{
  "abstract": "We study signal prediction and smoothing in hidden Markov models whose latent signal is a multi-type Wright-Fisher diffusion and whose discrete-time observations are categorical. We consider a repeated-sampling regime with finitely many inspection times and large within-time samples. Under neutrality and parent-independent mutation, the Bayesian predictive and smoothing laws admit exact representations as mixtures of Dirichlet distributions. We show that the one-step predictive and local smoothing laws converge in total variation to the corresponding Wright-Fisher transition and bridge laws determined by the neighboring population frequencies, thereby justifying plug-in approximations based on empirical proportions. For prediction, we derive explicit finite-sample bounds for this approximation and for bounded predictive functionals such as diversity, together with a finite-sample concentration bound for the marginal smoother. The joint posterior at the inspection times concentrates at the target frequencies and satisfies a Bernstein-von Mises limit with distinct interior and boundary regimes, with Gaussian and Gamma limits on different scales. The results allow arbitrary dependence across inspection times. A key technical ingredient is a fixed-interval tail bound for the coalescent-based dual death process.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.22444",
  "author_total": 4,
  "authors": [
    {
      "name": "Luigi M. Malgieri"
    },
    {
      "name": "Filippo Ascolani"
    },
    {
      "name": "Matteo Giordano"
    },
    {
      "name": "Matteo Ruggiero"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dshtt90p0b4h2.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.22444",
  "fulltext_url": null,
  "id": "dshtt90p0b4h2",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.22444",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
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  "metadata_licence": "CC0-1.0",
  "native_subjects": [
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      "arxiv",
      "math.PR"
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      "arxiv",
      "math.ST"
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    [
      "arxiv",
      "q-bio.PE"
    ],
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      "2610|Stochastic processes and statistical mechanics"
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  "openalex": "W7214129260",
  "pdf_url": "https://arxiv.org/pdf/2609.22444",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dshtt90p0b4h2.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:53Z",
      "native_id": "2609.22444",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.22444"
    }
  ],
  "subjects": [
    {
      "field": "biology",
      "origin": "arxiv:q-bio.PE",
      "subfield": "evolutionary-biology"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "Asymptotics and finite sample bounds for prediction and smoothing in Wright-Fisher hidden Markov models",
  "title_text": "Asymptotics and finite sample bounds for prediction and smoothing in Wright-Fisher hidden Markov models",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:59Z",
  "url": "https://research.draconitic.com/paper/dshtt90p0b4h2",
  "venue": "arXiv",
  "versions": []
}