{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,19]],"date-time":"2026-09-19T01:18:51Z","timestamp":1789780731684,"version":"4.0.1"},"reference-count":27,"publisher":"Oxford University Press (OUP)","issue":"2","license":[{"start":{"date-parts":[[2020,2,11]],"date-time":"2020-02-11T00:00:00Z","timestamp":1581379200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"funder":[{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100008982","name":"National Science Foundation","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100008982","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2020,6,1]]},"abstract":"<jats:title>Summary<\/jats:title>\n               <jats:p>The histogram is widely used as a simple, exploratory way of displaying data, but it is usually not clear how to choose the number and size of the bins. We construct a confidence set of distribution functions that optimally deal with the two main tasks of the histogram: estimating probabilities and detecting features such as increases and modes in the distribution. We define the essential histogram as the histogram in the confidence set with the fewest bins. Thus the essential histogram is the simplest visualization of the data that optimally achieves the main tasks of the histogram. The only assumption we make is that the data are independent and identically distributed. We provide a fast algorithm for computing the essential histogram and illustrate our method with examples.<\/jats:p>","DOI":"10.1093\/biomet\/asz081","type":"journal-article","created":{"date-parts":[[2019,12,22]],"date-time":"2019-12-22T12:07:47Z","timestamp":1577016467000},"page":"347-364","source":"Crossref","is-referenced-by-count":14,"title":["The essential histogram"],"prefix":"10.1093","volume":"107","author":[{"given":"Housen","family":"Li","sequence":"first","affiliation":[{"name":"Institute for Mathematical Stochastics, Georg-August-Universit\u00e4t G\u00f6ttingen, Goldschmidstr. 7, 37077 G\u00f6ttingen, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Axel","family":"Munk","sequence":"additional","affiliation":[{"name":"Institute for Mathematical Stochastics, Georg-August-Universit\u00e4t G\u00f6ttingen, Goldschmidstr. 7, 37077 G\u00f6ttingen, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hannes","family":"Sieling","sequence":"additional","affiliation":[{"name":"Institute for Mathematical Stochastics, Georg-August-Universit\u00e4t G\u00f6ttingen, Goldschmidstr. 7, 37077 G\u00f6ttingen, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Guenther","family":"Walther","sequence":"additional","affiliation":[{"name":"Department of Statistics, Stanford University, Sequoia Hall, 390 Serra Mall, Stanford, California 94305, U.S.A"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2020,2,11]]},"reference":[{"key":"2020071623321178200_B1","doi-asserted-by":"crossref","first-page":"357","DOI":"10.2307\/2347385","article-title":"A look at some data on the Old Faithful geyser","volume":"39","author":"Azzalini,","year":"1990","journal-title":"Appl. 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