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This formulation allows to deal with the classical and quantum case in a single, unifying mathematical framework. The derivation of the Cramer\u2013Rao and Helstrom bounds for parametric statistical models with discrete and finite outcome spaces is presented.<\/jats:p>","DOI":"10.3390\/e22111332","type":"journal-article","created":{"date-parts":[[2020,11,23]],"date-time":"2020-11-23T08:18:23Z","timestamp":1606119503000},"page":"1332","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Differential Geometric Aspects of Parametric Estimation Theory for States on Finite-Dimensional C\u2217-Algebras"],"prefix":"10.3390","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8987-1181","authenticated-orcid":false,"given":"Florio M.","family":"Ciaglia","sequence":"first","affiliation":[{"name":"Max Planck Institute for Mathematics in the Sciences, 04103 Leipzig, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5258-6590","authenticated-orcid":false,"given":"J\u00fcrgen","family":"Jost","sequence":"additional","affiliation":[{"name":"Max Planck Institute for Mathematics in the Sciences, 04103 Leipzig, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4268-6923","authenticated-orcid":false,"given":"Lorenz","family":"Schwachh\u00f6fer","sequence":"additional","affiliation":[{"name":"Faculty of Mathematics, TU Dortmund University, 44221 Dortmund, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2020,11,23]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Amari, S.I. 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