{
  "abstract": "Conditional generative models, including diffusion models and ensemble forecasters, often produce predictive samples without a tractable likelihood representation. Such sample-based predictive distributions can be systematically biased and poorly calibrated. We propose bias-corrected conformal probability integral transform (PIT) calibration, a split-sample post-processing framework that outputs a calibrated predictive distribution rather than a single fixed-level prediction interval. The method first estimates an affine location-scale correction on a held-out bias split, then calibrates randomized PIT values using a conformal calibrator. The resulting predictive law is represented as a weighted empirical distribution on the generator order statistics, enabling the direct computation of threshold-coherent exceedance probabilities, arbitrary quantiles, highest-density intervals, expected tail losses, and calibrated resamples. In contrast, standard conformal prediction primarily provides fixed-level prediction sets or threshold decisions and does not directly estimate predictive probabilities or high-density regions. We establish finite-sample calibration in probability under exchangeability and show how an optional split-conformal wrapper based on a PIT-centrality score gives nested prediction intervals with finite-sample marginal coverage at user-specified levels. Simulation studies with controlled misspecification and a WeatherBench-2 precipitation-forecasting application demonstrate substantial improvements in probabilistic calibration and downstream distributional summaries relative to uncalibrated sample-based forecasts and interval-only conformal baselines.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.19035",
  "author_total": 4,
  "authors": [
    {
      "name": "Wen-Ting Wang"
    },
    {
      "name": "ShengLi Tzeng"
    },
    {
      "name": "Yu-Ting Fan"
    },
    {
      "name": "Hsin-Cheng Huang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0rjvt5ykjq6h0.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.19035",
  "fulltext_url": null,
  "id": "0rjvt5ykjq6h0",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.19035",
  "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",
      "stat.ME"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2609.19035",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0rjvt5ykjq6h0.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:10Z",
      "native_id": "2609.19035",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.19035"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ME",
      "subfield": "statistics"
    }
  ],
  "title": "Calibrated Predictive Distributions from Sample-Based Generators",
  "title_text": "Calibrated Predictive Distributions from Sample-Based Generators",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:10Z",
  "url": "https://research.draconitic.com/paper/0rjvt5ykjq6h0",
  "venue": "arXiv",
  "versions": []
}