Which ergodic averages have finite asymptotic variance?

George Deligiannidis, Anthony Lee

Research output: Contribution to journalArticle (Academic Journal)

2 Citations (Scopus)
110 Downloads (Pure)

Abstract

We show that the class of L2 functions for which ergodic averages of a reversible Markov chain have finite asymptotic variance is determined by the class of L2 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 L2 functions of the primary variable in a pseudo-marginal Markov chain to have finite asymptotic variance.

Original languageEnglish
Pages (from-to)2309-2334
Number of pages26
JournalAnnals of Applied Probability
Volume28
Issue number4
Early online date9 Aug 2018
DOIs
Publication statusPublished - Aug 2018

Keywords

  • Asymptotic variance
  • Independent metropolis–Hastings
  • Jump chain
  • Markov chain monte carlo
  • Pseudo-marginal method

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