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計算統(tǒng)計(英文版)(Computational Statistics ) 版權信息
- ISBN：9787030731890
- 條形碼：9787030731890 ; 978-7-03-073189-0
- 裝幀：一般膠版紙
- 冊數(shù)：暫無
- 重量：暫無
- 所屬分類：>
計算統(tǒng)計(英文版)(Computational Statistics ) 內容簡介
計算統(tǒng)計（英文版）旨在為統(tǒng)計專業(yè)高年級本科生,研究生提供常用的現(xiàn)代復雜計算方法。它強調計算作為一個基本工具在數(shù)據(jù)分析、統(tǒng)計推斷、統(tǒng)計理論與方法的發(fā)展中的中心地位。包括產生隨機變量的方法、幾個重要的優(yōu)化方法、蒙特卡洛積分方法、貝葉斯計算中的MCMC方法、Bootstrap方法。本書通過組合傳統(tǒng)教材和課堂PPT各自的優(yōu)點，設置了經緯兩條主線，運用塊狀結構呈現(xiàn)知識點，使得每個知識點自我包含，并采用彩色印刷，方便教與學。另外在介紹重要概念時，注重啟發(fā)，邏輯順暢,條理清楚。本書可供統(tǒng)計學專業(yè)和數(shù)據(jù)科學與大數(shù)據(jù)技術專業(yè)的本科生、研究生、教師、科研工作者計算統(tǒng)計英文或雙語課程的教材使用，也可作為其他相關專業(yè)人員的參考資料。
計算統(tǒng)計(英文版)(Computational Statistics ) 目錄
Contents
Preface
Chapter 1 Generation of Random Variables 1
1.1 The Inversion Method 3
1.1.1 Generating samples from continuous distributions 3
1.1.2 Generating samples from discrete distributions 7
1.2 The Grid Method 12
1.3 The Rejection Method 15
1.3.1 Generating samples from continuous distributions 15
1.3.2 The efficiency of the rejection method 18
1.3.3 Several examples 20
1.3.4 Log-concave densities 24
1.4 The Sampling/Importance Resampling (SIR) Method 27
1.4.1 The SIR without replacement 28
1.4.2 Theoretical justification 30
1.5 The Stochastic Representation (SR) Method.32
1.5.1 The‘d=’operator 32
1.5.2 Many-to-one SR for univariate case 34
1.5.3 SR for multivariate case 36
1.5.4 Mixture representation 39
1.6 The Conditional Sampling Method 42
Exercise 1 47
Chapter 2 Optimization 53
2.1 A Review of Some Standard Concepts 54
2.1.1 Order relations 54
2.1.2 Stationary points 57
2.1.3 Convex and concave functions 60
2.1.4 Mean value theorem 61
2.1.5 Taylor theorem 63
2.1.6 Rates of convergence 64
2.1.7 The case of multiple dimensions 64
2.2 Newton’s Method and Its Variants 66
2.2.1 Newton’s method and root finding 67
2.2.2 Newton’s method and optimization 71
2.2.3 The Newton–Raphson algorithm 72
2.2.4 The Fisher scoring algorithm 75
2.2.5 Application to logistic regression 76
2.3 The Expectation–Maximization (EM) Algorithm 80
2.3.1 The formulation of the EM algorithm 81
2.3.2 The ascent property of the EM algorithm 89
2.3.3 Missing information principle and standard errors 92
2.4 The ECM Algorithm 95
2.5 Minorization–Maximization (MM) Algorithms 100
2.5.1 A brief review of MM algorithms 100
2.5.2 The MM idea 101
2.5.3 The quadratic lower–bound algorithm 103
2.5.4 The De Pierro algorithm 106
Exercise 2 115
Chapter 3 Integration 125
3.1 Laplace Approximations 126
3.2 Riemannian Simulation 129
3.2.1 Classical Monte Carlo integration 129
3.2.2 Motivation for Riemannian simulation 132
3.2.3 Variance of the Riemannian sum estimator 133
3.3 The Importance Sampling Method 135
3.3.1 The formulation of the importance sampling method 135
3.3.2 The weighted estimator 138
3.4 Variance Reduction 141
3.4.1 Antithetic variables 141
3.4.2 Control variables 145
Exercise 3 146
Chapter 4 Markov Chain Monte Carlo Methods 149
4.1 Bayes Formulae and Inverse Bayes Formulae (IBF) 151
4.1.1 The point，function- and sampling-wise IBF 152
4.1.2 Monte Carlo versions of the IBF 160
4.1.3 Generalization to the case of three random variables 163
4.2 The Bayesian Methodology 163
4.2.1 The posterior distribution 165
4.2.2 Nuisance parameters 167
4.2.3 Posterior predictive distribution 169
4.2.4 Bayes factor 172
4.2.5 Estimation of marginal likelihood 173
4.3 The Data Augmentation (DA) Algorithm 175
4.3.1 Missing data mechanism 175
4.3.2 The idea of data augmentation 177
4.3.3 The original DA algorithm 178
4.3.4 Connection with the IBF 180
4.4 The Gibbs sampler 181
4.4.1 The formulation of the Gibbs sampling 182
4.4.2 The two–block Gibbs sampling 184
4.5 The Exact IBF Sampling 187
4.6 The IBF sampler 191
4.6.1 Background and the basic idea 191
4.6.2 The formulation of the IBF sampler 192
4.6.3 Theoretical justification for choosing θ0 =.θ 194
Exercise 4 196
Chapter 5 Bootstrap Methods 203
5.1 Bootstrap Confidence Intervals 203
5.1.1 Parametric bootstrap 203
5.1.2 Non-parametric bootstrap 213
5.2 Hypothesis Testing with the Bootstrap 219
5.2.1 Testing equality of two unknown distributions 219
5.2.2 Testing equality of two group means 223
5.2.3 One–sample problem 228
Exercise 5 231
Appendix A Some Statistical Distributions and Stochastic
Processes 233
A.1 Discrete Distributions 233
A.1.1 Finite discrete distribution 233
A.1.2 Hypergeometric distribution 234
A.1.3 Binomial and related distributions 235
A.1.4 Poisson and related distributions 237
A.1.5 Negative–binomial and related distributions 240
A.1.6 Generalized Poisson and related distributions 242
A.1.7 Multinomial and related distributions 243
A.2 Continuous Distributions 245
A.2.1 Uniform， beta and Dirichlet distributions 245
A.2.2 Logistic and Laplace distributions 248
A.2.3 Exponential， gamma and inverse gamma distributions 249
A.2.4 Chi-square， F and inverse chi-square distributions 251
A.2.5 Normal， lognormal and inverse Gaussian distributions 252
A.2.6 Multivariate normal distribution 254
A.2.7 Student’s t and multivariate t distributions 255
A.2.8 Wishart and inverse Wishart distributions 256
A.3 Stochastic Processes 258
A.3.1 Homogeneous Poisson process 258
A.3.2 Nonhomogeneous Poisson process 259
Appendix B R Programming
Preface
Chapter 1 Generation of Random Variables 1
1.1 The Inversion Method 3
1.1.1 Generating samples from continuous distributions 3
1.1.2 Generating samples from discrete distributions 7
1.2 The Grid Method 12
1.3 The Rejection Method 15
1.3.1 Generating samples from continuous distributions 15
1.3.2 The efficiency of the rejection method 18
1.3.3 Several examples 20
1.3.4 Log-concave densities 24
1.4 The Sampling/Importance Resampling (SIR) Method 27
1.4.1 The SIR without replacement 28
1.4.2 Theoretical justification 30
1.5 The Stochastic Representation (SR) Method.32
1.5.1 The‘d=’operator 32
1.5.2 Many-to-one SR for univariate case 34
1.5.3 SR for multivariate case 36
1.5.4 Mixture representation 39
1.6 The Conditional Sampling Method 42
Exercise 1 47
Chapter 2 Optimization 53
2.1 A Review of Some Standard Concepts 54
2.1.1 Order relations 54
2.1.2 Stationary points 57
2.1.3 Convex and concave functions 60
2.1.4 Mean value theorem 61
2.1.5 Taylor theorem 63
2.1.6 Rates of convergence 64
2.1.7 The case of multiple dimensions 64
2.2 Newton’s Method and Its Variants 66
2.2.1 Newton’s method and root finding 67
2.2.2 Newton’s method and optimization 71
2.2.3 The Newton–Raphson algorithm 72
2.2.4 The Fisher scoring algorithm 75
2.2.5 Application to logistic regression 76
2.3 The Expectation–Maximization (EM) Algorithm 80
2.3.1 The formulation of the EM algorithm 81
2.3.2 The ascent property of the EM algorithm 89
2.3.3 Missing information principle and standard errors 92
2.4 The ECM Algorithm 95
2.5 Minorization–Maximization (MM) Algorithms 100
2.5.1 A brief review of MM algorithms 100
2.5.2 The MM idea 101
2.5.3 The quadratic lower–bound algorithm 103
2.5.4 The De Pierro algorithm 106
Exercise 2 115
Chapter 3 Integration 125
3.1 Laplace Approximations 126
3.2 Riemannian Simulation 129
3.2.1 Classical Monte Carlo integration 129
3.2.2 Motivation for Riemannian simulation 132
3.2.3 Variance of the Riemannian sum estimator 133
3.3 The Importance Sampling Method 135
3.3.1 The formulation of the importance sampling method 135
3.3.2 The weighted estimator 138
3.4 Variance Reduction 141
3.4.1 Antithetic variables 141
3.4.2 Control variables 145
Exercise 3 146
Chapter 4 Markov Chain Monte Carlo Methods 149
4.1 Bayes Formulae and Inverse Bayes Formulae (IBF) 151
4.1.1 The point，function- and sampling-wise IBF 152
4.1.2 Monte Carlo versions of the IBF 160
4.1.3 Generalization to the case of three random variables 163
4.2 The Bayesian Methodology 163
4.2.1 The posterior distribution 165
4.2.2 Nuisance parameters 167
4.2.3 Posterior predictive distribution 169
4.2.4 Bayes factor 172
4.2.5 Estimation of marginal likelihood 173
4.3 The Data Augmentation (DA) Algorithm 175
4.3.1 Missing data mechanism 175
4.3.2 The idea of data augmentation 177
4.3.3 The original DA algorithm 178
4.3.4 Connection with the IBF 180
4.4 The Gibbs sampler 181
4.4.1 The formulation of the Gibbs sampling 182
4.4.2 The two–block Gibbs sampling 184
4.5 The Exact IBF Sampling 187
4.6 The IBF sampler 191
4.6.1 Background and the basic idea 191
4.6.2 The formulation of the IBF sampler 192
4.6.3 Theoretical justification for choosing θ0 =.θ 194
Exercise 4 196
Chapter 5 Bootstrap Methods 203
5.1 Bootstrap Confidence Intervals 203
5.1.1 Parametric bootstrap 203
5.1.2 Non-parametric bootstrap 213
5.2 Hypothesis Testing with the Bootstrap 219
5.2.1 Testing equality of two unknown distributions 219
5.2.2 Testing equality of two group means 223
5.2.3 One–sample problem 228
Exercise 5 231
Appendix A Some Statistical Distributions and Stochastic
Processes 233
A.1 Discrete Distributions 233
A.1.1 Finite discrete distribution 233
A.1.2 Hypergeometric distribution 234
A.1.3 Binomial and related distributions 235
A.1.4 Poisson and related distributions 237
A.1.5 Negative–binomial and related distributions 240
A.1.6 Generalized Poisson and related distributions 242
A.1.7 Multinomial and related distributions 243
A.2 Continuous Distributions 245
A.2.1 Uniform， beta and Dirichlet distributions 245
A.2.2 Logistic and Laplace distributions 248
A.2.3 Exponential， gamma and inverse gamma distributions 249
A.2.4 Chi-square， F and inverse chi-square distributions 251
A.2.5 Normal， lognormal and inverse Gaussian distributions 252
A.2.6 Multivariate normal distribution 254
A.2.7 Student’s t and multivariate t distributions 255
A.2.8 Wishart and inverse Wishart distributions 256
A.3 Stochastic Processes 258
A.3.1 Homogeneous Poisson process 258
A.3.2 Nonhomogeneous Poisson process 259
Appendix B R Programming
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計算統(tǒng)計(英文版)(Computational Statistics ) 節(jié)選
Chapter 1 Generation of Random Variables 1 Why is this textbook important to you? 1.1 As a computational toolbox in the frequentist statistics In the frequent ist statistics， one of the main tasks is to find maximum likelihood estimates of the parameter vector， where 0 is the parameter space (see Chapter 2). Next， it is also important to calculate the standard deviation of or confidence interval ， where is an arbitrary function of 6 (see Chapters 1 and 5). 1.2 As a computational toolbox in the Bayesian statistics In the Bayesian statistics， one often needs to compute posterior moments such asand where can be viewed as a random variable and denotes the observed data (see Chapter 3). More importantly， we would like to generate samples from posterior distributions (see Chapters 1 and 4). 1.3 Benefiting your whole academic career This textbook can help you when you write academic papers， research reports， grant proposals， statistical books， thesis and so on. This textbook can also serve your other courses including assignments and projects. 2 Chapter 2 Why do we need chapter 1? We are faced with a dual world. 2.1 The real world: From practice Suppose that we have observed izations of a set of independent and If we could accept the null hypothesis Hq：where both the population density and the parameter vector 0 are unknown， then we can do many jobs. For example， we can estimate the ， and other unknown quantities. 2.2 The statistical world: From theory to practice Given a theoretical density function or a cumulative distribution function ， we want to generate a random sample from or ， which is the topic of Chapter 1. For example， we can use the sample average or the sample variance to estimate the population mean or the population variance， and so on. 3 Aims of chapter 1 In Chapter 1， we will introduce some basic Monte Carlo simulation techniques for generating random samples from univariate and multivariate distributions with known parameters. These techniques also play a critical role in Monte Carlo integration. We assume that random numbers or r.v.’s uniformly distributed in the unit interval can be satisfactorily produced on the computer. 1 Generation of Random Variables to theory，xn，which can be viewed as real-identically distributed We focus on methods for fast generating non-uniform r.v. 1.1 The Inversion Method 1.1.1Generating samples from continuous distributions 4 Formulation of the inversion method 4.1 A basic result 4.2 The inversion method 4.3 Several examples Example 1.1 Solution: Step 1: Step 2: R code: Equivalent R code: Comment 3: Example 1.2 Solution: Step 1: Step 2: R code: Example 1.3 Solution: Step 1: Step 2:
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