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August 2018 Which ergodic averages have finite asymptotic variance?
George Deligiannidis, Anthony Lee
Ann. Appl. Probab. 28(4): 2309-2334 (August 2018). DOI: 10.1214/17-AAP1358


We show that the class of $L^{2}$ functions for which ergodic averages of a reversible Markov chain have finite asymptotic variance is determined by the class of $L^{2}$ functions for which ergodic averages of its associated jump chain have finite asymptotic variance. This allows us to characterize completely which ergodic averages have finite asymptotic variance when the Markov chain is an independence sampler. From a practical perspective, the most important result identifies a simple sufficient condition for all ergodic averages of $L^{2}$ functions of the primary variable in a pseudo-marginal Markov chain to have finite asymptotic variance.


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George Deligiannidis. Anthony Lee. "Which ergodic averages have finite asymptotic variance?." Ann. Appl. Probab. 28 (4) 2309 - 2334, August 2018.


Received: 1 July 2016; Revised: 1 May 2017; Published: August 2018
First available in Project Euclid: 9 August 2018

zbMATH: 06974752
MathSciNet: MR3843830
Digital Object Identifier: 10.1214/17-AAP1358

Primary: 60F05 , 60J05 , 60J22 , 65C40

Keywords: asymptotic variance , independent Metropolis–Hastings , jump chain , Markov chain Monte Carlo , pseudo-marginal method

Rights: Copyright © 2018 Institute of Mathematical Statistics


Vol.28 • No. 4 • August 2018
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