Open Access
2015 Spectral bounds for certain two-factor non-reversible MCMC algorithms
Jeffrey Rosenthal, Peter Rosenthal
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Electron. Commun. Probab. 20: 1-10 (2015). DOI: 10.1214/ECP.v20-4528


We prove that the Markov operator corresponding to the two-variable, non-reversible Gibbs sampler has spectrum which is entirely real and non-negative, thus providing a first step towards the spectral analysis of MCMC algorithms in the non-reversible case. We also provide an extension to Metropolis-Hastings components, and connect the spectrum of an algorithm to the spectrum of its marginal chain.


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Jeffrey Rosenthal. Peter Rosenthal. "Spectral bounds for certain two-factor non-reversible MCMC algorithms." Electron. Commun. Probab. 20 1 - 10, 2015.


Accepted: 4 December 2015; Published: 2015
First available in Project Euclid: 7 June 2016

zbMATH: 1333.60165
MathSciNet: MR3434208
Digital Object Identifier: 10.1214/ECP.v20-4528

Primary: 60J05
Secondary: 47N30

Keywords: convergence rate , Gibbs sampler , marginal chain , MCMC algorithm , Metropolis-Hastings algorithm , non-reversible , operator , spectrum

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