Probability, Random Processes, and Statistical Analysis

Erscheinungsjahr 2011
ISBN: 978-0-521-89544-6
Verlag: Cambridge University Press

Buch, Englisch, 812 Seiten, HC gerader Rücken kaschiert, Format (B × H): 175 mm x 250 mm, Gewicht: 1559 g

Together with the fundamentals of probability, random processes and statistical analysis, this insightful book also presents a broad range of advanced topics and applications. There is extensive coverage of Bayesian vs. frequentist statistics, time series and spectral representation, inequalities, bound and approximation, maximum-likelihood estimation and the expectation-maximization (EM) algorithm, geometric Brownian motion and Itô process. Applications such as hidden Markov models (HMM), the Viterbi, BCJR, and Baum–Welch algorithms, algorithms for machine learning, Wiener and Kalman filters, and queueing and loss networks are treated in detail. The book will be useful to students and researchers in such areas as communications, signal processing, networks, machine learning, bioinformatics, econometrics and mathematical finance. With a solutions manual, lecture slides, supplementary materials and MATLAB programs all available online, it is ideal for classroom teaching as well as a valuable reference for professionals.

Autoren/Hrsg.

Kobayashi, Hisashi

Mark, Brian L.

Turin, William

Fachgebiete

• Mathematik | Informatik Mathematik Stochastik Mathematische Statistik
• Mathematik | Informatik EDV | Informatik Angewandte Informatik Bioinformatik
• Wirtschaftswissenschaften Volkswirtschaftslehre Volkswirtschaftslehre Allgemein Ökonometrie
• Naturwissenschaften Biowissenschaften Angewandte Biologie Bioinformatik
• Technische Wissenschaften Elektronik | Nachrichtentechnik Nachrichten- und Kommunikationstechnik Signalverarbeitung
• Mathematik | Informatik Mathematik Mathematik Interdisziplinär Finanz- und Versicherungsmathematik
• Technische Wissenschaften Technik Allgemein Mathematik für Ingenieure
• Mathematik | Informatik Mathematik Stochastik Wahrscheinlichkeitsrechnung
• Mathematik | Informatik EDV | Informatik Informatik Künstliche Intelligenz

Inhaltsverzeichnis

1. Introduction; Part I. Probability, Random Variables and Statistics: 2. Probability; 3. Discrete random variables; 4. Continuous random variables; 5. Functions of random variables and their distributions; 6. Fundamentals of statistical analysis; 7. Distributions derived from the normal distribution; Part II. Transform Methods, Bounds and Limits: 8. Moment generating function and characteristic function; 9. Generating function and Laplace transform; 10. Inequalities, bounds and large deviation approximation; 11. Convergence of a sequence of random variables, and the limit theorems; Part III. Random Processes: 12. Random process; 13. Spectral representation of random processes and time series; 14. Poisson process, birth-death process, and renewal process; 15. Discrete-time Markov chains; 16. Semi-Markov processes and continuous-time Markov chains; 17. Random walk, Brownian motion, diffusion and itô processes; Part IV. Statistical Inference: 18. Estimation and decision theory; 19. Estimation algorithms; Part V. Applications and Advanced Topics: 20. Hidden Markov models and applications; 21. Probabilistic models in machine learning; 22. Filtering and prediction of random processes; 23. Queuing and loss models.

Über Autor(innen)

Mark, Brian L.
Brian L. Mark is a Professor in the Department of Electrical and Computer Engineering at George Mason University. Prior to this, he was a Research Staff Member at the NEC C&C Research Laboratories in Princeton, New Jersey and in 2002 he received a National Science Foundation CAREER award.

Turin, William
William Turin is currently a Consultant at AT&T Labs Research. As a Member of Technical Staff at AT&T Bell Laboratories and later a Technology Consultant at AT&T Labs Research for 21 years, he developed methods for qualifying the performance of communication systems. He is the author of six books and numerous papers.

Kobayashi, Hisashi
Hisashi Kobayashi is the Sherman Fairchild University Professor Emeritus at Princeton University, where he was previously Dean of the School of Engineering and Applied Science. He also spent 15 years at the IBM Research Center, Yorktown Heights, NY, and was the Founding Director of the IBM Tokyo Research Laboratory. He is an IEEE Life Fellow, an IEICE Fellow, was elected to the Engineering Academy of Japan (1992) and received the 2005 Eduard Rhein Technology Award.