1 Programming 1.1 M file 1.1.1 Program Control Statements 1.1.2 M-File Functions 1.2 anonymous functions 2 Computational statistics with Matlab 2.1 Functions on Probability and Statistics 2.1.1 Probability distribution 2.1.2 Descriptive statistics 2.1.3 Statistical plotting 2.1.4 Linear model 2.1.5 Multivariate Statistics 2.2 Monte Carlo with Matlab 2.2.1 Monte Carlo Assessment of Hypothesis Testing 2.2.2 MCMC with matlab 3 Symbolic computation with matlab 3.1 Creating Symbolic Variables and Expressions 3.2 Calculus 4 Optimization 4.1 Unconstrained Minimization Example 4.2 Nonlinear Inequality Constrained Example

1 Introduction 1.1 GUI and Basic functions 1.1.1 Command Window 1.1.2 Command History 1.1.3 MatLab Help 2 Data in MatLab 2.1 Manipulating data 2.1.1 Creating Objects 2.1.2 Operators 3 Graphics 3.1 Use plotting tools 3.2 Use the command interface 3.2.1 Basic plots 3.2.2 Adding Plots to an Existing Graph 3.2.3 Multiple Plots in One Figure 3.2.4 Controlling the Axes 3.2.5 Axis Labels and Titles 3.3 Mesh and Surface Plots 3.4 Creating Specialized Plots 3.5 Advanced plotting

1 Numerical optimization methods in R 1.1 Root-finding in one dimension 1.1.1 Bisection method 1.1.2 Brent’s method 1.1.3 Newton’s method 1.1.4 Fisher scoring 1.2 multivariate optimization 1.2.1 Newton’s method and Fisher scoring 1.3 Numerical Integration 1.4 Maximum Likelihood Problems 1.5 Optimization Problems 1.5.1 One-dimension Optimization 1.5.2 multi-dimensional Optimization 1.6 Linear Programming

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

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