Information Geometry and Its Applications On the Occasion of Shun-i

The book gathers contributions from the fourth conference on Information Geometry and its Applications, which was held on June 12–17, 2016, at Liblice Castle, Czech Republic on the occasion of Shun-ichi Amari’s 80th birthday and was organized by the Czech

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Nihat Ay · Paolo Gibilisco  František Matúš   Editors

Information Geometry and Its Applications IGAIA IV, Liblice, Czech Republic, June 2016

Springer Proceedings in Mathematics & Statistics Volume 252

Springer Proceedings in Mathematics & Statistics This book series features volumes composed of selected contributions from workshops and conferences in all areas of current research in mathematics and statistics, including operation research and optimization. In addition to an overall evaluation of the interest, scientific quality, and timeliness of each proposal at the hands of the publisher, individual contributions are all refereed to the high quality standards of leading journals in the field. Thus, this series provides the research community with well-edited, authoritative reports on developments in the most exciting areas of mathematical and statistical research today.

More information about this series at http://www.springer.com/series/10533

Nihat Ay Paolo Gibilisco František Matúš •

Editors

Information Geometry and Its Applications On the Occasion of Shun-ichi Amari’s 80th Birthday, IGAIA IV, Liblice, Czech Republic, June 2016

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Editors Nihat Ay Information Theory of Cognitive Systems MPI for Mathematics in the Sciences Leipzig, Germany and Santa Fe Institute Santa Fe, NM, USA

Paolo Gibilisco Department of Economics and Finance University of Rome “Tor Vergata” Rome, Italy František Matúš Institute of Information Theory and Automation Academy of Sciences of the Czech Republic Prague, Czech Republic

ISSN 2194-1009 ISSN 2194-1017 (electronic) Springer Proceedings in Mathematics & Statistics ISBN 978-3-319-97797-3 ISBN 978-3-319-97798-0 (eBook) https://doi.org/10.1007/978-3-319-97798-0 Library of Congress Control Number: 2018950804 Mathematics Subject Classification (2010): 60A10, 62B05, 62B10, 62G05, 53B21, 53B05, 46B20, 94A15, 94A17, 94B27 © Springer Nature Switzerland AG 2018 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with re