1 Markov Chain Monte Carlo Methods 1.4 The Gibbs Sampler 1.4.1 The Slice Gibbs Sampler 1.5 Monitoring Convergence 1.5.1 Convergence diagnostics plots 1.5.2 Monte Carlo Error 1.5.3 The Gelman-Rubin Method 1.6 WinBUGS Introduction 1.6.1 Building Bayesian models in WinBUGS 1.6.2 Model specification in WinBUGS 1.6.3 Data and initial value specification 1.6.4 Compiling model and simulating values

1 Markov Chain Monte Carlo Methods 1.1 Introduction 1.1.1 Integration problems in Bayesian inference 1.1.2 Markov Chain Monte Carlo Integration 1.1.3 Markov Chain 1.2 The Metropolis-Hastings Algorithm 1.2.1 Metropolis-Hastings Sampler 1.2.2 The Metropolis Sampler 1.2.3 Random Walk Metropolis 1.2.4 The Independence Sampler 1.3 Single-component Metropolis Hastings Algorithms 1.4 Application: Logistic regression

1 Bootstrap and Jackknife 1.1 The Bootstrap 1.1.1 Bootstrap Estimation of Standard Error 1.1.2 Bootstrap Estimation of Bias 1.2 Jackknife 1.3 Jackknife-after-Bootstrap 1.4 Bootstrap Confidence Intervals 1.4.1 The Standard Normal Bootstrap Confidence Interval 1.4.2 The Percentile Bootstrap Confidence Interval 1.4.3 The Basic Bootstrap Confidence Interval 1.4.4 The Bootstrap t interval 1.5 Better Bootstrap Confidence Intervals 1.6 Application: Cross Validation

1 Monte Carlo Methods in Inference 1.1 Monte Carlo Methods for Estimation 1.1.1 Monte Carlo Estimation and Standard Error 1.1.2 Estimation of MSE 1.2 Estimating a confidence level 1.3 Monte Carlo Methods for Hypothesis Tests 1.4 Empirical Type I error rate 1.4.1 Power of a Test 1.4.2 Power Comparisons 1.5 Application: “Count Five” Test for Equal Variance

1 Monte Carlo Integration and Variance Reduction 1.1 Monte Carlo Integration 1.1.1 Simple Monte Carlo estimator 1.1.2 Variance and Efficiency 1.2 Variance Reduction 1.3 Antithetic Variables 1.4 Control Variates 1.4.1 Antithetic variate as control variate 1.4.2 Several control variates 1.5 Importance sampling 1.6 Stratified Sampling 1.7 Stratified Importance Sampling

1 Methods for Generating Random Variables 1.1 Generating Uniform(0,1) random number 1.2 Random Generators of Common Probability Distribution in R 1.2.1 The Inverse Transform Method 1.2.2 The Acceptance-Rejection Method 1.2.3 Transformation Methods 1.2.4 Sums and Mixtures 1.3 Multivariate Distribution 1.3.1 Multivariate Normal Distribution 1.3.2 Mixtures of Multivariate Normals 1.3.3 Wishart Distribution 1.3.4 Uniform Distribution on the d−Sphere 1.4 Stochastic Process

1 TEX介绍 2 TEX的宏包和扩展 3 环境集 4 LATEX命令集 5 页面版式命令 6 计数器命令 7 目录表 8 交叉引用和索引 9 宏包 10 LATEX中文化

1 Graphics with R 1.1 Managing graphics 1.1.1 Graphical Functions 1.1.2 Low-level plotting commands 1.1.3 Graphical Parameters 2 Statistical Analysis with R 2.1 Formulae 2.2 Generic Functions 2.3 Packages 3 Programming with R 3.1 Flow Control 3.2 Functions 3.3 Miscellaneous programming tips 3.4 Debugging 3.5 Efficient programming 3.6 R script editors

1 Introduction 1.1 R website 1.2 Differences between R and S 1.3 Start with R 2 Data with R 2.1 Objects 2.2 Reading data in a file 2.3 Saving data 2.4 generating data 2.5 Manipulating objects 2.5.1 Creating objects 2.5.2 Operators 2.5.3 Accessing the values of an object: the indexing system 2.5.4 Accessing the values of an object with names 2.5.5 Arithmetics and simple functions 2.5.6 Matrix Computation

中国科学技术大学：《数理统计》课程教学资源（课件讲义）第十四讲 回归分析（线性回归模型）