Dieses Buch nimmt den Leser mit auf eine anregende Reise rund um die Welt der Statistik. Auf eine ganz andere Art werden Theorie und Praxis Dozenten, Studenten und Praktikern nahe gebracht. Auf jeder Etappe dieser Reise untersuchen die Autoren ungewöhnliche und skurille Aspekte der Statistik, stellen historische, biographische und philosophische Dimensionen heraus. Die einzelnen Kapitel beginnen mit einem Ausblick auf das Thema, oftmals aus unterschiedlichen Blickwinkeln. Darauf folgen fünf Fragen, die zum Nachdenken anregen. Ziel ist es, die Kenntnisse der Leser zu erweitern und zu vertiefen. Zu den Fragen gibt es auch immer wieder unterhaltsame Rätsel, mit denen spannende Paradoxa aufgelöst werden. Die Leser können ihre eigenen Entdeckungen in der Welt der Statistik mit den ausführlichen Antworten der Autoren auf die jeweiligen Fragen vergleichen.

A glorious period of Hungarian mathematics started in 1900 when Lipót Fejér discovered the summability of Fourier series.This was followed by the discoveries of his disciples in Fourier analysis and in the theory of analytic functions. At the same time Frederic (Frigyes) Riesz created functional analysis and Alfred Haar gave the first example of wavelets. Later the topics investigated by Hungarian mathematicians broadened considerably, and included topology, operator theory, differential equations, probability, etc. The present volume, the first of two, presents some of the most remarkable results achieved in the twentieth century by Hungarians in analysis, geometry and stochastics. The book is accessible to anyone with a minimum knowledge of mathematics. It is supplemented with an essay on the history of Hungary in the twentieth century and biographies of those mathematicians who are no longer active. A list of all persons referred to in the chapters concludes the volume.

To achieve the complex task of interpreting what we see, our brains rely on statistical regularities and patterns in visual data. Knowledge of these regularities can also be considerably useful in visual computing disciplines, such as computer vision, computer graphics, and image processing. The field of natural image statistics studies the regularities to exploit their potential and better understand human vision. With numerous color figures throughout, Image Statistics in Visual Computing covers all aspects of natural image statistics, from data collection to analysis to applications in computer graphics, computational photography, image processing, and art. The authors keep the material accessible, providing mathematical definitions where appropriate to help readers understand the transforms that highlight statistical regularities present in images. The book also describes patterns that arise once the images are transformed and gives examples of applications that have successfully used statistical regularities. Numerous references enable readers to easily look up more information about a specific concept or application. A supporting website also offers additional information, including descriptions of various image databases suitable for statistics. Collecting state-of-the-art, interdisciplinary knowledge in one source, this book explores the relation of natural image statistics to human vision and shows how natural image statistics can be applied to visual computing. It encourages readers in both academic and industrial settings to develop novel insights and applications in all disciplines that relate to visual computing.

This book deals with two main topics. The first is a theory that aims to unify the many interpretations of probability presented in the literature. The second uses this comprehensive theory of probability to answer the questions of quantum mechanics that have long been debated. The entire book proposes original solutions that several experimental cases substantiate.