{
  "abstract": "Knowing that a response cannot be negative can inform predictive uncertainty, including extreme upper quantiles. This knowledge matters especially when a black-box system returns long vector responses at few covariate settings, leaving large uncertainty across many entries. We develop a framework that assembles predictive distributions feature by feature from distributional fits that incorporate nonnegativity, optionally around any given mean predictor. The fits come from a latent factor model that represents response intensity through nonnegative patterns whose amplitudes follow rectified Gaussian processes over covariates. A variational algorithm jointly learns the factorization and the latent posterior. Varying a conditional-dispersion parameter yields a spectrum of fits that show complementary strengths in estimating distributional shape features. An orthogonal quantile expansion motivates using L-moments or their ratios as features. We select a fit separately for each using scores computable from a single validation observation per entry, then assemble the selected estimates through the expansion. In simulations, this construction reduces extreme upper-quantile errors by 17-22% relative to the respective best single fit, despite the mode-seeking tendency of our variational inference. In a streamflow demonstration across agricultural catchments, using an external point simulation to supply the mean reduces miss rates of rare shortage by 86-91%.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.00695",
  "author_total": 1,
  "authors": [
    {
      "name": "Jialin Li"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/95r6jweksws3n.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.00695",
  "fulltext_url": null,
  "id": "95r6jweksws3n",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.00695",
  "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",
      "stat.ME"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.00695",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/95r6jweksws3n.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:21Z",
      "native_id": "2611.00695",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.00695"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ME",
      "subfield": "statistics"
    }
  ],
  "title": "Nonnegativity Shapes Predictive Uncertainty: Complementary Model Fits and Quantile Construction",
  "title_text": "Nonnegativity Shapes Predictive Uncertainty: Complementary Model Fits and Quantile Construction",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:35Z",
  "url": "https://research.draconitic.com/paper/95r6jweksws3n",
  "venue": "arXiv",
  "versions": []
}