Electronic Journal of Statistics

Weighted batch means estimators in Markov chain Monte Carlo

Ying Liu and James M. Flegal

Full-text: Open access

Abstract

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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1539137549

Digital Object Identifier
doi:10.1214/18-EJS1483

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

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

Rights
Creative Commons Attribution 4.0 International License.

Citation

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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