{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,15]],"date-time":"2025-12-15T19:47:29Z","timestamp":1765828049130,"version":"build-2065373602"},"reference-count":31,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2021,3,8]],"date-time":"2021-03-08T00:00:00Z","timestamp":1615161600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Statistical methods to produce inferences based on samples from finite populations have been available for at least 70 years. Topics such as Survey Sampling and Sampling Theory have become part of the mainstream of the statistical methodology. A wide variety of sampling schemes as well as estimators are now part of the statistical folklore. On the other hand, while the Bayesian approach is now a well-established paradigm with implications in almost every field of the statistical arena, there does not seem to exist a conventional procedure\u2014able to deal with both continuous and discrete variables\u2014that can be used as a kind of default for Bayesian survey sampling, even in the simple random sampling case. In this paper, the Bayesian analysis of samples from finite populations is discussed, its relationship with the notion of superpopulation is reviewed, and a nonparametric approach is proposed. Our proposal can produce inferences for population quantiles and similar quantities of interest in the same way as for population means and totals. Moreover, it can provide results relatively quickly, which may prove crucial in certain contexts such as the analysis of quick counts in electoral settings.<\/jats:p>","DOI":"10.3390\/e23030318","type":"journal-article","created":{"date-parts":[[2021,3,8]],"date-time":"2021-03-08T12:12:18Z","timestamp":1615205538000},"page":"318","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Bayesian Analysis of Finite Populations under Simple Random Sampling"],"prefix":"10.3390","volume":"23","author":[{"given":"Manuel","family":"Mendoza","sequence":"first","affiliation":[{"name":"Departamento de Estad\u00edstica, Instituto Tecnol\u00f3gico Aut\u00f3nomo de M\u00e9xico, R\u00edo Hondo 1, Ciudad de M\u00e9xico 01080, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3445-8015","authenticated-orcid":false,"given":"Alberto","family":"Contreras-Crist\u00e1n","sequence":"additional","affiliation":[{"name":"Departamento de Probabilidad y Estad\u00edstica, Instituto de Investigaciones en Matem\u00e1ticas Aplicadas y en Sistemas, Universidad Nacional Aut\u00f3noma de M\u00e9xico, Apartado Postal 20-126, Ciudad de M\u00e9xico 01000, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4706-5226","authenticated-orcid":false,"given":"Eduardo","family":"Guti\u00e9rrez-Pe\u00f1a","sequence":"additional","affiliation":[{"name":"Departamento de Probabilidad y Estad\u00edstica, Instituto de Investigaciones en Matem\u00e1ticas Aplicadas y en Sistemas, Universidad Nacional Aut\u00f3noma de M\u00e9xico, Apartado Postal 20-126, Ciudad de M\u00e9xico 01000, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,3,8]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"558","DOI":"10.2307\/2342192","article-title":"On the two different aspects of the representative method: The method of stratified sampling and the method of purposive selection","volume":"97","author":"Neyman","year":"1934","journal-title":"J. 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