Computable upper bounds on the distance to stationarity for Jovanovski and Madras’s Gibbs sampler
Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 24 (2015) no. 4, pp. 935-947.

Une borne supérieure est obtenue pour la distance de Wasserstein à la stationnarité pour une classe de chaînes de Markov sur . Ce résultat, qui est une généralisation du théorème 2.2 de Diaconis et al. (2009), est appliqué à l’échantillonneur de Gibbs introduit et analysé par Jovanovski et Madras (2014). La borne de Wasserstein qui en résulte est transformée en une borne en variation totale (en utilisant des résultats de Madras et Sezer (2010)), qui est ensuite comparée à une autre borne obtenue par Jovanovski et Madras (2014).

An upper bound on the Wasserstein distance to stationarity is developed for a class of Markov chains on . This result, which is a generalization of Diaconis et al.’s (2009) Theorem 2.2, is applied to a Gibbs sampler Markov chain that was introduced and analyzed by Jovanovski and Madras (2014). The resulting Wasserstein bound is converted into a total variation bound (using results from Madras and Sezer (2010)), and the total variation bound is compared to an alternative bound derived by Jovanovski and Madras (2014).

DOI : 10.5802/afst.1470
Hobert, James P. 1 ; Khare, Kshitij 1

1 Department of Statistics, University of Florida
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Hobert, James P.; Khare, Kshitij. Computable upper bounds on the distance to stationarity for Jovanovski and Madras’s Gibbs sampler. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 24 (2015) no. 4, pp. 935-947. doi : 10.5802/afst.1470. http://www.numdam.org/articles/10.5802/afst.1470/

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