Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Zh. Vychisl. Mat. Mat. Fiz.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2024, Volume 64, Number 4, paper published in the English version journal (Mi zvmmf11739)  

Papers published in the English version of the journal

Diffusion approximations and control variates for MCMC

N. Brossea, A. Durmusa, S. Meynb, E. Moulinesa, S. Samsonovc

a École Polytechnique, Paris, France
b University of Florida, Gainesville, Florida, USA
c National Research University Higher School of Economics, Moscow, Russia
Abstract: A new method is introduced for the construction of control variates to reduce the variance of additive functionals of Markov Chain Monte Carlo (MCMC) samplers. These control variates are obtained by minimizing the asymptotic variance associated with the Langevin diffusion over a family of functions. To motivate our approach, we then show that the asymptotic variance of some well-known MCMC algorithms, including the Random Walk Metropolis and the (Metropolis) Unadjusted/Adjusted Langevin Algorithm, are well approximated by that of the Langevin diffusion. We finally theoretically justify the use of a class of linear control variates we introduce. In particular, we show that the variance of the resulting estimators is smaller, for a given computational complexity, than the standard Monte Carlo estimator. Several examples of Bayesian inference problems support our findings showing, in some cases, very significant reduction of the variance.
Key words: control variables, MCMC algorithms, Langevin-diffusion.
Received: 10.06.2023
Revised: 11.09.2023
Accepted: 07.06.2024
English version:
Computational Mathematics and Mathematical Physics, 2024, Volume 64, Issue 4, Pages 693–738
DOI: https://doi.org/10.1134/S0965542524700167
Document Type: Article
Language: English
Citation: N. Brosse, A. Durmus, S. Meyn, E. Moulines, S. Samsonov, “Diffusion approximations and control variates for MCMC”, Comput. Math. Math. Phys., 64:4 (2024), 693–738
Citation in format AMSBIB
\Bibitem{BroDurMey24}
\by N.~Brosse, A.~Durmus, S.~Meyn, E.~Moulines, S.~Samsonov
\paper Diffusion approximations and control variates for MCMC
\jour Comput. Math. Math. Phys.
\yr 2024
\vol 64
\issue 4
\pages 693--738
\mathnet{http://mi.mathnet.ru/zvmmf11739}
\crossref{https://doi.org/10.1134/S0965542524700167}
Linking options:
  • https://www.mathnet.ru/eng/zvmmf11739
  • Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024