{
  "abstract": "End-to-end digital twins can be constructed by fitting separate stage models and connecting them after inference. We investigate the Frequentist prediction properties of a commonly used Monte Carlo simulation scheme that forwards complete predictive draws through such a chain when measured stage outputs contain independent normal errors, but the latent stage means are deterministic. Analytical two-stage examples show persistent asymptotic interval and coverage inflation and, with quadratic propagation, mean bias dependent on the parameters to be estimated. Simulations of four- and eight-stage linear-quadratic univariate chains with 7, 15 or 30 training runs demonstrate pronounced input-dependent distortions. A diagnostic using error-free latent training predictors shows that the effect is mainly not attributable to errors in variables, but to the MCSim approach even showing underestimation of coverage. We propose a model-based bootstrap: an initial chain forwards fitted means, bootstrap chains are refitted on fixed-center bootstrap data while forwarding their mean prediction, and a target-stage future error enters a studentized prediction root. Across the investigated scenarios, relative mean bias is substantially reduced, and coverage is closer to the nominal 90%. At sample size 30, the eight-stage bootstrap has mean width ratios of 1.16-1.42 relative to the known-parameter normal reference, compared with 4.11-4.97 for observed-to-observed MCSim. These results support improved endpoint prediction in the tested setting. Further investigations of the bootstrap scheme in the supplement for a bivariate 6-stage process show similar satisfactory results.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.05225",
  "author_total": 3,
  "authors": [
    {
      "name": "Lukas Madenach"
    },
    {
      "name": "Timo Bailer"
    },
    {
      "name": "Tobias Eilert"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/322qbvxer9yss.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.05225",
  "fulltext_url": null,
  "id": "322qbvxer9yss",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.05225",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.LG"
    ],
    [
      "arxiv",
      "stat.ME"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.05225",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/322qbvxer9yss.ris",
  "sources": [
    {
      "first_seen": "2026-11-04T15:21:34Z",
      "native_id": "2611.05225",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.05225"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ME",
      "subfield": "statistics"
    }
  ],
  "title": "Post-Inference Model Chaining: A Problem Statement and a Model-based Bootstrap for Training End-to-End Digital Twins",
  "title_text": "Post-Inference Model Chaining: A Problem Statement and a Model-based Bootstrap for Training End-to-End Digital Twins",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:44Z",
  "url": "https://research.draconitic.com/paper/322qbvxer9yss",
  "venue": "arXiv",
  "versions": []
}