1 EM optimization method 1.1 EM algorithm 1.2 Convergence 1.3 Usage in exponential families 1.4 Usage in finite normal mixtures 1.5 Variance estimation 1.5.1 Louis method 1.5.2 SEM algorithm 1.5.3 Bootstrap method 1.5.4 Empirical Information 1.6 EM Variants 1.6.1 Improving the E step 1.6.2 Improving the M step 1.7 Pros and Cons

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

《实用统计软件》课程教学资源（阅读材料）A History of Markov Chain Monte Carlo——Subjective Recollections from Incomplete Data

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

《实用统计软件》课程教学资源（阅读材料）T. DiCiccio and B.Efron（1996）, Bootstrap Confidence Intervals, Statistical Science, 3,189-228

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

《实用统计软件》课程教学资源（阅读材料）图像合成方面应用的一个介绍 Monte Carlo Integration

《实用统计软件》课程教学资源（阅读材料）多元分类问题中的应用 Variance Reduction with Monte Carlo Estimates of Error Rates in Multivariate Classication

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