{"paper":{"title":"Markov Chain Monte Carlo confidence intervals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR","stat.TH"],"primary_cat":"math.ST","authors_text":"Yves F. Atchad\\'e","submitted_at":"2012-09-04T16:52:43Z","abstract_excerpt":"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 Gaussia"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.0703","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}