Markov Chain Monte Carlo confidence intervals

作者：Atchade Yves F^*

来源：Bernoulli, 2016, 22(3): 1808-1838.

DOI：10.3150/15-BEJ712

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

For a reversible and ergodic Markov chain {X-n, n >= 0} 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(2)(P)(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.

• 出版日期2016-8