## Bernoulli

• Bernoulli
• Volume 20, Number 4 (2014), 1698-1716.

### Convergence rate and concentration inequalities for Gibbs sampling in high dimension

#### Abstract

The objective of this paper is to study the Gibbs sampling for computing the mean of observable in very high dimension – a powerful Markov chain Monte Carlo method. Under the Dobrushin’s uniqueness condition, we establish some explicit and sharp estimate of the exponential convergence rate and prove some Gaussian concentration inequalities for the empirical mean.

#### Article information

Source
Bernoulli, Volume 20, Number 4 (2014), 1698-1716.

Dates
First available in Project Euclid: 19 September 2014

https://projecteuclid.org/euclid.bj/1411134441

Digital Object Identifier
doi:10.3150/13-BEJ537

Mathematical Reviews number (MathSciNet)
MR3263086

Zentralblatt MATH identifier
06368414

#### Citation

Wang, Neng-Yi; Wu, Liming. Convergence rate and concentration inequalities for Gibbs sampling in high dimension. Bernoulli 20 (2014), no. 4, 1698--1716. doi:10.3150/13-BEJ537. https://projecteuclid.org/euclid.bj/1411134441

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