Bernoulli

  • Bernoulli
  • Volume 22, Number 3 (2016), 1808-1838.

Markov Chain Monte Carlo confidence intervals

Yves F. Atchadé

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Abstract

For a reversible and ergodic Markov chain $\{X_{n},n\geq0\}$ with invariant distribution $\pi$, we show that a valid confidence interval for $\pi(h)$ can be constructed whenever the asymptotic variance $\sigma^{2}_{P}(h)$ is finite and positive. We do not impose any additional condition on the convergence rate of the Markov chain. The confidence interval is derived using the so-called fixed-b lag-window estimator of $\sigma_{P}^{2}(h)$. We also derive a result that suggests that the proposed confidence interval procedure converges faster than classical confidence interval procedures based on the Gaussian distribution and standard central limit theorems for Markov chains.

Article information

Source
Bernoulli, Volume 22, Number 3 (2016), 1808-1838.

Dates
Received: February 2014
Revised: October 2014
First available in Project Euclid: 16 March 2016

Permanent link to this document
https://projecteuclid.org/euclid.bj/1458133000

Digital Object Identifier
doi:10.3150/15-BEJ712

Mathematical Reviews number (MathSciNet)
MR3474834

Zentralblatt MATH identifier
1345.60074

Keywords
Berry–Esseen bounds confidence interval lag-window estimators martingale approximation MCMC reversible Markov chains

Citation

Atchadé, Yves F. Markov Chain Monte Carlo confidence intervals. Bernoulli 22 (2016), no. 3, 1808--1838. doi:10.3150/15-BEJ712. https://projecteuclid.org/euclid.bj/1458133000


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