{
  "abstract": "Tweedie's formula expresses a conditional mean in terms of a score function, and this connects score-driven models with Bayesian updating. We show that the score-driven update is identical to a Bayesian update in some special cases. More generally, we show that score-driven updating is a local approximation to Bayesian updating, with an error of second order in the predictive variance. The second-order approximation error has two components, one from the curvature of the log likelihood and one from the asymmetry of the posterior distribution. Implicit score-driven (ISD) updating, which evaluates the score at the updated parameter, corrects for the former but not the latter. A simple correction for the second component leads to an improved third-order approximation, which we denote ISD*. Numerical experiments show substantial gains from ISD and ISD*.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.15902",
  "author_total": 2,
  "authors": [
    {
      "name": "Peter Reinhard Hansen"
    },
    {
      "name": "Chen Tong"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6bbmgnnjfn13n.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.15902",
  "fulltext_url": null,
  "id": "6bbmgnnjfn13n",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.15902",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "econ.EM"
    ],
    [
      "arxiv",
      "stat.ME"
    ],
    [
      "openalex",
      "1702|Target Tracking and Data Fusion in Sensor Networks"
    ]
  ],
  "openalex": "W7161537488",
  "pdf_url": "https://arxiv.org/pdf/2605.15902",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6bbmgnnjfn13n.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:33:54Z",
      "native_id": "2605.15902",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.15902"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ME",
      "subfield": "statistics"
    }
  ],
  "title": "Tweedie's Formula and Score-Driven Updating",
  "title_text": "Tweedie's Formula and Score-Driven Updating",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:54Z",
  "url": "https://research.draconitic.com/paper/6bbmgnnjfn13n",
  "venue": "arXiv",
  "versions": []
}