Nihat Ay studied mathematics and physics at the Ruhr University Bochum and received his Ph.D. in mathematics from the University of Leipzig in 2001. He was a Postdoc at the Santa Fe Institute and at the Redwood Center for Theoretical Neuroscience, UC Berkeley. Since 2005, he has been group leader at the Max Planck Institute for Mathematics in the Sciences in Leipzig, heading the Information Theory of Cognitive Systems group. His research interests are information geometry, complexity and information theory, mathematical learning theory, embodied cognitive systems, graphical models and causality, and robustness theory. Nihat Ay is Professor at the Santa Fe Institute and honorary Professor of information geometry at the University of Leipzig.

Jürgen Jost studied mathematics, physics, economics and philosophy in Bonn 1975-1980. He received his Ph.D. in mathematics in 1980, and was a Postdoc at IAS Princeton, UC San Diego, CMA Canberra and Bonn, a Professor at Ruhr University Bochum 1984-1996, and has been a Director of the Max Planck Institute for Mathematics in the Sciences, Leipzig, since 1996. He is an Honorary Professor of Leipzig University, external member of the Santa Fe Institute. He received the DFG Leibniz Award in 1993, and an ERC advanced grant in 2010. His research interests are Riemannian geometry, geometric analysis, dynamical systems, information theory, network analysis, mathematical biology and neurobiology, mathematical economics and complex systems theory.

Hông Vân Lê studied mathematics at the Moscow State University and received her Ph.D. in mathematics in 1987 and her DrSc in mathematics in 1990. She was a Postdoc at the Moscow State University, the International Center for Theoretical Physics (ICTP) in Trieste, the Max Planck Institute for Mathematics in Bonn, a Heisenberg Fellow at the Max Planck Institute for Mathematics in Bonn, the Henri Poincaré Institute in Paris, the Newton Institute in Cambridge and Leipzig University, a research associate at the Max Planck Institute for Mathematics in the Sciences in Leipzig, foreign Professor at the Abdus Salam School of Mathematics in Lahore, visiting Professor at the Vietnam National University for Sciences in Hanoi. She was awarded the Moscow Mathematical Society prize in 1990, the ICTP prize in 1991, and a DFG Heisenberg fellowship in 1994. Since 2005 she has been a senior researcher at the Czech Academy of Sciences Institute of Mathematics. Her research interests are Riemannian geometry, symplectic topology, representation theory, differential topology and information geometry.

Lorenz Schwachhöfer studied mathematics and computer science in Darmstadt, New Orleans (Tulane) and Philadelphia (UPenn) where he received his Ph.D. in 1992. He was a Postdoc in St.Louis (Washington Univ.), Bonn (Max Planck Institute for Mathematics) and Leipzig University where he completed his habilitation in 1998. He was a Professor (Chargé de cours) at ULB Brussels (2000-2003), and since 2003 he has been a full Professor at TU Dortmund University. In 2010, he received the Royal Academy of Science (Belgium) E. Catalan prize. His main research interests are in differential geometry and differential topology, representation theory and information geometry.

Will become standard reference of the field

Introduces new mathematical treatment of parametrised measure models

Includes general results on sufficient statistics, Cramér-Rao inequality, uniqueness of Fisher metric and Amari-Chentsov tensor

Provides new applications of information geometry

Includes supplementary material: [...]