{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,3]],"date-time":"2026-09-03T08:52:53Z","timestamp":1788425573682,"version":"build-2803163510"},"reference-count":34,"publisher":"The Econometric Society","issue":"3","funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100007229","name":"Harvard University","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100007229","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100007229","name":"Harvard University","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100007229","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100006919","name":"Massachusetts Institute of Technology","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100006919","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004721","name":"University of Tokyo","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100004721","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100005595","name":"University of California","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100005595","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100013729","name":"International Association for Applied Econometrics","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100013729","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100005326","name":"Yale University","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100005326","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["ECTA"],"abstract":"<jats:p>\n                    We cast the problem of communicating scientific uncertainty as one of reporting a posterior distribution on an unknown parameter to an audience of Bayesian decision\u2010makers. We establish novel bounds on the audience's regret when the analyst reports an approximation to a posterior that the audience treats as exact. Under a palatable restriction on the audience's decision problems, the bounds take an especially convenient form. Under a further restriction on the audience's priors, a bootstrap distribution can be used as a stand\u2010in posterior. We propose a practical recipe for checking whether a conventional statistical report (say, a normal parameterized by a point estimate and standard error) is a good approximation, and for improving the report if it is not. We illustrate our proposals using the articles in the 2021\n                    <jats:italic>American Economic Review<\/jats:italic>\n                    that use a bootstrap for inference.\n                  <\/jats:p>","DOI":"10.3982\/ecta22613","type":"journal-article","created":{"date-parts":[[2026,6,2]],"date-time":"2026-06-02T09:09:52Z","timestamp":1780391392000},"page":"843-875","source":"Crossref","is-referenced-by-count":2,"title":["Communicating Scientific Uncertainty via Approximate Posteriors"],"prefix":"10.3982","volume":"94","author":[{"given":"Isaiah","family":"Andrews","sequence":"first","affiliation":[{"name":"MIT"},{"name":"NBER"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jesse M.","family":"Shapiro","sequence":"additional","affiliation":[{"name":"Harvard University"},{"name":"NBER"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"2359","published-online":{"date-parts":[[2026]]},"reference":[{"key":"ecta70042-bib-0001","unstructured":"Andrews, Isaiah and Jesse Shapiro (2025), \u201cBootstrap Census.\u201d Zenodo. https:\/\/doi.org\/10.5281\/zenodo.17085552."},{"key":"ecta70042-bib-0002","doi-asserted-by":"crossref","unstructured":"Andrews, Isaiah and Jesse M. Shapiro (2026), \u201cSupplement to \u2018Communicating Scientific Uncertaintyvia Approximate Posteriors\u2019.\u201d Econometrica Supplemental Material, 94, https:\/\/doi.org\/10.3982\/ECTA22613.","DOI":"10.3982\/ECTA22613"},{"issue":"5","key":"ecta70042-bib-0003","doi-asserted-by":"crossref","first-page":"2117","DOI":"10.3982\/ECTA18155","volume":"89","author":"Andrews","year":"2021","journal-title":"Econometrica"},{"issue":"1","key":"ecta70042-bib-0004","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1002\/jae.2843","volume":"37","author":"Angelini","year":"2022","journal-title":"Journal of Applied Econometrics"},{"issue":"2","key":"ecta70042-bib-0005","doi-asserted-by":"crossref","DOI":"10.1016\/j.jeconom.2023.105604","volume":"238","author":"Angelini","year":"2024","journal-title":"Journal of Econometrics"},{"key":"ecta70042-bib-0006","unstructured":"Athey, Susan and Guido W. Imbens (2023), \u201cIn Search of the Third Number: What to Report Beyond Point Estimates and Standard Errors.\u201d https:\/\/youtu.be\/i-K9a6UhtsE?si=-rBsjVgY2p3c_DLc, Berkeley Initiative for Transparency in the Social Sciences Keynote Lecture; video accessed in December 2023."},{"issue":"1","key":"ecta70042-bib-0007","doi-asserted-by":"crossref","first-page":"6","DOI":"10.1038\/s41562-017-0189-z","volume":"2","author":"Benjamin","year":"2018","journal-title":"Nature Human Behaviour"},{"issue":"1","key":"ecta70042-bib-0008","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1023\/A:1003114420352","volume":"49","author":"Beran","year":"1997","journal-title":"Annals of the Institute of Statistical Mathematics"},{"issue":"5","key":"ecta70042-bib-0009","first-page":"1941","volume":"42","author":"Castillo","year":"2014","journal-title":"Annals of Statistics"},{"key":"ecta70042-bib-0010","unstructured":"Cavaliere, Giuseppe, Luca Fanelli, and Iliyan Georgiev (2025), \u201cBootstrap Diagnostic Tests.\u201d arXiv econ.EM. arXiv:2509.01351. 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Accessed on 07 August 2023."}],"container-title":["Econometrica"],"original-title":[],"language":"en","deposited":{"date-parts":[[2026,6,2]],"date-time":"2026-06-02T09:11:55Z","timestamp":1780391515000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.econometricsociety.org\/doi\/10.3982\/ECTA22613"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026]]},"references-count":34,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2026]]}},"alternative-id":["10.3982\/ECTA22613"],"URL":"https:\/\/doi.org\/10.3982\/ecta22613","relation":{},"ISSN":["0012-9682"],"issn-type":[{"value":"0012-9682","type":"print"}],"subject":[],"published":{"date-parts":[[2026]]}}}