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On the spectral analysis of second-order Markov chains

Persi DiaconisLaurent Miclo — 2013

Annales de la faculté des sciences de Toulouse Mathématiques

Second order Markov chains which are trajectorially reversible are considered. Contrary to the reversibility notion for usual Markov chains, no symmetry property can be deduced for the corresponding transition operators. Nevertheless and even if they are not diagonalizable in general, we study some features of their spectral decompositions and in particular the behavior of the spectral gap under appropriate perturbations is investigated. Our quantitative and qualitative results confirm that the...

Metropolis :

Gilles LebeauPersi Diaconis

Séminaire Équations aux dérivées partielles

Ceci n’est pas une œuvre de fiction. Cependant, toute ressemblance avec des théorèmes connus serait purement fortuite et le fruit du hasard.

Hit and run as a unifying device

Hans C. AndersenPersi Diaconis — 2007

Journal de la société française de statistique

We present a generalization of hit and run algorithms for Markov chain Monte Carlo problems that is ‘equivalent’ to data augmentation and auxiliary variables. These algorithms contain the Gibbs sampler and Swendsen-Wang block spin dynamics as special cases. The unification allows theorems, examples, and heuristics developed in one domain to illuminate parallel domains.

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