FIRST COURSE IN PROBABILITY FOR COMPUTER AND DATA

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"In this undergraduate text, the author has distilled the core of probabilistic ideas and methods for computer and data science. The book emphasizes probabilistic and computational thinking rather than theorems and proofs. It provides insights and motivates the students by telling them why probability works and how to apply it. The unique features of the book are as follows: Bayesian probability with real-life cases in law and medicine; Logistic regression and naïve Bayes; Real-world applications of probability; Interweaving Monte Carlo simulation and probability; Gentle introduction to Markov chains and Markov chain Monte Carlo simulation. This book contains many worked examples. Numerous instructive problems scattered throughout the text are given along with problem-solving strategies. Several of the problems extend previously covered material. Answers to all problems and worked-out solutions to selected problems are also provided. Henk Tijms is the author of several textbooks in the area of applied probability and stochastic optimization. In 2008, he received the prestigious INFORMS Expository Writing Award for his work. He also contributed engaging probability puzzles to The New York Times' former Numberplay column. Request Inspection Copy Sample Chapter(s) Preface Chapter 1: Combinatorics and a Few Calculus Facts Contents: Preface Combinatorics and a Few Calculus Facts: Combinatorial Analysis The Exponential and Logarithmic Functions Fundamentals of Probability: Foundation of Probability The Concept of Conditional Probability The Law of Conditional Probability Bayesian Approach to Inference The Concept of Random Variable Expected Value and Standard Deviation Independent Random Variables and the Square Root Law Generating Functions Inequalities and the Law of Large Numbers Additional Material Useful Probability Distributions: The Binomial Distribution The Hypergeometric Distribution The Poisson Distribution The Normal Probability Density Central Limit Theorem and the Normal Distribution More on Probability Densities The Poisson Process The Q-Q Plot and the Chi-Square Test The Bivariate Normal Density Real-World Applications of Probability: Fraud in a Canadian Lottery Bombs over London in World War II Winning the Lottery Twice Santa Claus and a Baby Whisperer Birthdays and 500 Oldsmobiles Cash Winfall Lottery: A Revenue Model for Stats Geeks Coupon Collecting Benford's Law What is Casino Credit Worth? Devil's Card Game: A Psychological Test Monte Carlo Simulation and Probability: Introduction Simulation Tools Probability Applications of Simulation Bootstrap Method in Data Analysis Statistical Analysis of Simulation Output A Gentle Introduction to Markov Chains: Markov Chain Model Absorbing Markov Chains The Gambler's Ruin Problem Long-Run Behavior of Markov Chains Markov Chain Monte Carlo Simulation Solutions to Selected Problems Index Readership: Undergraduate students in computer and data science, business analytics, and operations research. Data scientists working at companies."

A First Course in Probability (10版)

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書名：A First Course in Probability 10/E 作者：ROSS 出版社：Pearson 出版日期：2019/11/00 ISBN：9781292269207 內容簡介 　　A First Course in Probability offers an elementary introduction to the theory of probability for students in mathematics, statistics, engineering, and the sciences. Through clear and intuitive explanations, it attempts to present not only the mathematics of probability theory, but also the many diverse possible applications of this subject through numerous examples. The 10th Edition includes many new and updated problems, exercises, and text material chosen both for inherent interest and for use in building student intuition about probability. 目錄 Ch 1 Combinatorial Analysis Ch 2 Axioms of Probability Ch 3 Conditional Probability and Independence Ch 4 Random Variables Ch 5 Continuous Random Variables Ch 6 Jointly Distributed Random Variables Ch 7 Properties of Expectation Ch 8 Limit Theorems Ch 9 Additional Topics in Probability Ch10 Simulation

Time Series Analysis (Wiley Series in Probability and Statistics)

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【簡介】 A modern and accessible guide to the analysis of introductory time series data Featuring an organized and self-contained guide, Time Series Analysis provides a broad introduction to the most fundamental methodologies and techniques of time series analysis. The book focuses on the treatment of univariate time series by illustrating a number of well-known models such as ARMA and ARIMA. Providing contemporary coverage, the book features several useful and newlydeveloped techniques such as weak and strong dependence, Bayesian methods, non-Gaussian data, local stationarity, missing values and outliers, and threshold models. Time Series Analysis includes practical applications of time series methods throughout, as well as: Real-world examples and exercise sets that allow readers to practice the presented methods and techniques Numerous detailed analyses of computational aspects related to the implementation of methodologies including algorithm efficiency, arithmetic complexity, and process time End-of-chapter proposed problems and bibliographical notes to deepen readers’ knowledge of the presented material Appendices that contain details on fundamental concepts and select solutions of the problems implemented throughout A companion website with additional data fi les and computer codes Time Series Analysis is an excellent textbook for undergraduate and beginning graduate-level courses in time series as well as a supplement for students in advanced statistics, mathematics, economics, finance, engineering, and physics. The book is also a useful reference for researchers and practitioners in time series analysis, econometrics, and finance. Wilfredo Palma, PhD, is Professor of Statistics in the Department of Statistics at Pontificia Universidad Católica de Chile. He has published several refereed articles and has received over a dozen academic honors and awards. His research interests include time series analysis, prediction theory, state space systems, linear models, and econometrics. He is the author of Long-Memory Time Series: Theory and Methods, also published by Wiley. 【目錄】 Preface xiii Acknowledgments xvii Acronyms xix 1 Introduction 1 1.1 Time Series Data 2 1.2 Random Variables and Statistical Modeling 16 1.3 Discrete-Time Models 22 1.4 Serial Dependence 22 1.5 Nonstationarity 25 1.6 Whiteness Testing 32 1.7 Parametric and Nonparametric Modeling 36 1.8 Forecasting 38 1.9 Time Series Modeling 38 1.10 Bibliographic Notes 39 Problems 39 2 Linear Processes 43 2.1 Definition 44 2.2 Stationarity 44 2.3 Invertibility 45 2.4 Causality 46 2.5 Representations of Linear Processes 46 2.6 Weak and Strong Dependence 49 2.7 ARMA Models 51 2.8 Autocovariance Function 56 2.9 ACF and Partial ACF Functions 57 2.10 ARFIMA Processes 64 2.11 Fractional Gaussian Noise 71 2.12 Bibliographic Notes 72 Problems 72 3 State Space Models 89 3.1 Introduction 90 3.2 Linear Dynamical Systems 92 3.3 State space Modeling of Linear Processes 96 3.4 State Estimation 97 3.5 Exogenous Variables 113 3.6 Bibliographic Notes 114 Problems 114 4 Spectral Analysis 121 4.1 Time and Frequency Domains 122 4.2 Linear Filters 122 4.3 Spectral Density 123 4.4 Periodogram 125 4.5 Smoothed Periodogram 128 4.6 Examples 130 4.7 Wavelets 136 4.8 Spectral Representation 138 4.9 Time-Varying Spectrum 140 4.10 Bibliographic Notes 145 Problems 145 5 Estimation Methods 151 5.1 Model Building 152 5.2 Parsimony 152 5.3 Akaike and Schwartz Information Criteria 153 5.4 Estimation of the Mean 153 5.5 Estimation of Autocovariances 154 5.6 Moment Estimation 155 5.7 Maximum-Likelihood Estimation 156 5.8 Whittle Estimation 157 5.9 State Space Estimation 160 5.10 Estimation of Long-Memory Processes 161 5.11 Numerical Experiments 178 5.12 Bayesian Estimation 180 5.13 Statistical Inference 184 5.14 Illustrations 189 5.15 Bibliographic Notes 193 Problems 194 6 Nonlinear Time Series 209 6.1 Introduction 210 6.2 Testing for Linearity 211 6.3 Heteroskedastic Data 212 6.4 ARCH Models 213 6.5 GARCH Models 216 6.6 ARFIMA-GARCH Models 218 6.7 ARCH(1) Models 220 6.8 APARCH Models 222 6.9 Stochastic Volatility 222 6.10 Numerical Experiments 223 6.11 Data Applications 225 6.12 Value at Risk 236 6.13 Autocorrelation of Squares 241 6.14 Threshold autoregressive models 247 6.15 Bibliographic Notes 252 Problems 253 7 Prediction 267 7.1 Optimal Prediction 268 7.2 One-Step Ahead Predictors 268 7.3 Multistep Ahead Predictors 275 7.4 Heteroskedastic Models 276 7.5 Prediction Bands 281 7.6 Data Application 287 7.7 Bibliographic Notes 289 Problems 289 8 Nonstationary Processes 295 8.1 Introduction 296 8.2 Unit Root Testing 297 8.3 ARIMA Processes 298 8.4 Locally Stationary Processes 301 8.5 Structural Breaks 326 8.6 Bibliographic Notes 331 Problems 332 9 Seasonality 337 9.1 SARIMA Models 338 9.2 SARFIMA Models 351 9.3 GARMA Models 353 9.4 Calculation of the Asymptotic Variance 355 9.5 Autocovariance Function 355 9.6 Monte Carlo Studies 359 9.7 Illustration 362 9.8 Bibliographic Notes 364 Problems 365 10 Time Series Regression 369 10.1 Motivation 370 10.2 Definitions 373 10.3 Properties of the LSE 375 10.4 Properties of the BLUE 376 10.5 Estimation of the Mean 379 10.6 Polynomial Trend 382 10.7 Harmonic Regression 386 10.8 Illustration: Air Pollution Data 388 10.9 Bibliographic Notes 392 Problems 392 11 Missing Values and Outliers 399 11.1 Introduction 400 11.2 Likelihood Function with Missing Values 401 11.3 Effects of Missing Values on ML Estimates 405 11.4 Effects of Missing Values on Prediction 407 11.5 Interpolation of Missing Data 410 11.6 Spectral Estimation with Missing Values 418 11.7 Outliers and Intervention Analysis 421 11.8 Bibliographic Notes 434 Problems 435 12 Non-Gaussian Time Series 441 12.1 Data Driven Models 442 12.2 Parameter Driven Models 452 12.3 Estimation 453 12.4 Data Illustrations 466 12.5 Zero-Inflated Models 477 12.6 Bibliographic Notes 483 Problems 483 Appendix A: Complements 487 A.1 Projection Theorem 488 A.2 Wold Decomposition 490 A.3 Bibliographic Notes 497 Appendix B: Solutions to Selected Problems 499 Appendix C: Data and Codes 557 References 559 Topic Index 573 Author Index 577