On WAIC for Dependent Data: A Covariance-Corrected Framework with Linear-Time Complexity

[2608.14895] On WAIC for Dependent Data: A Covariance-Corrected Framework with Linear-Time Complexity Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Statistics > Methodology arXiv:2608.14895 (stat) [Submitted on 14 Aug 2026] Title: On WAIC for Dependent Data: A Covariance-Corrected Framework with Linear-Time Complexity Authors: Safaa K. Kadhem View a PDF of the paper titled On WAIC for Dependent Data: A Covariance-Corrected Framework with Linear-Time Complexity, by Safaa K. Kadhem View PDF HTML (experimental) Abstract: The Widely Applicable Information Criterion (WAIC) is a cornerstone of Bayesian model selection, but its conditional independence assumption renders it inappropriate for sequential and spatially correlated data - a limitation that leads to systematically underestimated model complexity and over-optimistic predictive assessments. We introduce CC-WAIC, a principled generalization of WAIC that explicitly incorporates the full posterior covariance structure of log-likelihood contributions. CC-WAIC reduces exactly to WAIC when independence holds, making it a natural extension rather than an ad-hoc modification. To overcome the prohibitive computational cost of the full covariance matrix, we develop a linear-time implementation using a banded covariance approximation that reduces complexity, with theoretical guarantees on the approximation error. We further introduce an effective sample size correction to mitigate finite-sample bias in MCMC estimation. Through extensive simulations on Hidden Markov Models and real-world applications to Old Faithful geyser data and S&P 500 volatility modelling, we demonstrate that CC-WAIC substantially outperforms WAIC, LOO-CV, iWAIC, and WAICNF, particularly under strong temporal dependence and limited sample sizes. The proposed criterion offers a computationally scalable and theoretically grounded tool for Bayesian model selection in the dependent data settings that are ubiquitous across modern science. Limitations include reliance on exponential mixing and exact conditional likelihoods; extensions to long-memory processes and approximate inference are discussed. Subjects: Methodology (stat.ME) Cite as: arXiv:2608.14895 [stat.ME] (or arXiv:2608.14895v1 [stat.ME] for this version) https://doi.org/10.48550/arXiv.2608.14895 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Safaa Kadhem [ view email ] [v1] Fri, 14 Aug 2026 21:02:01 UTC (426 KB) Full-text links: Access Paper: View a PDF of the paper titled On WAIC for Dependent Data: A Covariance-Corrected Framework with Linear-Time Complexity, by Safaa K. Kadhem View PDF HTML (experimental) TeX Source view license Current browse context: stat.ME < prev | next > new | recent | 2026-08 Change to browse by: stat References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

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