Convergence rates of symmetric scan Gibbs sampler

Neng-Yi WANG

Front. Math. China ›› 2019, Vol. 14 ›› Issue (5) : 941 -955.

PDF (270KB)
Front. Math. China ›› 2019, Vol. 14 ›› Issue (5) : 941 -955. DOI: 10.1007/s11464-019-0791-7
RESEARCH ARTICLE
RESEARCH ARTICLE

Convergence rates of symmetric scan Gibbs sampler

Author information +
History +
PDF (270KB)

Abstract

We consider the symmetric scan Gibbs sampler, and give some explicit estimates of convergence rates on the Wasserstein distance for this Markov chain Monte Carlo under the Dobrushin uniqueness condition.

Keywords

Markov chain Monte Carlo / symmetric scan Gibbs sampler / coupling method / Wasserstein metric

Cite this article

Download citation ▾
Neng-Yi WANG. Convergence rates of symmetric scan Gibbs sampler. Front. Math. China, 2019, 14(5): 941-955 DOI:10.1007/s11464-019-0791-7

登录浏览全文

4963

注册一个新账户 忘记密码

References

[1]

Besag J, Green P, Higdon D, Mengersen K. Bayesian computation and stochastic systems. Statist Sci, 1995, 10(1): 3–41

[2]

Djellout H, Guillin A, Wu L M. Transportation cost-information inequalities and application to random dynamical systems and diffusions. Ann Probab, 2004, 32(3B): 2702–2732

[3]

Dobrushin R L. The description of a random field by means of conditional probabilities and condition of its regularity. Theory Probab Appl, 1968, 13(2): 197–224

[4]

Dobrushin R L. Prescribing a system of random variables by conditional distributions. Theory Probab Appl, 1970, 15(3): 458–486

[5]

Durmus A, Fort G, Moulines E. Subgeometric rates of convergence in Wasserstein distance for Markov chains. Ann Inst Henri Poincare Probab Stat, 2016, 52(4): 1799–1822

[6]

Dyer M, Goldberg L A, Jerrum M. Dobrushin conditions and systematic scan. Combin Probab Comput, 2008, 17(6): 761–779

[7]

Gibbs A L. Convergence in the Wasserstein metric for Markov chain Monte Carlo algorithms with applications to image restoration. Stoch Models, 2004, 20(4): 473–492

[8]

Joulin A, Ollivier Y. Curvature, concentration, and error estimates for Markov chain Monte Carlo. Ann Probab, 2010, 38(6): 2418–2442

[9]

Madras N, Sezer D. Quantitative bounds for Markov chain convergence: Wasserstein and total variation distances. Bernoulli, 2010, 16(3): 882–908

[10]

Marton K. Measure concentration for Euclidean distance in the case of dependent random variables. Ann Probab, 2004, 32(3B): 2526–2544

[11]

Robert C P, Casella G. Monte Carlo Statistical Methods. 2nd ed. New York: Springer, 2004

[12]

Roberts G O, Rosenthal J S. General state space Markov chains and MCMC algorithms. Probab Surv, 2004, 1: 20–71

[13]

Roberts G O, Sahu S K. Updating schemes, correlation structure, blocking and parameterization for the Gibbs sampler. J R Stat Soc Ser B Stat Methodol, 1997, 59(2): 291–317

[14]

Villani C. Topics in Optimal Transportation. Grad Stud Math, Vol 58. Providence: Amer Math Soc, 2003

[15]

Wang F Y. Functional Inequalities, Markov Semigroups and Spectral Theory. Beijing: Science Press, 2005

[16]

Wang N Y, Wu L M. Convergence rate and concentration inequalities for Gibbs sampling in high dimension. Bernoulli, 2014, 20(4): 1698{1716

[17]

Wu L M. Poincaré and transportation inequalities for Gibbs measures under the Dobrushin uniqueness condition. Ann Probab, 2006, 34(5): 1960–1989

RIGHTS & PERMISSIONS

Higher Education Press and Springer-Verlag GmbH Germany, part of Springer Nature

AI Summary AI Mindmap
PDF (270KB)

441

Accesses

0

Citation

Detail

Sections
Recommended

AI思维导图

/