{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,27]],"date-time":"2025-11-27T10:55:16Z","timestamp":1764240916816,"version":"3.46.0"},"reference-count":24,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2025,11,27]],"date-time":"2025-11-27T00:00:00Z","timestamp":1764201600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Information"],"abstract":"<jats:p>Exchangeability is a foundational concept in Bayesian statistics, crucial for ensuring the validity and generalizability of inferences from experimental data. This paper presents a theoretical and computational framework for understanding the role of exchangeability in the reliability of scientific conclusions, with specific reference to psychology, neuroimaging, and clinical trials. We build on de Finetti\u2019s representation theorem to show how exchangeability enables using hierarchical Bayesian models, and we analyze how its violation can lead to interpretative errors and paradoxes, such as Simpson\u2019s Paradox. In addition to theoretical discussion, we present practical strategies to evaluate and enforce exchangeability, including randomization, matching, stratification, and hierarchical modeling. We also introduce computational tools\u2014such as the Shuffle Test and Stratified Bootstrap\u2014to empirically test for exchangeability and detect latent structures in the data. The novelty of this work lies in unifying theoretical reasoning and empirical testing within a single framework that bridges de Finetti\u2019s representation theorem and resampling-based diagnostics. By providing concrete tools to evaluate exchangeability prior to model fitting, the proposed approach introduces a pre-analysis verification step that strengthens the reliability and transparency of Bayesian inference. Our results emphasize that exchangeability is not merely a technical assumption, but a structural property that governs the coherence and informational integrity of the data. This framework provides both conceptual clarity and operational tools for researchers aiming to perform robust Bayesian inference in complex and heterogeneous datasets.<\/jats:p>","DOI":"10.3390\/info16121034","type":"journal-article","created":{"date-parts":[[2025,11,27]],"date-time":"2025-11-27T10:25:16Z","timestamp":1764239116000},"page":"1034","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Exchangeability and Bayesian Inference: A Theoretical and Computational Framework for Reliable Experimental Data Analysis"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0822-862X","authenticated-orcid":false,"given":"Tommaso","family":"Costa","sequence":"first","affiliation":[{"name":"GCS-fMRI, Koelliker Hospital and Department of Psychology, University of Turin, 10124 Turin, Italy"},{"name":"FOCUS Laboratory, Department of Psychology, University of Turin, 10124 Turin, Italy"},{"name":"Neuroscience Institute of Turin (NIT), 10124 Turin, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mario","family":"Ferraro","sequence":"additional","affiliation":[{"name":"GCS-fMRI, Koelliker Hospital and Department of Psychology, University of Turin, 10124 Turin, Italy"},{"name":"FOCUS Laboratory, Department of Psychology, University of Turin, 10124 Turin, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,11,27]]},"reference":[{"key":"ref_1","unstructured":"Anderson, C. (2025, November 17). The end of theory: The data deluge makes the scientific method obsolete. Wired Magazine, 23 June 2008, pp. 16\u201317. Available online: https:\/\/www.wired.com\/2008\/06\/pb-theory\/."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1016\/j.spl.2018.02.016","article-title":"Statistics for big data: A perspective","volume":"136","year":"2018","journal-title":"Stat. Probab. Lett."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Open Science Collaboration (2015). Estimating the reproducibility of psychological science. Science, 349, aac4716.","DOI":"10.1126\/science.aac4716"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"84","DOI":"10.1038\/s41586-020-2314-9","article-title":"Variability in the analysis of a single neuroimaging dataset by many teams","volume":"582","author":"Holzmeister","year":"2020","journal-title":"Nature"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Ioannidis, J.P.A. (2005). Why most published research findings are false. PLoS Med., 2.","DOI":"10.1371\/journal.pmed.0020124"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1359","DOI":"10.1177\/0956797611417632","article-title":"False-positive psychology: Undisclosed flexibility in data collection and analysis allows presenting anything as significant","volume":"22","author":"Simmons","year":"2011","journal-title":"Psychol. Sci."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"0021","DOI":"10.1038\/s41562-016-0021","article-title":"A manifesto for reproducible science","volume":"1","author":"Nosek","year":"2017","journal-title":"Nat. Hum. Behav."},{"key":"ref_8","first-page":"251","article-title":"Funzione caratteristica di un fenomeno aleatorio","volume":"4","year":"1931","journal-title":"Atti Della R. Accad. Naz. Dei Lincei"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"745","DOI":"10.1214\/aop\/1176994663","article-title":"Finite exchangeable sequences","volume":"8","author":"Diaconis","year":"1980","journal-title":"Ann. Probab."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Aldous, D.J. (1985). Exchangeability and Related Topics, Springer. Lecture Notes in Mathematics.","DOI":"10.1007\/BFb0099421"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Gelman, A., and Hill, J. (2007). Data Analysis Using Regression and Multilevel\/Hierarchical Models, Cambridge University Press.","DOI":"10.32614\/CRAN.package.arm"},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Kruschke, J.K. (2014). Doing Bayesian Data Analysis: A Tutorial with R, JAGS, and Stan, Academic Press. [2nd ed.].","DOI":"10.1016\/B978-0-12-405888-0.00008-8"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"6841","DOI":"10.1103\/PhysRevE.52.6841","article-title":"Estimating functions of probability distributions from a finite set of samples","volume":"52","author":"Wolpert","year":"1995","journal-title":"Phys. Rev. E"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1264","DOI":"10.1080\/01621459.2018.1491403","article-title":"Invariant causal prediction for sequential data","volume":"114","author":"Pfister","year":"2019","journal-title":"J. Am. Stat. Assoc."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1584","DOI":"10.1002\/sim.5686","article-title":"Methods for dealing with time-dependent confounding","volume":"32","author":"Daniel","year":"2013","journal-title":"Stat. Med."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Gelman, A., Carlin, J.B., Stern, H.S., and Rubin, D.B. (2013). Bayesian Data Analysis, CRC Press. [3rd ed.].","DOI":"10.1201\/b16018"},{"key":"ref_17","first-page":"333","article-title":"On individual risk","volume":"194","author":"Dawid","year":"2013","journal-title":"Synthese"},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Efron, B., and Tibshirani, R.J. (1993). An Introduction to the Bootstrap, Chapman & Hall\/CRC.","DOI":"10.1007\/978-1-4899-4541-9"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1093\/biomet\/70.1.41","article-title":"The central role of the propensity score in observational studies for causal effects","volume":"70","author":"Rosenbaum","year":"1983","journal-title":"Biometrika"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"238","DOI":"10.1111\/j.2517-6161.1951.tb00088.x","article-title":"The interpretation of interaction in contingency tables","volume":"13","author":"Simpson","year":"1951","journal-title":"J. R. Stat. Soc. Ser. B (Methodol.)"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"364","DOI":"10.1080\/01621459.1972.10482387","article-title":"On Simpson\u2019s Paradox and the Sure-Thing Principle","volume":"67","author":"Blyth","year":"1972","journal-title":"J. Am. Stat. Assoc."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Pearl, J. (2009). Causality: Models, Reasoning, and Inference, Cambridge University Press.","DOI":"10.1017\/CBO9780511803161"},{"key":"ref_23","unstructured":"De Finetti, B. (1974). Theory of Probability: A Critical Introductory Treatment (Vol. 1 & 2), Wiley."},{"key":"ref_24","first-page":"111","article-title":"The concept of exchangeability and its applications","volume":"4","author":"Bernardo","year":"1996","journal-title":"Far East J. Math. Sci."}],"container-title":["Information"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2078-2489\/16\/12\/1034\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,11,27]],"date-time":"2025-11-27T10:48:53Z","timestamp":1764240533000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2078-2489\/16\/12\/1034"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,11,27]]},"references-count":24,"journal-issue":{"issue":"12","published-online":{"date-parts":[[2025,12]]}},"alternative-id":["info16121034"],"URL":"https:\/\/doi.org\/10.3390\/info16121034","relation":{},"ISSN":["2078-2489"],"issn-type":[{"value":"2078-2489","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,11,27]]}}}