{"paper":{"title":"Non-asymptotic confidence intervals for MCMC in practice","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Benjamin M. Gyori, Daniel Paulin","submitted_at":"2012-12-10T10:04:20Z","abstract_excerpt":"Using concentration inequalities, we give non-asymptotic confidence intervals for estimates obtained by Markov chain Monte Carlo (MCMC) simulations, when using the approximation $\\mathbb{E}_{\\pi} f\\approx (1/(N-t_0))\\cdot \\sum_{i=t_0+1}^N f(X_i)$. To allow the application of non-asymptotic error bounds in practice, here we state bounds formulated in terms of the spectral properties of the chain and the properties of $f$ and propose estimators of the parameters appearing in the bounds, including the spectral gap, mixing time, and asymptotic variance. We introduce a method for setting the burn-i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.2016","kind":"arxiv","version":6},"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"}