Journal article
Which ergodic averages have finite asymptotic variance?
- 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.
- Publication status:
- Published
- Peer review status:
- Peer reviewed
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(Preview, Version of record, pdf, 264.3KB, Terms of use)
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- Publisher copy:
- 10.1214/17-AAP1358
Authors
+ Engineering and Physical Sciences Research Council
More from this funder
- Funding agency for:
- Lee, A
- Grant:
- EP/N510129/1
- Publisher:
- Institute of Mathematical Statistics
- Journal:
- Annals of Applied Probability More from this journal
- Volume:
- 28
- Issue:
- 4
- Pages:
- 2309-2334
- Publication date:
- 2018-08-09
- Acceptance date:
- 2017-09-27
- DOI:
- ISSN:
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1050-5164
- Keywords:
- Pubs id:
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pubs:844674
- UUID:
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uuid:5dadc546-389b-45f8-aab8-f1c31e993b2d
- Local pid:
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pubs:844674
- Source identifiers:
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844674
- Deposit date:
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2018-04-28
Terms of use
- Copyright holder:
- Institute of Mathematical Statistics
- Copyright date:
- 2018
- Notes:
- © Institute of Mathematical Statistics, 2018. This is the publisher's version of the article. The final version is available online from Institute of Mathematical Statistics at: 10.1214/17-AAP1358
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