{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:44:37Z","timestamp":1760237077178,"version":"build-2065373602"},"reference-count":11,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2020,2,20]],"date-time":"2020-02-20T00:00:00Z","timestamp":1582156800000},"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>In the previous work of the author, a non-trivial symmetry of the relative entropy in the information geometry of normal distributions was discovered. The same symmetry also appears in the symplectic\/contact geometry of Hilbert modular cusps. Further, it was observed that a contact Hamiltonian flow presents a certain Bayesian inference on normal distributions. In this paper, we describe Bayesian statistics and the information geometry in the language of current geometry in order to spread our interest in statistics through general geometers and topologists. Then, we foliate the space of multivariate normal distributions by symplectic leaves to generalize the above result of the author. This foliation arises from the Cholesky decomposition of the covariance matrices.<\/jats:p>","DOI":"10.3390\/e22020240","type":"journal-article","created":{"date-parts":[[2020,2,21]],"date-time":"2020-02-21T08:59:47Z","timestamp":1582275587000},"page":"240","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Global Geometry of Bayesian Statistics"],"prefix":"10.3390","volume":"22","author":[{"given":"Atsuhide","family":"Mori","sequence":"first","affiliation":[{"name":"Department of Mathematics, Osaka Dental University, Osaka 573-1121, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,2,20]]},"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":"Ay, N., Jost, J., Le, H.V., and Schwachh\u00f6fer, L. (2017). Information Geometry, Springer.","DOI":"10.1007\/978-3-319-56478-4"},{"key":"ref_3","unstructured":"Felice, N., and Ay, N. (2018). Towards a Canonical Divergence within Information Geometry. arXiv."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"291","DOI":"10.32917\/hmj\/1544238029","article-title":"Information geometry in a global setting","volume":"48","author":"Mori","year":"2018","journal-title":"Hiroshima Math. J."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Mori, A. (2020). A concurrence theorem for alpha-connections on the space of t-distributions and its application. Hokkaido Math. J., in press.","DOI":"10.14492\/hokmj\/1602036023"},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Geiges, H. (2008). An Introduction to Contact Topology, Cambridge University Press.","DOI":"10.1017\/CBO9780511611438"},{"key":"ref_7","unstructured":"Hawkes, P. (2007). Bayesian information geometry: Application to prior selection on statistical manifolds. Advances in Imaging and Electron Physics 146, Elsevier."},{"key":"ref_8","first-page":"183","article-title":"Hilbert modular surfaces","volume":"19","author":"Hirzebruch","year":"1973","journal-title":"Enseign. Math."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"287","DOI":"10.1007\/s00222-012-0412-5","article-title":"Weak and strong fillability of higher dimensional contact manifolds","volume":"192","author":"Massot","year":"2013","journal-title":"Invent. Math."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1760","DOI":"10.1016\/j.geomphys.2012.04.002","article-title":"On Poisson geometries related to noncommutative emergent gravity","volume":"62","author":"Kuntner","year":"2012","journal-title":"J. Geom. Phys."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"375","DOI":"10.1016\/0040-9383(86)90050-9","article-title":"Symplectic manifolds with no K\u00e4hler structure","volume":"25","author":"Cordero","year":"1986","journal-title":"Topology"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/22\/2\/240\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T08:59:26Z","timestamp":1760173166000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/22\/2\/240"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,2,20]]},"references-count":11,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2020,2]]}},"alternative-id":["e22020240"],"URL":"https:\/\/doi.org\/10.3390\/e22020240","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2020,2,20]]}}}