{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,1]],"date-time":"2025-12-01T11:21:50Z","timestamp":1764588110354,"version":"build-2065373602"},"reference-count":11,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2020,4,20]],"date-time":"2020-04-20T00:00:00Z","timestamp":1587340800000},"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>When using Bayesian inference, one needs to choose a prior distribution for parameters. The well-known Jeffreys prior is based on the Riemann metric tensor on a statistical manifold. Takeuchi and Amari defined the    \u03b1   -parallel prior, which generalized the Jeffreys prior by exploiting a higher-order geometric object, known as a Chentsov\u2013Amari tensor. In this paper, we propose a new prior based on the Weyl structure on a statistical manifold. It turns out that our prior is a special case of the    \u03b1   -parallel prior with the parameter    \u03b1    equaling     \u2212 n    , where n is the dimension of the underlying statistical manifold and the minus sign is a result of conventions used in the definition of    \u03b1   -connections. This makes the choice for the parameter    \u03b1    more canonical. We calculated the Weyl prior for univariate Gaussian and multivariate Gaussian distribution. The Weyl prior of the univariate Gaussian turns out to be the uniform prior.<\/jats:p>","DOI":"10.3390\/e22040467","type":"journal-article","created":{"date-parts":[[2020,4,21]],"date-time":"2020-04-21T03:23:06Z","timestamp":1587439386000},"page":"467","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Weyl Prior and Bayesian Statistics"],"prefix":"10.3390","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1435-1621","authenticated-orcid":false,"given":"Ruichao","family":"Jiang","sequence":"first","affiliation":[{"name":"Department of Mathematics, The University of British Columbia Okanagan, Kelowna, BC V1V 1V7, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Javad","family":"Tavakoli","sequence":"additional","affiliation":[{"name":"Department of Mathematics, The University of British Columbia Okanagan, Kelowna, BC V1V 1V7, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yiqiang","family":"Zhao","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Carlton University, Ottawa, ON K1S 5B6, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,4,20]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Amari, S. (2016). Information Geometry and Its Applications, Springer.","DOI":"10.1007\/978-4-431-55978-8"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Calin, O., and Udriste, C. (2014). Geometric Modeling in Probability and Statistics, Springer.","DOI":"10.1007\/978-3-319-07779-6"},{"key":"ref_3","unstructured":"Nielsen, F. (2018). An elementary introduction to information geometry. arXiv."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"567","DOI":"10.1016\/j.difgeo.2006.02.003","article-title":"Equiaffine structures on statistical manifolds and Bayesian statistics","volume":"24","author":"Matsuzoe","year":"2006","journal-title":"Differ. Geom. Its Appl."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Ciambelli, L., and Leigh, R.G. (2019). Weyl Connections and their Role in Holography. arXiv.","DOI":"10.1103\/PhysRevD.101.086020"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"3902","DOI":"10.1098\/rspa.2012.0342","article-title":"Weyl geometry and the nonlinear mechanics of distributed point defects","volume":"468","author":"Yavari","year":"2012","journal-title":"Proc. R. Soc. A"},{"key":"ref_7","unstructured":"Kobayashi, S., and Nomizu, K. (1963). Foundations of Differential Geometry, Wiley."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1011","DOI":"10.1109\/TIT.2004.842703","article-title":"\u03b1-parallel prior and its properties","volume":"51","author":"Takeuchi","year":"2005","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"145","DOI":"10.4310\/jdg\/1214429379","article-title":"Weyl manifolds","volume":"4","author":"Folland","year":"1970","journal-title":"J. Differ. Geom."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"2675","DOI":"10.1073\/pnas.69.9.2675","article-title":"Conformally flat manifolds","volume":"69","author":"Kulkarni","year":"1972","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Calin, O., Matsuzoe, H., and Zhang, J. (2009). Generalizations of conjugate connections. Trends in Differential Geometry, Complex Analysis and Mathematical Physics, World Scientific.","DOI":"10.1142\/9789814277723_0004"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/22\/4\/467\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,13]],"date-time":"2025-10-13T13:21:30Z","timestamp":1760361690000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/22\/4\/467"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,4,20]]},"references-count":11,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2020,4]]}},"alternative-id":["e22040467"],"URL":"https:\/\/doi.org\/10.3390\/e22040467","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2020,4,20]]}}}