Probability, Random Processes, and Statistical Analysis : Applications to Communications , Signal Processing, Queueing Theory and Mathematical Finance (Hardcover)

Hisashi Kobayashi, Brian L. Mark, William Turin

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商品描述

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 Ito^ process. Applications such as hidden Markov models (HMM), the Viterbi, BCJR, and Baum-Welch algorithms, algorithms for machine learning, Wiener and Kalman filters, queueing and loss networks, and 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 ito^ 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.

商品描述(中文翻譯)

除了概率、隨機過程和統計分析的基礎知識外,這本富有洞察力的書還介紹了廣泛的高級主題和應用。書中詳細介紹了貝葉斯統計與頻率主義統計、時間序列和頻譜表示、不等式、界限和近似、最大似然估計和期望最大化(EM)算法、幾何布朗運動和Ito^過程等。書中還詳細討論了隱馬可夫模型(HMM)、Viterbi、BCJR和Baum-Welch算法、機器學習算法、Wiener和Kalman濾波器、排隊和損失網絡等應用。這本書對通信、信號處理、網絡、機器學習、生物信息學、計量經濟學和數學金融等領域的學生和研究人員非常有用。書中提供了解答手冊、講義幻燈片、補充材料和MATLAB程序的線上資源,非常適合課堂教學,也是專業人士的寶貴參考資料。

目錄:
1. 引言
第一部分:概率、隨機變量和統計:
2. 概率
3. 離散隨機變量
4. 連續隨機變量
5. 隨機變量的函數及其分佈
6. 統計分析的基礎知識
7. 從正態分佈中得出的分佈
第二部分:變換方法、界限和極限:
8. 矩生成函數和特徵函數
9. 生成函數和拉普拉斯變換
10. 不等式、界限和大偏差近似
11. 隨機變量序列的收斂和極限定理
第三部分:隨機過程:
12. 隨機過程
13. 隨機過程和時間序列的頻譜表示
14. 泊松過程、出生-死亡過程和更新過程
15. 離散時間馬可夫鏈
16. 半馬可夫過程和連續時間馬可夫鏈
17. 隨機遊走、布朗運動、擴散和Ito^過程
第四部分:統計推斷:
18. 估計和決策理論
19. 估計算法
第五部分:應用和高級主題:
20. 隱馬可夫模型和應用
21. 機器學習中的概率模型
22. 隨機過程的濾波和預測
23. 排隊和損失模型。