{"paper":{"title":"On Large Lag Smoothing for Hidden Markov Models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.ME","authors_text":"Ajay Jasra, Jeremie Houssineau, Sumeetpal S. Singh","submitted_at":"2018-04-19T12:41:28Z","abstract_excerpt":"In this article we consider the smoothing problem for hidden Markov models (HMM). Given a hidden Markov chain $\\{X_n\\}_{n\\geq 0}$ and observations $\\{Y_n\\}_{n\\geq 0}$, our objective is to compute $\\mathbb{E}[\\varphi(X_0,\\dots,X_k)|y_{0},\\dots,y_n]$ for some real-valued, integrable functional $\\varphi$ and $k$ fixed, $k \\ll n$ and for some realisation $(y_0,\\dots,y_n)$ of $(Y_0,\\dots,Y_n)$. We introduce a novel application of the multilevel Monte Carlo (MLMC) method with a coupling based on the Knothe-Rosenblatt rearrangement. We prove that this method can approximate the afore-mentioned quanti"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.07117","kind":"arxiv","version":1},"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"}