## Bernoulli

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

### Markov Chain Monte Carlo confidence intervals

#### 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
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

#### 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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