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Existing uncertainty quantification (UQ) methods often rely on unverifiable assumptions and produce miscalibrated intervals. This paper evaluates conformal prediction (CP) as a distribution-free framework for generating prediction intervals with rigorous coverage guarantees. Using a large-scale dataset from Southeastern Railway in the UK, we show that UQ methods such as quantile regression (QR), Monte Carlo dropout and deep ensembles (DE) frequently under- or over-cover nominal levels. By contrast, CP corrects miscalibration across models, ensuring valid marginal coverage. Conformalized QR (CQR) achieves the best efficiency by producing adaptively sized intervals while maintaining calibration. To address heterogeneity across stations, we apply Mondrian CP (MCP), which enforces conditional coverage within strata. Empirical results confirm MCP delivers reliable intervals for each subgroup. Our work demonstrates that CP is a model-agnostic, robust framework for trustworthy UQ, offering a practical pathway to reliable risk assessment in transportation and other high-stakes domains.<\/jats:p>\n                  <jats:p>This article is part of the theme issue \u2018Advancing uncertainty quantification in AI systems\u2019.<\/jats:p>","DOI":"10.1098\/rsta.2025.0075","type":"journal-article","created":{"date-parts":[[2026,8,27]],"date-time":"2026-08-27T08:08:03Z","timestamp":1787818083000},"source":"Crossref","is-referenced-by-count":1,"title":["Uncertainty quantification in train delay prediction with conformal prediction"],"prefix":"10.1098","volume":"384","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0711-8039","authenticated-orcid":false,"given":"Rui","family":"Luo","sequence":"first","affiliation":[{"name":"Department of Systems Engineering, City University of Hong Kong 1 , Hong Kong"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0002-5058-1520","authenticated-orcid":false,"given":"Xiaoyi","family":"Su","sequence":"additional","affiliation":[{"name":"Department of Systems Engineering, City University of Hong Kong 1 , Hong Kong"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6198-9295","authenticated-orcid":false,"given":"Khuong An","family":"Nguyen","sequence":"additional","affiliation":[{"name":"Department of Computer Science, Royal Holloway University of London 2 , Egham, UK"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"175","published-online":{"date-parts":[[2026,8,27]]},"reference":[{"key":"2026082704075616200_bib1","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.tra.2015.05.005","article-title":"Drivers of customer satisfaction with public transport services","volume":"78","author":"Mouwen","year":"2015","journal-title":"Transp. 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