{"paper":{"title":"Observed Fisher Information in hidden Markov models - Application to a noisy Gaussian random walk","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.CO","authors_text":"Alexandra Lefebvre, Gr\\'egory Nuel (LPSM (UMR\\_8001))","submitted_at":"2026-06-01T11:49:19Z","abstract_excerpt":"In this work we provide analytical and closed-form expressions for the exact computation of the score and the observed Fisher information matrix in a Gaussian random walk observed through Gaussian noise. Our method is based on the Oakes' identity and, as for the computation of the log-likelihood, its complexity in time is linear in the length of the sequence with the forward-backward (or Baum-Welch) algorithm. We illustrate the method over various simulation studies and provide parameter estimates computed with the Newton-Raphson algorithm along with confidence intervals."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.02118","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.02118/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}