{
  "abstract": "Fractional Brownian motion (fBM) is a model of anomalous diffusion parameterised by a Hurst exponent $H \\in (0,1)$ and a generalised diffusion coefficient $D_H > 0$. We jointly estimate $H$ and $D_H$ using maximum likelihood (MLE) from density measurements with Poisson counting noise and single-particle trajectory with Gaussian localisation error. We show that one density measurement in time cannot infer both $H$ and $D_H$ and that several time points are needed, which matters most for inference precision. For trajectories, we show that a neural network trained with a squared error loss approximates the posterior mean of $H$, which can be computed exactly at negligible cost. Paired with the profile-likelihood estimate of $D_H$, the posterior mean has the lowest root mean squared error in both $H$ and $D_H$, except near $H=0$ and $H=1$ where MLE estimates $H$ better. In vesicle trajectories from two cell types, $H$ and $D_H$ form a continuum rather than distinct modes of motion. The posterior probability that each window within a track is subdiffusive or superdiffusive shows that $26\\%$ of MRC5 fibroblast and $21\\%$ of HeLa vesicle trajectories contain both subdiffusive and superdiffusive windows, against $2\\%$ and $7\\%$ expected from estimation uncertainty alone. Intracellular cargoes therefore switch between subdiffusion and superdiffusion over time rather than forming populations with fixed $H$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.19888",
  "author_total": 3,
  "authors": [
    {
      "name": "Daniel S. Han"
    },
    {
      "name": "Vaishnavi Ananthanarayanan"
    },
    {
      "name": "Matthew J. Simpson"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8a24n5pqzszns.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.19888",
  "fulltext_url": null,
  "id": "8a24n5pqzszns",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.19888",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cond-mat.stat-mech"
    ],
    [
      "arxiv",
      "physics.bio-ph"
    ],
    [
      "arxiv",
      "q-bio.QM"
    ],
    [
      "arxiv",
      "stat.ME"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
    [
      "openalex",
      "2611|Fractional Differential Equations Solutions"
    ]
  ],
  "openalex": "W7221984926",
  "pdf_url": "https://arxiv.org/pdf/2610.19888",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8a24n5pqzszns.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:31Z",
      "native_id": "2610.19888",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.19888"
    }
  ],
  "subjects": [
    {
      "field": "biology",
      "origin": "arxiv:q-bio.QM",
      "subfield": "bioinformatics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ME",
      "subfield": "statistics"
    },
    {
      "field": "physics",
      "origin": "arxiv:physics.bio-ph",
      "subfield": "biological-medical"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Maximum likelihood, neural networks and posterior mean for inferring fractional Brownian motion parameters",
  "title_text": "Maximum likelihood, neural networks and posterior mean for inferring fractional Brownian motion parameters",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:42Z",
  "url": "https://research.draconitic.com/paper/8a24n5pqzszns",
  "venue": "arXiv",
  "versions": []
}