{
  "abstract": "Structural ensemble refinement is widely used to integrate molecular simulations with experimental measurements. While most applications focus on the maximum-a-posteriori (MAP) ensemble, Bayesian sampling of the posterior distribution can provide uncertainty estimates and posterior averages for arbitrary observables. A notable step in this direction was introduced by the Bayesian Energy Landscape Tilting (BELT) framework, where sampling is performed on a family of maximum-entropy ensembles parametrized by Lagrange multipliers. Here, we show that Bayesian sampling in this setting requires an explicit choice of ensemble-counting measure. In particular, the flat measure in Lagrange-multiplier space used in the original BELT formulation leads to a posterior distribution that is formally non-normalizable for finite reference trajectories. We propose the Jeffreys measure as an invariant ensemble-counting prescription, restoring normalizability in the finite-sample situations considered here, and providing a consistent definition of posterior averages. Using both an analytically tractable Gaussian model and maximum-entropy refinement of RNA oligomer simulations, we compare different ensemble-counting measures and show that they can significantly affect Bayesian estimates. The resulting methodology has been implemented in the \\texttt{MDRefine} software package.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.18495",
  "author_total": 2,
  "authors": [
    {
      "name": "Ivan Gilardoni"
    },
    {
      "name": "Giovanni Bussi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ch0t46snxyvng.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.18495",
  "fulltext_url": null,
  "id": "ch0t46snxyvng",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.18495",
  "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",
      "physics.bio-ph"
    ],
    [
      "arxiv",
      "physics.chem-ph"
    ],
    [
      "arxiv",
      "physics.comp-ph"
    ],
    [
      "arxiv",
      "q-bio.BM"
    ],
    [
      "openalex",
      "1312|Protein Structure and Dynamics"
    ]
  ],
  "openalex": "W7165200475",
  "pdf_url": "https://arxiv.org/pdf/2606.18495",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ch0t46snxyvng.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:28:36Z",
      "native_id": "2606.18495",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.18495"
    }
  ],
  "subjects": [
    {
      "field": "biochemistry",
      "origin": "arxiv:q-bio.BM",
      "subfield": "biophysics"
    },
    {
      "field": "chemistry",
      "origin": "arxiv:physics.chem-ph",
      "subfield": "physical"
    },
    {
      "field": "physics",
      "origin": "arxiv:physics.bio-ph",
      "subfield": "biological-medical"
    },
    {
      "field": "physics",
      "origin": "arxiv:physics.comp-ph",
      "subfield": "computational"
    }
  ],
  "title": "Bayesian Sampling of Structural Ensembles: The Role of Ensemble-Counting Measures",
  "title_text": "Bayesian Sampling of Structural Ensembles: The Role of Ensemble-Counting Measures",
  "type": "preprint",
  "updated_at": "2026-10-30T12:28:41Z",
  "url": "https://research.draconitic.com/paper/ch0t46snxyvng",
  "venue": "arXiv",
  "versions": []
}