{
  "abstract": "Data augmentation is now a standard device across capture--recapture and occupancy analysis: adding a fixed number M of all-zero encounter histories replaces a model of unknown dimension with one of fixed dimension. Although M is often treated as a computational tuning choice, it also specifies a finite superpopulation and hence a binomial support constraint on the number of undetected individuals. In a Bayesian implementation that constraint appears as an induced prior; in a likelihood implementation it is the same finite-support assumption reached by another route. That the Bernoulli specification for the inclusion indicators induces a binomial prior on abundance is established (Schofield & Barker 2014); our concern is what that choice costs in estimated uncertainty. We develop the argument using a simple closed-population abundance estimation problem. We show that augmented occupancy and Huggins conditional-likelihood analyses give numerically identical point estimates of N once M is sufficiently large. Their uncertainty estimates, however, need not agree. We distinguish two sources of discrepancy. First, when M is small relative to the number of undetected individuals, the finite binomial ceiling truncates the likelihood or posterior and suppresses uncertainty. Second, once that ceiling no longer binds, Taylor-series (Delta-method) approximations still understate variance, because the quantity of interest is a strongly non-linear function of the estimated parameters and local linearization does not reproduce its curvature. Gauss-Hermite quadrature on the unconstrained logit scale recovers much of the shortfall and approaches the MCMC posterior benchmark, though a small residual remains that does not close as M grows, reflecting the distinction between asymptotic likelihood theory and finite-sample Bayesian inference. Neither mechanism is peculiar to abundance estimation: the first follows from the augmented representation itself, the second from any derived quantity that is a non-linear function of estimated parameters. We close with framework-specific guidance for choosing M.",
  "abstract_shown": true,
  "affiliations": [
    "Cornell University"
  ],
  "article_type": "New results",
  "arxiv": null,
  "author_total": 3,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "E. G. Cooch"
    },
    {
      "name": "D. I. MacKenzie"
    },
    {
      "name": "J. A. Royle"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/btrbd3gess388.bib",
  "cited_by": 0,
  "doi": "10.64898/2026.08.31.748288",
  "fulltext_url": "https://www.biorxiv.org/content/10.64898/2026.08.31.748288v1.full",
  "id": "btrbd3gess388",
  "issns": [],
  "landing_url": "https://www.biorxiv.org/content/10.64898/2026.08.31.748288v1",
  "language": null,
  "licence": "CC-BY",
  "licence_label": "CC BY",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "biorxiv",
      "ecology"
    ],
    [
      "openalex",
      "2613|Census and Population Estimation"
    ]
  ],
  "openalex": "W7204939641",
  "pdf_url": "https://www.biorxiv.org/content/10.64898/2026.08.31.748288v1.full.pdf",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-31",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/btrbd3gess388.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:23Z",
      "native_id": "10.64898/2026.08.31.748288",
      "source": "biorxiv",
      "url": "https://www.biorxiv.org/content/10.64898/2026.08.31.748288v1"
    }
  ],
  "subjects": [
    {
      "field": "biology",
      "origin": "biorxiv:ecology",
      "subfield": "ecology"
    }
  ],
  "title": "The Hidden Prior: Variance Constraints Under Data Augmentation",
  "title_text": "The Hidden Prior: Variance Constraints Under Data Augmentation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:23Z",
  "url": "https://research.draconitic.com/paper/btrbd3gess388",
  "venue": "bioRxiv",
  "versions": []
}