- 计算统计(英文版全彩印刷)(精)
- - 作者：编者:田国梁|责编:王胡权
  - 出版社：科学
  - ISBN：9787030731890
  - 出版日期：2023/03/01
  - 页数：336
- 售价：75.2

内容大纲
本书是基于作者在香港大学和南方科技大学共14年计算统计教学的经验，同时结合国内其他高校学生和教师的具体情况精心撰写而成的，本书主要内容包括：产生随机变量的方法、几个重要的优化方法、蒙特卡洛积分方法、贝叶斯计算中的MCMC方法，Bootstrap方法等。本书通过组合传统教科书和课堂PPT各自的优点，设置了经纬两条主线，运用块状结构呈现知识点，使得每个知识点自我包含，方便教学；另外在介绍重要概念时，注重启发，逻辑顺畅，条理清楚。
本书可供重点高校理工类本科生或一年级研究生作为计算统计英文或双语课程的教材使用，也可作为其他相关专业人员的参考资料。
作者介绍
田国梁，曾在美国马里兰大学从事医学统计研究六年、香港大学任教八年，现为南方科技大学统计与数据科学系教授、博士生导师，国际统计学会（ISI）当选会员，曾任Computational Statistics & Data Analysis等四个国际统计期刊的副主编，研究领域为计算统计、生物统计和社会统计，发表140余篇学术论文，出版3本英文专著和1本英文教材，主持国家自然科学基金面上项目两项。2021年被评为深圳市优秀教师，荣获南方科技大学2021年度“年度教授奖”和“优秀书院导师奖”。
目录
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
    A.1.6  Generalized Poisson and related distributions
    A.1.7  Multinomial and related distributions
  A.2  Continuous Distributions
    A.2.1  Uniform, beta and Dirichlet distributions
    A.2.2  Logistic and Laplace distributions
    A.2.3  Exponential, gamma and inverse gamma distributions
    A.2.4  Chi-square, F and inverse chi-square distributions
    A.2.5  Normal, lognormal and inverse Gaussian distributions
    A.2.6  Multivariate normal distribution
    A.2.7  Student's t and multivariate t distributions
    A.2.8  Wishart and inverse Wishart distributions
  A.3  Stochastic Processes
    A.3.1  Homogeneous Poisson process
    A.3.2  Nonhomogeneous Poisson process
Appendix B  R Programming
  B.1  Basic Commands
    B.1.1  Expressions
    B.1.2  Assignment operator
  B.2  Vectors and Matrices
    B.2.1  Vectors
    B.2.2  Matrices
  B.3  Lists, Data Frames and Arrays
    B.3.1  Lists
    B.3.2  Data frames
    B.3.3  Arrays
  B.4  Flow Control
  B.5  User Functions
  B.6  Some Commonly-Used R Functions for Data Analysis
Appendix C  Introduction of Latent Variables Methods
  C.1  MLEs of Parameters in t Distribution
  C.2  MLEs of Parameters in the Poisson Additive Model
  C.3  MLEs of Parameters in Constrained Normal Models
  C.4  Binormal Model with Missing Data
List of Figures
List of Tables
List of Acronyms
List of Symbols
References
Subject Index

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