Large Deviation Techniques in Decision, Simulation and Estimation (Probability & Mathematical Statistics S.) - Tapa dura

Random Data Analysis and Measurement Procedures Second Edition Julius S. Bendat and Allan G. Piersol The latest techniques for analysis and measurement of stationary and nonstationary random data passing through physical systems are described in this extensive revision and update. It includes new modern data processing procedures and new statistical error analysis formulas for the evaluation of estimates in single input/output and multiple input/output problems, plus new material on Hilbert transforms, multiple array models, and more. Chapters on statistical errors in basic and advanced estimates represent the most complete derivation and summary of these matters in print. 1986 (0 471-04000-2) 566 pp. Linear Stochastic Systems Peter E. Caines This outstanding text provides a unified and mathematically rigorous exposition of linear stochastic system theory The comprehensive format includes a full treatment of the fundamentals of stochastic processes and the construction of stochastic systems. It then presents an integrated view of the interrelated theories of prediction, realization (or modeling), parameter estimation and control. It also features in-depth coverage of system identification, with chapters on maximum likelihood estimation for Gaussian ARMAX and state space systems, minimum prediction error identification methods, nonstationary system identification, linear-quadratic stochastic control and concludes with a discussion of stochastic adaptive control. 1988 (0 471-08101-9) 874 pp. Introduction to the theory of Coverage Processes Peter Hall Coverage processes are finding increasing application in such diverse areas as queueing theory, ballistics, and physical chemistry. Drawing on methodology from several areas of probability theory and mathematics, this monograph provides a succinct and rigorous development of the mathematical theory of models for random coverage patterns. 1988 (0 471-85702-5) 408 pp.

Large deviation theory is a branch of probability concerned with explaining the behavior of certain types of rare events. Large Deviation Techniques in Decision, Simulation, and Estimation is an introductory level exposition for a nonmathematical audience of the major results and techniques available in this area. It is excellent for applied statisticians, communications engineers, statistical signal processors, information theorists, and even large deviation theorists interested in the major application areas of their field. Applications of large deviation theory are stressed throughout with entire chapters devoted to hypothesis testing, parameter estimation, fast simulation methodologies, and information theory. In a relaxed fashion, it introduces most of the major ideas and models of the subject. In addition, several new results are presented in various application areas. For example, it gives:

• New analysis and design techniques for hypothesis testing (signal detection) systems
• A new methodology, which is shown to be uniquely optimal, for the simulation of certain classes of rare events
• A proof based entirely upon large deviation theory of the source coding with respect to a fidelity criterion theorem of Shannon
• New expositions and explanations of many standard large deviation theory results
• An overview of some crucial but little known optimality results for parameter estimators

The first part of the text is a heuristic overview and introduction to the major themes of large deviation theory. The second part is concerned with applications of the theory to specific problems in hypothesis testing, simulation, parameter estimation, and information theory. Each chapter has many examples, sample calculations, and extensive exercises at the end, with complete solutions given in the appendix. This is the only readable, mathematically nonrigorous probability book. Large Deviation Techniques in Decision, Simulation, and Estimation is excellent for electrical engineers in academia involved in communications, information, and stochastic control theory, for industrial engineers and computer scientists concerned with simulation techniques, for statisticians interested in hypothesis testing and parameter estimation, and for mathematicians.