Highly useful text studies logarithmic measures of information and their application to testing statistical hypotheses. Includes numerous worked examples and problems. References. Glossary. Appendix. 1968 2nd, revised edition.
The relevance of information theory to statistical theory and its applications to stochastic processes is a unifying influence in these TOPICS. The integral representation of discrimination information is presented in these TOPICS reviewing various approaches used in the literature, and is also developed herein using intrinsically information-theoretic methods. Log likelihood ratios associated with various stochastic processes are computed by an application of minimum discrimination information estimates. Linear discriminant functionals are used in the information-theoretic analysis of a variety of stochastic processes. Sections are numbered serially within each chapter, with a decimal notation for subsections. Equations, examples, theorems and lemmas, are numbered serially within each section with a decimal notation. The digits to the left of the decimal point represent the section and the digits to the right of the decimal point the serial number within the section. When reference is made to a section, equation, example, theorem or lemma within the same chapter only the section number or equation number, etc., is given. When the reference is to a section ,equation, etc., in a different chapter, then in addition to the section or equation etc., number, the chapter number is also given. References to the bibliography are by the author's name followed by the year of publication in parentheses. The transpose of a matrix is denoted by a prime; thus one-row matrices are denoted by primes as the transposes of one-column matrices (vectors).
Highly useful text studies logarithmic measures of information and their application to testing statistical hypotheses. Includes numerous worked examples and problems. References. Glossary. Appendix. 1968 2nd, revised edition.
The relevance of information theory to statistical theory and its applications to stochastic processes is a unifying influence in these TOPICS. The integral representation of discrimination information is presented in these TOPICS reviewing various approaches used in the literature, and is also developed herein using intrinsically information-theoretic methods. Log likelihood ratios associated with various stochastic processes are computed by an application of minimum discrimination information estimates. Linear discriminant functionals are used in the information-theoretic analysis of a variety of stochastic processes. Sections are numbered serially within each chapter, with a decimal notation for subsections. Equations, examples, theorems and lemmas, are numbered serially within each section with a decimal notation. The digits to the left of the decimal point represent the section and the digits to the right of the decimal point the serial number within the section. When reference is made to a section, equation, example, theorem or lemma within the same chapter only the section number or equation number, etc., is given. When the reference is to a section ,equation, etc., in a different chapter, then in addition to the section or equation etc., number, the chapter number is also given. References to the bibliography are by the author's name followed by the year of publication in parentheses. The transpose of a matrix is denoted by a prime; thus one-row matrices are denoted by primes as the transposes of one-column matrices (vectors).
Basic Concepts in Information Theory and Coding is an outgrowth of a one semester introductory course that has been taught at the University of Southern California since the mid-1960s. Lecture notes from that course have evolved in response to student reaction, new technological and theoretical develop ments, and the insights of faculty members who have taught the course (in cluding the three of us). In presenting this material, we have made it accessible to a broad audience by limiting prerequisites to basic calculus and the ele mentary concepts of discrete probability theory. To keep the material suitable for a one-semester course, we have limited its scope to discrete information theory and a general discussion of coding theory without detailed treatment of algorithms for encoding and decoding for various specific code classes. Readers will find that this book offers an unusually thorough treatment of noiseless self-synchronizing codes, as well as the advantage of problem sections that have been honed by reactions and interactions of several gen erations of bright students, while Agent 00111 provides a context for the discussion of abstract concepts.
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