{
  "abstract": "We study how the response of a Bayesian posterior statistic to future observations changes as information accumulates. For a non-decreasing function $T$, define $Π_n^T=\\E[T(Θ)\\vert \\mathcal F_n]$, where $Θ$ has an arbitrary prior and the observations come from a one-parameter exponential family. Conditioning on the same current value of $Π^T$, we show that the posterior statistic after additional observations is larger in convex order when the current posterior is based on fewer observations. We also prove preservation of convexity: the expected value of a convex function of the future posterior statistic is convex in the current posterior statistic. Together, these two properties provide structural tools for establishing time-monotonicity results in dynamic Bayesian decision and optimal stopping problems. If the exponential family contains an infinitely divisible distribution, the results extend to a continuous-time observation model through a family of Lévy processes.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.05065",
  "author_total": 2,
  "authors": [
    {
      "name": "Erhan Bayraktar"
    },
    {
      "name": "Yuqiong Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8tcw6wqax0jb0.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.05065",
  "fulltext_url": null,
  "id": "8tcw6wqax0jb0",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.05065",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.PR"
    ],
    [
      "arxiv",
      "math.ST"
    ],
    [
      "arxiv",
      "stat.TH"
    ],
    [
      "openalex",
      "2613|Probability and Statistical Research"
    ]
  ],
  "openalex": "W7211871477",
  "pdf_url": "https://arxiv.org/pdf/2609.05065",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8tcw6wqax0jb0.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:18Z",
      "native_id": "2609.05065",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.05065"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "Convex order and preservation of convexity for Bayesian posterior updates",
  "title_text": "Convex order and preservation of convexity for Bayesian posterior updates",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:25Z",
  "url": "https://research.draconitic.com/paper/8tcw6wqax0jb0",
  "venue": "arXiv",
  "versions": []
}