{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,5,31]],"date-time":"2024-05-31T09:14:45Z","timestamp":1717146885404},"reference-count":14,"publisher":"World Scientific Pub Co Pte Lt","issue":"03","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Open Syst. Inf. Dyn."],"published-print":{"date-parts":[[2012,9]]},"abstract":"<jats:p> Taken traditionally as a no-go theorem against the theoretical organization of inductive processes, Duhem-Quine thesis may interfere with the essence of statistical inference. This difficulty can be resolved by \"Micro-Macro duality\" [9, 10] which clarifies the importance of specifying the pertinent aspects and accuracy relevant to concrete contexts of scientific discussions and which ensures the matching between what is to be described and what to describe in the form of the validity of duality relations. This consolidates the foundations of the inverse problem, induction method, and statistical inference crucial for the sound relations between theory and experiments. To achieve the purpose, we propose here the large deviation strategy (LDS for short) on the basis of Micro-Macro duality, quadrality scheme, and large deviation principle. In reference to the quadrality scheme consisting of dynamics, algebra of observables together with its states and universal notion of classifying space, LDS will be seen to consist of the corresponding four levels; we discuss in detail its first and second levels, respectively, in this paper and the succeeding one, aiming at establishing statistical inference concerning observables. <\/jats:p>","DOI":"10.1142\/s1230161212500217","type":"journal-article","created":{"date-parts":[[2012,9,21]],"date-time":"2012-09-21T08:00:39Z","timestamp":1348214439000},"page":"1250021","source":"Crossref","is-referenced-by-count":5,"title":["Large Deviation Strategy for Inverse Problem I"],"prefix":"10.1142","volume":"19","author":[{"given":"Izumi","family":"Ojima","sequence":"first","affiliation":[{"name":"Research Institute for Mathematical Sciences, Kyoto University, Kyoto 606\u20138502, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kazuya","family":"Okamura","sequence":"additional","affiliation":[{"name":"Research Institute for Mathematical Sciences, Kyoto University, Kyoto 606\u20138502, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2012,9,21]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/62.3.547"},{"key":"rf2","volume-title":"Methods of information geometry","volume":"191","author":"Amari S.","year":"2000"},{"key":"rf3","volume-title":"Operator algebras and quantum statistical mechanics","volume":"1","author":"Bratteli O.","year":"2002"},{"key":"rf4","volume-title":"Large deviations techniques and applications","author":"Dembo A.","year":"2002"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4613-8533-2"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-02813-1"},{"key":"rf7","first-page":"725","volume":"69","author":"Krein M. G.","journal-title":"Doklady Akad. Nauk SSSR"},{"key":"rf8","volume-title":"Categories for the working mathematician","author":"MacLane S.","year":"1998"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1023\/A:1025175907589"},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.1088\/1742-6596\/201\/1\/012017"},{"key":"rf13","volume-title":"Theory of operator algebras II","author":"Takesaki M.","year":"2002"},{"key":"rf14","first-page":"1","volume":"45","author":"Tannaka T.","journal-title":"T\u00f4hoku Math. J."},{"key":"rf15","doi-asserted-by":"crossref","first-page":"187","DOI":"10.1215\/kjm\/1250524377","volume":"6","author":"Tatsuuma N.","journal-title":"J. Math. Kyoto Univ."},{"key":"rf16","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511800474"}],"container-title":["Open Systems &amp; Information Dynamics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1230161212500217","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T18:16:59Z","timestamp":1565201819000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S1230161212500217"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,9]]},"references-count":14,"journal-issue":{"issue":"03","published-online":{"date-parts":[[2012,9,21]]},"published-print":{"date-parts":[[2012,9]]}},"alternative-id":["10.1142\/S1230161212500217"],"URL":"https:\/\/doi.org\/10.1142\/s1230161212500217","relation":{},"ISSN":["1230-1612","1793-7191"],"issn-type":[{"value":"1230-1612","type":"print"},{"value":"1793-7191","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,9]]}}}