IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v13y2025i7p1084-d1620991.html
   My bibliography  Save this article

Convergence of Limiting Cases of Continuous-Time, Discrete-Space Jump Processes to Diffusion Processes for Bayesian Inference

Author

Listed:
  • Aaron Lanterman

    (School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, GA 30332, USA)

Abstract

Jump-diffusion algorithms are applied to sampling from Bayesian posterior distributions. We consider a class of random sampling algorithms based on continuous-time jump processes. The semigroup theory of random processes lets us show that limiting cases of certain jump processes acting on discretized spaces converge to diffusion processes as the discretization is refined. One of these processes leads to the familiar Langevin diffusion equation; another leads to an entirely new diffusion equation.

Suggested Citation

  • Aaron Lanterman, 2025. "Convergence of Limiting Cases of Continuous-Time, Discrete-Space Jump Processes to Diffusion Processes for Bayesian Inference," Mathematics, MDPI, vol. 13(7), pages 1-10, March.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:7:p:1084-:d:1620991
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/13/7/1084/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/13/7/1084/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Ghaderi, Susan & Ahookhosh, Masoud & Arany, Adam & Skupin, Alexander & Patrinos, Panagiotis & Moreau, Yves, 2024. "Smoothing unadjusted Langevin algorithms for nonsmooth composite potential functions," Applied Mathematics and Computation, Elsevier, vol. 464(C).
    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.
    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. Delis, Manthos D. & Tsionas, Mike G., 2018. "Measuring management practices," International Journal of Production Economics, Elsevier, vol. 199(C), pages 65-77.
    2. 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.
    3. Aknouche, Abdelhakim & Dimitrakopoulos, Stefanos, 2020. "On an integer-valued stochastic intensity model for time series of counts," MPRA Paper 105406, University Library of Munich, Germany.
    4. 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.
    5. Tsionas, Mike G. & Michaelides, Panayotis G., 2017. "Neglected chaos in international stock markets: Bayesian analysis of the joint return–volatility dynamical system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 482(C), pages 95-107.
    6. Shao, Wei & Guo, Guangbao & Meng, Fanyu & Jia, Shuqin, 2013. "An efficient proposal distribution for Metropolis–Hastings using a B-splines technique," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 465-478.
    7. Anandamayee Majumdar & Corinna Gries & Jason Walker, 2011. "A non-stationary spatial generalized linear mixed model approach for studying plant diversity," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(9), pages 1935-1950, October.
    8. Reihaneh Entezari & Patrick E. Brown & Jeffrey S. Rosenthal, 2020. "Bayesian spatial analysis of hardwood tree counts in forests via MCMC," Environmetrics, John Wiley & Sons, Ltd., vol. 31(4), June.
    9. Peter Neal & Gareth Roberts, 2008. "Optimal Scaling for Random Walk Metropolis on Spherically Constrained Target Densities," Methodology and Computing in Applied Probability, Springer, vol. 10(2), pages 277-297, June.
    10. Katiane S. Conceição & Marinho G. Andrade & Victor Hugo Lachos & Nalini Ravishanker, 2024. "Bayesian Inference for Zero-Modified Power Series Regression Models," Mathematics, MDPI, vol. 13(1), pages 1-30, December.
    11. 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.
    12. 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).
    13. Rishikesh Yadav & Raphaël Huser & Thomas Opitz, 2021. "Spatial hierarchical modeling of threshold exceedances using rate mixtures," Environmetrics, John Wiley & Sons, Ltd., vol. 32(3), May.
    14. Xiang, Fei & Neal, Peter, 2014. "Efficient MCMC for temporal epidemics via parameter reduction," Computational Statistics & Data Analysis, Elsevier, vol. 80(C), pages 240-250.
    15. 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).
    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. Mattingly, J. C. & Stuart, A. M. & Higham, D. J., 2002. "Ergodicity for SDEs and approximations: locally Lipschitz vector fields and degenerate noise," Stochastic Processes and their Applications, Elsevier, vol. 101(2), pages 185-232, October.
    18. 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.
    19. 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.
    20. Panagiotis Papastamoulis & Fotios S. Milienos, 2025. "Bayesian inference and cure rate modeling for event history data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 34(1), pages 1-27, 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:gam:jmathe:v:13:y:2025:i:7:p:1084-:d:1620991. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.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.