Statistical Implications Of Turing S Formula
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Statistical Implications of Turing's Formula
Features a broad introduction to recent research on Turing’s formula and presents modern applications in statistics, probability, information theory, and other areas of modern data science Turing's formula is, perhaps, the only known method for estimating the underlying distributional characteristics beyond the range of observed data without making any parametric or semiparametric assumptions. This book presents a clear introduction to Turing’s formula and its connections to statistics. Topics with relevance to a variety of different fields of study are included such as information theory; statistics; probability; computer science inclusive of artificial intelligence and machine learning; big data; biology; ecology; and genetics. The author provides examinations of many core statistical issues within modern data science from Turing's perspective. A systematic approach to long-standing problems such as entropy and mutual information estimation, diversity index estimation, domains of attraction on general alphabets, and tail probability estimation is presented in light of the most up-to-date understanding of Turing's formula. Featuring numerous exercises and examples throughout, the author provides a summary of the known properties of Turing's formula and explains how and when it works well; discusses the approach derived from Turing's formula in order to estimate a variety of quantities, all of which mainly come from information theory, but are also important for machine learning and for ecological applications; and uses Turing's formula to estimate certain heavy-tailed distributions. In summary, this book: • Features a unified and broad presentation of Turing’s formula, including its connections to statistics, probability, information theory, and other areas of modern data science • Provides a presentation on the statistical estimation of information theoretic quantities • Demonstrates the estimation problems of several statistical functions from Turing's perspective such as Simpson's indices, Shannon's entropy, general diversity indices, mutual information, and Kullback–Leibler divergence • Includes numerous exercises and examples throughout with a fundamental perspective on the key results of Turing’s formula Statistical Implications of Turing's Formula is an ideal reference for researchers and practitioners who need a review of the many critical statistical issues of modern data science. This book is also an appropriate learning resource for biologists, ecologists, and geneticists who are involved with the concept of diversity and its estimation and can be used as a textbook for graduate courses in mathematics, probability, statistics, computer science, artificial intelligence, machine learning, big data, and information theory. Zhiyi Zhang, PhD, is Professor of Mathematics and Statistics at The University of North Carolina at Charlotte. He is an active consultant in both industry and government on a wide range of statistical issues, and his current research interests include Turing's formula and its statistical implications; probability and statistics on countable alphabets; nonparametric estimation of entropy and mutual information; tail probability and biodiversity indices; and applications involving extracting statistical information from low-frequency data space. He earned his PhD in Statistics from Rutgers University.
Security in Computing Systems
Author: Joachim Biskup
language: en
Publisher: Springer Science & Business Media
Release Date: 2008-11-14
This monograph on Security in Computing Systems: Challenges, Approaches and Solutions aims at introducing, surveying and assessing the fundamentals of se- rity with respect to computing. Here, “computing” refers to all activities which individuals or groups directly or indirectly perform by means of computing s- tems, i. e. , by means of computers and networks of them built on telecommuni- tion. We all are such individuals, whether enthusiastic or just bowed to the inevitable. So, as part of the ‘‘information society’’, we are challenged to maintain our values, to pursue our goals and to enforce our interests, by consciously desi- ing a ‘‘global information infrastructure’’ on a large scale as well as by approp- ately configuring our personal computers on a small scale. As a result, we hope to achieve secure computing: Roughly speaking, computer-assisted activities of in- viduals and computer-mediated cooperation between individuals should happen as required by each party involved, and nothing else which might be harmful to any party should occur. The notion of security circumscribes many aspects, ranging from human qua- ties to technical enforcement. First of all, in considering the explicit security requirements of users, administrators and other persons concerned, we hope that usually all persons will follow the stated rules, but we also have to face the pos- bility that some persons might deviate from the wanted behavior, whether ac- dently or maliciously.
A Normal Country
Author: Andrei Shleifer
language: en
Publisher: Harvard University Press
Release Date: 2005
This book offers a firsthand glimpse into the intellectual challenges that Russia's turbulent transition generated. It deals with many of the most important reforms, from Gorbachev's half-hearted "perestroika," to the mass privatization program, to the efforts to build legal and regulatory institutions of a market economy.