{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:35:49Z","timestamp":1760243749781,"version":"build-2065373602"},"reference-count":14,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2012,11,7]],"date-time":"2012-11-07T00:00:00Z","timestamp":1352246400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>We explore the meaning of information about quantities of interest. Our approach is divided in two scenarios: the analysis of observations and the planning of an experiment. First, we review the Sufficiency, Conditionality and Likelihood principles and how they relate to trivial experiments. Next, we review Blackwell Sufficiency and show that sampling without replacement is Blackwell Sufficient for sampling with replacement. Finally, we unify the two scenarios presenting an extension of the relationship between Blackwell Equivalence and the Likelihood Principle.<\/jats:p>","DOI":"10.3390\/e14112254","type":"journal-article","created":{"date-parts":[[2012,11,7]],"date-time":"2012-11-07T11:03:15Z","timestamp":1352286195000},"page":"2254-2264","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Statistical Information: A Bayesian Perspective"],"prefix":"10.3390","volume":"14","author":[{"given":"Rafael B.","family":"Stern","sequence":"first","affiliation":[{"name":"Department of Statistics, Carnegie Mellon University, 5000 Forbes Ave, Pittsburgh, PA 15213, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6315-7484","authenticated-orcid":false,"given":"Carlos A. de B.","family":"Pereira","sequence":"additional","affiliation":[{"name":"Instituto de Matem\u00e1tica e Estat\u00edstica, Universidade de S\u00e3o Paulo, Rua do Mat\u00e3o 1010, 05508-900, S\u00e3o Paulo, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2012,11,7]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Ghosh, J.K. (1988). Statistical Information and Likelihood : A Collection of Critical Essays, Springer.","DOI":"10.1007\/978-1-4612-3894-2_4"},{"key":"ref_2","unstructured":"Torgersen, E.N. (1991). Comparison of Experiments, Cambridge Press."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"269","DOI":"10.1080\/01621459.1962.10480660","article-title":"On the foundations of statistical inference","volume":"57","author":"Birnbaum","year":"1962","journal-title":"J. Am. Stat. Assoc."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Ghosh, J.K. (1988). Statistical Information & Likelihood, Springer.","DOI":"10.1007\/978-1-4612-3894-2"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"112","DOI":"10.1080\/00031305.1976.10479154","article-title":"Inference for a bernoulli process (a bayesian view)","volume":"30","author":"Lindley","year":"1976","journal-title":"Am. 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Stat."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"515","DOI":"10.1046\/j.1467-9884.2003.00376.x","article-title":"When is one experiment \"always better than\" another?","volume":"52","author":"Goel","year":"2003","journal-title":"Statistician"},{"key":"ref_11","first-page":"99","article-title":"A note on blackwell sufficiency and skibinsky characterization of distributions","volume":"45","author":"Basu","year":"1983","journal-title":"Sankhya A"},{"key":"ref_12","unstructured":"Ferrari, P., and Galves, A. (2000). Coupling and Regeneration for Stochastic Processes, Sociedad Venezoelana de Matematicas."},{"key":"ref_13","unstructured":"DeGroot, M.H. (1970). Optimal Statistical Decisions, Wiley."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"404","DOI":"10.1214\/aoms\/1177704567","article-title":"Uncertainty, information, and sequential experiments","volume":"33","author":"DeGroot","year":"1971","journal-title":"Ann. Math. Stat."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/14\/11\/2254\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T21:53:22Z","timestamp":1760219602000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/14\/11\/2254"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,11,7]]},"references-count":14,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2012,11]]}},"alternative-id":["e14112254"],"URL":"https:\/\/doi.org\/10.3390\/e14112254","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2012,11,7]]}}}