Abstract
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.
Citation
Neng-Yi Wang. "Concentration inequalities for Gibbs sampling under $d_{l_{2}}$-metric." Electron. Commun. Probab. 19 1 - 11, 2014. https://doi.org/10.1214/ECP.v19-3502
Information