計算統計 (英文版) (Computational Statistics ) 9787030731890 田國梁

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書名：計算統計 (英文版) (Computational Statistics )
ISBN：9787030731890
出版社：科學
著編譯者：田國梁
頁數：336
所在地：中國大陸 *此為代購商品
書號：1513251
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【台灣高等教育出版社簡體書】 計算統計 (英文版) (Computational Statistics ) 787030731890 田國梁

內容簡介

本書是基於作者在香港大學和南方科技大學共14年計算統計教學的經驗，同時結合國內其他高校學生和教師的具體情況精心撰寫而成的，本書主要內容包括：產生隨機變數的方法、幾個重要的優化方法、蒙特卡洛積分方法、貝葉斯計算中的MCMC方法，Bootstrap方法等。本書通過組合傳統教科書和課堂PPT各自的優點，設置了經緯兩條主線，運用塊狀結構呈現知識點，使得每個知識點自我包含，方便教學；另外在介紹重要概念時，注重啟發，邏輯順暢，條理清楚。 本書可供重點高校理工類本科生或一年級研究生作為計算統計英文或雙語課程的教材使用，也可作為其他相關專業人員的參考資料。

作者簡介

田國梁，曾在美國馬里蘭大學從事醫學統計研究六年、香港大學任教八年，現為南方科技大學統計與數據科學系教授、博士生導師，國際統計學會（ISI）當選會員，曾任Computational Statistics & Data Analysis等四個國際統計期刊的副主編，研究領域為計算統計、生物統計和社會統計，發表140餘篇學術論文，出版3本英文專著和1本英文教材，主持國家自然科學基金面上項目兩項。2021年被評為深圳市優秀教師，榮獲南方科技大學2021年度「年度教授獎」和「優秀書院導師獎」。

目錄

Contents
Preface
Chapter 1 Generation of Random Variables
1 1 The Inversion Method
1 1 1 Generating samples from continuous distributions
1 1 2 Generating samples from discrete distributions
1 2 The Grid Method
1 3 The Rejection Method
1 3 1 Generating samples from continuous distributions
1 3 2 The efficiency of the rejection method
1 3 3 Several examples
1 3 4 Log-concave densities
1 4 The Sampling/Importance Resampling (SIR) Method
1 4 1 The SIR without replacement
1 4 2 Theoretical justification
1 5 The Stochastic Representation (SR) Method
1 5 1 The『d='operator
1 5 2 Many-to-one SR for univariate case
1 5 3 SR for multivariate case
1 5 4 Mixture representation
1 6 The Conditional Sampling Method
Exercise 1
Chapter 2 Optimization
2 1 A Review of Some Standard Concepts
2 1 1 Order relations
2 1 2 Stationary points
2 1 3 Convex and concave functions
2 1 4 Mean value theorem
2 1 5 Taylor theorem
2 1 6 Rates of convergence
2 1 7 The case of multiple dimensions
2 2 Newton's Method and Its Variants
2 2 1 Newton's method and root finding
2 2 2 Newton's method and optimization
2 2 3 The Newton-Raphson algorithm
2 2 4 The Fisher scoring algorithm
2 2 5 Application to logistic regression
2 3 The Expectation-Maximization (EM) Algorithm
2 3 1 The formulation of the EM algorithm
2 3 2 The ascent property of the EM algorithm
2 3 3 Missing information principle and standard errors
2 4 The ECM Algorithm
2 5 Minorization-Maximization (MM) Algorithms
2 5 1 A brief review of MM algorithms
2 5 2 The MM idea
2 5 3 The quadratic lower-bound algorithm
2 5 4 The De Pierro algorithm
Exercise 2
Chapter 3 Integration
3 1 Laplace Approximations
3 2 Riemannian Simulation
3 2 1 Classical Monte Carlo integration
3 2 2 Motivation for Riemannian simulation
3 2 3 Variance of the Riemannian sum estimator
3 3 The Importance Sampling Method
3 3 1 The formulation of the importance sampling method
3 3 2 The weighted estimator
3 4 Variance Reduction
3 4 1 Antithetic variables
3 4 2 Control variables
Exercise 3
Chapter 4 Markov Chain Monte Carlo Methods
4 1 Bayes Formulae and Inverse Bayes Formulae (IBF)
4 1 1 The point，function- and sampling-wise IBF
4 1 2 Monte Carlo versions of the IBF
4 1 3 Generalization to the case of three random variables
4 2 The Bayesian Methodology
4 2 1 The posterior distribution
4 2 2 Nuisance parameters
4 2 3 Posterior predictive distribution
4 2 4 Bayes factor
4 2 5 Estimation of marginal likelihood
4 3 The Data Augmentation (DA) Algorithm
4 3 1 Missing data mechanism
4 3 2 The idea of data augmentation
4 3 3 The original DA algorithm
4 3 4 Connection with the IBF
4 4 The Gibbs sampler
4 4 1 The formulation of the Gibbs sampling
4 4 2 The two-block Gibbs sampling
4 5 The Exact IBF Sampling
4 6 The IBF sampler
4 6 1 Background and the basic idea
4 6 2 The formulation of the IBF sampler
4 6 3 Theoretical justification for choosing θ0 = θ
Exercise 4
Chapter 5 Bootstrap Methods
5 1 Bootstrap Confidence Intervals
5 1 1 Parametric bootstrap
5 1 2 Non-parametric bootstrap
5 2 Hypothesis Testing with the Bootstrap
5 2 1 Testing equality of two unknown distributions
5 2 2 Testing equality of two group means
5 2 3 One-sample problem
Exercise 5
Appendix A Some Statistical Distributions and Stochastic Processes
A 1 Discrete Distributions
A 1 1 Finite discrete distribution
A 1 2 Hypergeometric distribution
A 1 3 Binomial and related distributions
A 1 4 Poisson and related distributions
A 1 5 Negative-binomial and related distributions

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