariance matrix using the variational Bayesian adaptive Kalman filter (VB-AKF). A strong law of large numbers for the VBAM algorithm is proven. The empirical convergence results for three simulated examples and for two real data examples are also provided.

Suggested Citation

  • Mbalawata, Isambi S. & Särkkä, Simo & Vihola, Matti & Haario, Heikki, 2015. "Adaptive Metropolis algorithm using variational Bayesian adaptive Kalman filter," Computational Statistics & Data Analysis, Elsevier, vol. 83(C), pages 101-115.
  • Handle: RePEc:eee:csdana:v:83:y:2015:i:c:p:101-115
    DOI: 10.1016/j.csda.2014.10.006
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947314002989
    Download Restriction: Full text for ScienceDirect subscribers only.

    File URL: https://libkey.io/10.1016/j.csda.2014.10.006?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. Roberts, G. O. & Gilks, W. R., 1994. "Convergence of Adaptive Direction Sampling," Journal of Multivariate Analysis, Elsevier, vol. 49(2), pages 287-298, May.
    2. Vihola, Matti, 2011. "On the stability and ergodicity of adaptive scaling Metropolis algorithms," Stochastic Processes and their Applications, Elsevier, vol. 121(12), pages 2839-2860.
    3. David G. Luenberger & Yinyu Ye, 2008. "Linear and Nonlinear Programming," International Series in Operations Research and Management Science, Springer, edition 0, number 978-0-387-74503-9, December.
    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. Kang, Kai & Maroulas, Vasileios & Schizas, Ioannis & Bao, Feng, 2018. "Improved distributed particle filters for tracking in a wireless sensor network," Computational Statistics & Data Analysis, Elsevier, vol. 117(C), pages 90-108.

    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. Alp Atakan & Mehmet Ekmekci & Ludovic Renou, 2021. "Cross-verification and Persuasive Cheap Talk," Papers 2102.13562, arXiv.org, revised Apr 2021.
    2. Bauwens, Luc & Bos, Charles S. & van Dijk, Herman K. & van Oest, Rutger D., 2004. "Adaptive radial-based direction sampling: some flexible and robust Monte Carlo integration methods," Journal of Econometrics, Elsevier, vol. 123(2), pages 201-225, December.
    3. Tanaka, Ken'ichiro & Toda, Alexis Akira, 2015. "Discretizing Distributions with Exact Moments: Error Estimate and Convergence Analysis," University of California at San Diego, Economics Working Paper Series qt7g23r5kh, Department of Economics, UC San Diego.
    4. Ashrafi, M. & Khanjani, M.J. & Fadaei-Kermani, E. & Barani, G.A., 2015. "Farm drainage channel network optimization by improved modified minimal spanning tree," Agricultural Water Management, Elsevier, vol. 161(C), pages 1-8.
    5. Sergey Badikov & Antoine Jacquier & Daphne Qing Liu & Patrick Roome, 2016. "No-arbitrage bounds for the forward smile given marginals," Papers 1603.06389, arXiv.org, revised Oct 2016.
    6. Szidarovszky, Ferenc & Luo, Yi, 2014. "Incorporating risk seeking attitude into defense strategy," Reliability Engineering and System Safety, Elsevier, vol. 123(C), pages 104-109.
    7. repec:jss:jstsof:07:i04 is not listed on IDEAS
    8. Rafał Wiśniowski & Krzysztof Skrzypaszek & Tomasz Małachowski, 2020. "Selection of a Suitable Rheological Model for Drilling Fluid Using Applied Numerical Methods," Energies, MDPI, vol. 13(12), pages 1-17, June.
    9. Yuichi Takano & Renata Sotirov, 2012. "A polynomial optimization approach to constant rebalanced portfolio selection," Computational Optimization and Applications, Springer, vol. 52(3), pages 645-666, July.
    10. Nadia Demarteau & Thomas Breuer & Baudouin Standaert, 2012. "Selecting a Mix of Prevention Strategies against Cervical Cancer for Maximum Efficiency with an Optimization Program," PharmacoEconomics, Springer, vol. 30(4), pages 337-353, April.
    11. Vittorio Nicolardi, 2013. "Simultaneously Balancing Supply--Use Tables At Current And Constant Prices: A New Procedure," Economic Systems Research, Taylor & Francis Journals, vol. 25(4), pages 409-434, December.
    12. Alina R. Battalova* & Nadezhda A. Opokina, 2018. "Economic-Mathematical Model of the Structure of Nutrition of Population in the Region," The Journal of Social Sciences Research, Academic Research Publishing Group, pages 275-280:1.
    13. Hee Su Roh & Yinyu Ye, 2015. "Market Making with Model Uncertainty," Papers 1509.07155, arXiv.org, revised Nov 2015.
    14. Takafumi Kanamori & Akiko Takeda, 2014. "Numerical study of learning algorithms on Stiefel manifold," Computational Management Science, Springer, vol. 11(4), pages 319-340, October.
    15. Bo Hu & Yuan Ji & Kam-Wah Tsui, 2008. "Bayesian Estimation of Inverse Dose Response," Biometrics, The International Biometric Society, vol. 64(4), pages 1223-1230, December.
    16. Minghui Lai & Weili Xue & Qian Hu, 2019. "An Ascending Auction for Freight Forwarder Collaboration in Capacity Sharing," Transportation Science, INFORMS, vol. 53(4), pages 1175-1195, July.
    17. Joao R. Faria & Peter Mcadam & Bruno Viscolani, 2023. "Monetary Policy, Neutrality, and the Environment," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 55(7), pages 1889-1906, October.
    18. Lee, Sunghoon & Yun, Seokwon & Kim, Jin-Kuk, 2019. "Development of novel sub-ambient membrane systems for energy-efficient post-combustion CO2 capture," Applied Energy, Elsevier, vol. 238(C), pages 1060-1073.
    19. G. Constante-Flores & A. J. Conejo & S. Constante-Flores, 2022. "Solving certain complementarity problems in power markets via convex programming," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(3), pages 465-491, October.
    20. I. Espejo & R. Páez & J. Puerto & A. M. Rodríguez-Chía, 2022. "Minimum cost b-matching problems with neighborhoods," Computational Optimization and Applications, Springer, vol. 83(2), pages 525-553, November.
    21. Mengyi Ying & Min Sun, 2017. "Some feasibility sampling procedures in interval methods for constrained global optimization," Journal of Global Optimization, Springer, vol. 67(1), pages 379-397, January.

    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:csdana:v:83:y:2015:i:c:p:101-115. 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/locate/csda .

    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.