{
  "abstract": "Held-out log-likelihood is the standard currency for comparing statistical models of neural spike trains, and is often reported as bits per spike relative to a homogeneous Poisson baseline. The units of this metric are difficult to reason about: it is rarely obvious whether an improvement of, say, $0.34$ bits per spike is a large effect or a negligible one. This note develops an interpretation of held-out log-likelihood borrowed from game-theoretic statistics. If $L$ denotes a model's expected log-likelihood ratio to the homogeneous Poisson baseline, then we show that $-\\log(α) / L$ represents the number of heldout time bins of recording needed to reject the baseline at level $α$ under a particular null hypothesis testing procedure based on a betting game. Thus, a simple re-scaling of the log-likelihood yields an intuitive metric of model performance in units of recording time which answers \"how much held out data would I need, on average, to disprove the null.\" We illustrate the construction on head-direction cells recorded in mouse anterior thalamus, where a generalized linear model reaches significance in roughly $120$ ms of held-out data for a strongly tuned cell and roughly $11$ s for a moderately tuned cell.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.28779",
  "author_total": 1,
  "authors": [
    {
      "name": "Alex H. Williams"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1kz0w6w4e5tns.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.28779",
  "fulltext_url": null,
  "id": "1kz0w6w4e5tns",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.28779",
  "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",
      "q-bio.NC"
    ],
    [
      "arxiv",
      "stat.ME"
    ],
    [
      "openalex",
      "2805|Neural dynamics and brain function"
    ]
  ],
  "openalex": "W7172314442",
  "pdf_url": "https://arxiv.org/pdf/2607.28779",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1kz0w6w4e5tns.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:29Z",
      "native_id": "2607.28779",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.28779"
    }
  ],
  "subjects": [
    {
      "field": "biology",
      "origin": "arxiv:q-bio.NC",
      "subfield": "neuroscience"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ME",
      "subfield": "statistics"
    }
  ],
  "title": "Bits per Spike as a Betting Game: An Interpretable Unit for Held-Out Log-Likelihood in Neural Data Analysis",
  "title_text": "Bits per Spike as a Betting Game: An Interpretable Unit for Held-Out Log-Likelihood in Neural Data Analysis",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:34Z",
  "url": "https://research.draconitic.com/paper/1kz0w6w4e5tns",
  "venue": "arXiv",
  "versions": []
}