Electronic Communications in Probability

Concentration inequalities for Gibbs sampling under $d_{l_{2}}$-metric

Neng-Yi Wang

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The aim of this paper is to investigate the Gibbs sampling that's used for computing the mean of observables with respect to some function $f$ depending on a very small number of variables. For this type of observable, by using the $d_{l_{2}}$-metric one obtains the sharp concentration estimate for the empirical mean, which in particular yields the correct speed in the concentration for $f$ depending on a single observable.

Article information

Electron. Commun. Probab., Volume 19 (2014), paper no. 63, 11 pp.

Accepted: 18 September 2014
First available in Project Euclid: 7 June 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60E15: Inequalities; stochastic orderings
Secondary: 65C05: Monte Carlo methods

concentration inequality Gibbs sampling coupling method Dobrushin's uniqueness condition $d_{l_2}$-metric

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Wang, Neng-Yi. Concentration inequalities for Gibbs sampling under $d_{l_{2}}$-metric. Electron. Commun. Probab. 19 (2014), paper no. 63, 11 pp. doi:10.1214/ECP.v19-3502. https://projecteuclid.org/euclid.ecp/1465316765

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