Electronic Journal of Statistics

Weighted batch means estimators in Markov chain Monte Carlo

Ying Liu and James M. Flegal

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This paper proposes a family of weighted batch means variance estimators, which are computationally efficient and can be conveniently applied in practice. The focus is on Markov chain Monte Carlo simulations and estimation of the asymptotic covariance matrix in the Markov chain central limit theorem, where conditions ensuring strong consistency are provided. Finite sample performance is evaluated through auto-regressive, Bayesian spatial-temporal, and Bayesian logistic regression examples, where the new estimators show significant computational gains with a minor sacrifice in variance compared with existing methods.

Article information

Electron. J. Statist., Volume 12, Number 2 (2018), 3397-3442.

Received: July 2017
First available in Project Euclid: 10 October 2018

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60J22: Computational methods in Markov chains [See also 65C40]
Secondary: 62F15: Bayesian inference

Batch means confidence regions covariance matrix estimation long run variance Markov chain Monte Carlo strong consistency

Creative Commons Attribution 4.0 International License.


Liu, Ying; Flegal, James M. Weighted batch means estimators in Markov chain Monte Carlo. Electron. J. Statist. 12 (2018), no. 2, 3397--3442. doi:10.1214/18-EJS1483. https://projecteuclid.org/euclid.ejs/1539137549

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