{"paper":{"title":"On the Poisson equation for Metropolis-Hastings chains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ME"],"primary_cat":"math.PR","authors_text":"Aleksandar Mijatovic, Jure Vogrinc","submitted_at":"2015-11-23T21:16:15Z","abstract_excerpt":"This paper defines an approximation scheme for a solution of the Poisson equation of a geometrically ergodic Metropolis-Hastings chain $\\Phi$. The approximations give rise to a natural sequence of control variates for the ergodic average $S_k(F)=(1/k)\\sum_{i=1}^{k} F(\\Phi_i)$, where $F$ is the force function in the Poisson equation. The main result of the paper shows that the sequence of the asymptotic variances (in the CLTs for the control-variate estimators) converges to zero and gives a rate of this convergence. Numerical examples in the case of a double-well potential are discussed."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.07464","kind":"arxiv","version":2},"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"}