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Title:
Probability, random processes, and statistical analysis
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Publication Information:
Cambridge ; New York : Cambridge University Press, 2012
Physical Description:
xxxi, 780 p. : ill. ; 26 cm.
ISBN:
9780521895446
Abstract:
"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 It's 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"-- Provided by publisher.

"Probability, Random Processes, and Statistical Analysis Together with the fundamentals of probability, random processes, and statistical analysis, this insightful book also presents a broad range of advanced topics and applications not covered in other textbooks. Advanced topics include: - Bayesian inference and conjugate priors - Chernoff bound and large deviation approximation - Principal component analysis and singular value decomposition - Autoregressive moving average (ARMA) time series - Maximum likelihood estimation and the EM algorithm - Brownian motion, geometric Brownian motion, and Ito process - Black-Scholes differential equation for option pricing"-- Provided by publisher.
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30000010297751 QA274.2 K63 2012 Open Access Book Book
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Summary

Summary

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.


Table of Contents

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