2014, XXIII, 375 p. 22 illus., 3 illus. in color. With online files/update.
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Comprehensive treatment of probability theory from the framework of differential geometry
Well-chosen problems covering a diverse spectrum of topics
Use of hands-on software to clarify and understand informational geometry concepts
This book covers topics of Informational Geometry, a field which deals with the differential geometric study of the manifold probability density functions. This is a field that is increasingly attracting the interest of researchers from many different areas of science, including mathematics, statistics, geometry, computer science, signal processing, physics and neuroscience. It is the authors’ hope that the present book will be a valuable reference for researchers and graduate students in one of the aforementioned fields.
This textbook is a unified presentation of differential geometry and probability theory, and constitutes a text for a course directed at graduate or advanced undergraduate students interested in applications of differential geometry in probability and statistics. The book contains over 100 proposed exercises meant to help students deepen their understanding, and it is accompanied by software that is able toprovide numerical computations of several information geometric objects. The reader will understand a flourishing field of mathematics in which very few books have been written so far.
Content Level »Research
Keywords »Entropy - Fisher information - Informational geometry - Probability density function - Statistical manifolds