Convergence rate and concentration inequalities for Gibbs sampling in high dimension
arXiv:1410.4329 · doi:10.3150/13-BEJ537
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.
arXiv commentPublished in at http://dx.doi.org/10.3150/13-BEJ537 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm)
References in corpus (6)
- General state space Markov chains and MCMC algorithms
- Transportation cost-information inequalities and applications to random dynamical systems and diffusions
- Curvature, concentration and error estimates for Markov chain Monte Carlo
- Measure concentration for Euclidean distance in the case of dependent random variables
- Poincaré and transportation inequalities for Gibbs measures under the Dobrushin uniqueness condition
- Weak transport inequalities and applications to exponential inequalities and oracle inequalities