IDEAS home Printed from https://ideas.repec.org/a/bla/scjsta/v49y2022i2p657-680.html
   My bibliography  Save this article

An n‐dimensional Rosenbrock distribution for Markov chain Monte Carlo testing

Author

Listed:
  • Filippo Pagani
  • Martin Wiegand
  • Saralees Nadarajah

Abstract

The Rosenbrock function is a ubiquitous benchmark problem in numerical optimization, and variants have been proposed to test the performance of Markov chain Monte Carlo algorithms on distributions with a curved and narrow shape. In this work we discuss the Rosenbrock distribution and the advantages and limitations of its current n‐dimensional extensions. We then propose a new extension to arbitrary dimensions called the Hybrid Rosenbrock distribution, which addresses all the limitations that affect the current extensions. The Hybrid Rosenbrock distribution is composed of conditional normal kernels arranged in such a way that preserves the key features of the original Rosenbrock kernel. Moreover, due to its structure, the Hybrid Rosenbrock distribution is analytically tractable, and possesses several desirable properties which make it an excellent test model for computational algorithms. We conclude with numerical experiments that show how commonly used Markov chain Monte Carlo algorithms may fail to explore densities with curved correlation structure, restating the importance of a reliable benchmark problem for this class of densities.

Suggested Citation

  • Filippo Pagani & Martin Wiegand & Saralees Nadarajah, 2022. "An n‐dimensional Rosenbrock distribution for Markov chain Monte Carlo testing," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(2), pages 657-680, June.
    • Handle: RePEc:bla:scjsta:v:49:y:2022:i:2:p:657-680
    DOI: 10.1111/sjos.12532
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/sjos.12532
    Download Restriction: no
    File URL: https://libkey.io/10.1111/sjos.12532?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
    ---><---

    References listed on IDEAS

    as
    1. Pierre Del Moral & Arnaud Doucet & Ajay Jasra, 2006. "Sequential Monte Carlo samplers," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(3), pages 411-436, June.
    2. Sangjoon Kim & Neil Shephard & Siddhartha Chib, 1998. "Stochastic Volatility: Likelihood Inference and Comparison with ARCH Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 65(3), pages 361-393.
    3. Carpenter, Bob & Gelman, Andrew & Hoffman, Matthew D. & Lee, Daniel & Goodrich, Ben & Betancourt, Michael & Brubaker, Marcus & Guo, Jiqiang & Li, Peter & Riddell, Allen, 2017. "Stan: A Probabilistic Programming Language," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 76(i01).
    4. Ole F. Christensen & Gareth O. Roberts & Jeffrey S. Rosenthal, 2005. "Scaling limits for the transient phase of local Metropolis–Hastings algorithms," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(2), pages 253-268, April.
    5. 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.
    Full references (including those not matched with items on IDEAS)

    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. Dellaportas, Petros & Titsias, Michalis K. & Petrova, Katerina & Plataniotis, Anastasios, 2023. "Scalable inference for a full multivariate stochastic volatility model," Journal of Econometrics, Elsevier, vol. 232(2), pages 501-520.
    2. Jeremy Heng & Arnaud Doucet & Yvo Pokern, 2021. "Gibbs flow for approximate transport with applications to Bayesian computation," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 83(1), pages 156-187, February.
    3. Gael M. Martin & David T. Frazier & Christian P. Robert, 2020. "Computing Bayes: Bayesian Computation from 1763 to the 21st Century," Monash Econometrics and Business Statistics Working Papers 14/20, Monash University, Department of Econometrics and Business Statistics.
    4. Agudze, Komla M. & Billio, Monica & Casarin, Roberto & Ravazzolo, Francesco, 2022. "Markov switching panel with endogenous synchronization effects," Journal of Econometrics, Elsevier, vol. 230(2), pages 281-298.
    5. Dimitris Korobilis & Davide Pettenuzzo, 2020. "Machine Learning Econometrics: Bayesian algorithms and methods," Papers 2004.11486, arXiv.org.
    6. Nicolas Chopin & Mathieu Gerber, 2017. "Sequential quasi-Monte Carlo: Introduction for Non-Experts, Dimension Reduction, Application to Partly Observed Diffusion Processes," Working Papers 2017-35, Center for Research in Economics and Statistics.
    7. Ramis Khabibullin & Sergei Seleznev, 2022. "Fast Estimation of Bayesian State Space Models Using Amortized Simulation-Based Inference," Papers 2210.07154, arXiv.org.
    8. Antonio A. F. Santos, 2021. "Bayesian Estimation for High-Frequency Volatility Models in a Time Deformed Framework," Computational Economics, Springer;Society for Computational Economics, vol. 57(2), pages 455-479, February.
    9. Hannaford, Naomi E. & Heaps, Sarah E. & Nye, Tom M.W. & Curtis, Thomas P. & Allen, Ben & Golightly, Andrew & Wilkinson, Darren J., 2023. "A sparse Bayesian hierarchical vector autoregressive model for microbial dynamics in a wastewater treatment plant," Computational Statistics & Data Analysis, Elsevier, vol. 179(C).
    10. Kreuzer, Alexander & Czado, Claudia, 2021. "Bayesian inference for a single factor copula stochastic volatility model using Hamiltonian Monte Carlo," Econometrics and Statistics, Elsevier, vol. 19(C), pages 130-150.
    11. Kim C. Raath & Katherine B. Ensor, 2023. "Wavelet-L2E Stochastic Volatility Models: an Application to the Water-Energy Nexus," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(1), pages 150-176, May.
    12. Drovandi, Christopher C. & Pettitt, Anthony N. & Henderson, Robert D. & McCombe, Pamela A., 2014. "Marginal reversible jump Markov chain Monte Carlo with application to motor unit number estimation," Computational Statistics & Data Analysis, Elsevier, vol. 72(C), pages 128-146.
    13. Topaloglou, Nikolas & Tsionas, Mike G., 2020. "Stochastic dominance tests," Journal of Economic Dynamics and Control, Elsevier, vol. 112(C).
    14. Li, Dan & Clements, Adam & Drovandi, Christopher, 2021. "Efficient Bayesian estimation for GARCH-type models via Sequential Monte Carlo," Econometrics and Statistics, Elsevier, vol. 19(C), pages 22-46.
    15. 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.
    16. Didit Nugroho & Takayuki Morimoto, 2015. "Estimation of realized stochastic volatility models using Hamiltonian Monte Carlo-Based methods," Computational Statistics, Springer, vol. 30(2), pages 491-516, June.
    17. Marina Riabiz & Wilson Ye Chen & Jon Cockayne & Pawel Swietach & Steven A. Niederer & Lester Mackey & Chris. J. Oates, 2022. "Optimal thinning of MCMC output," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(4), pages 1059-1081, September.
    18. repec:bla:istatr:v:83:y:2015:i:3:p:405-435 is not listed on IDEAS
    19. Kreuzer, Alexander & Dalla Valle, Luciana & Czado, Claudia, 2023. "Bayesian multivariate nonlinear state space copula models," Computational Statistics & Data Analysis, Elsevier, vol. 188(C).
    20. Golchi, Shirin & Campbell, David A., 2016. "Sequentially Constrained Monte Carlo," Computational Statistics & Data Analysis, Elsevier, vol. 97(C), pages 98-113.
    21. Damien McParland & Szymon Baron & Sarah O’Rourke & Denis Dowling & Eamonn Ahearne & Andrew Parnell, 2019. "Prediction of tool-wear in turning of medical grade cobalt chromium molybdenum alloy (ASTM F75) using non-parametric Bayesian models," Journal of Intelligent Manufacturing, Springer, vol. 30(3), pages 1259-1270, March.

    More about this item

    Statistics

    Access and download statistics

    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:bla:scjsta:v:49:y:2022:i:2:p:657-680. 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: Wiley Content Delivery (email available below). General contact details of provider: http://www.blackwellpublishing.com/journal.asp?ref=0303-6898 .

    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.