Computational statistics and statistical computing are two areas that employ computational, graphical, and numerical approaches to solve statistical problems. This course covers the traditional core material of computational statistics, with an emphasis on using the R language via an examples-based approach.

1. Introduction of R
2. Methods for Generating Random Variables
Transformation and Inverse method
Box-Muller and Polar Marsaglia method
Bivariate Normal Random Variables
Accept-Reject Methods
4.Monte Carlo Integration and variance reduction
Buffon`s Needle problem
Antithetic variate, control variate
Stratified sampling
Importance Sampling
Stratified Importance Sampling
5. Monte Carlo Methods for Inferential Statistics
Classical Inferential Statistics
Monte Carlo Methods for Inferential Statistics
Bootstrap Methods  Moore14.pdf
6. Data Partitioning
Cross-Validation
Jackknife
Jackknife-after-Bootstrap
7. Permutation Tests
Tests for Equal Distributions
Multivariate Tests for Equal Distributions
8.Markov Chain Monte Carlo
The Metropolis-Hastings algorithm
Gibbs sampler.
9.Kernel Density Estimation
Univariate Density Estimation
Kernel Density Estimation
Bivariate and Multivariate Density Estimation

作業與上機演練

Rizzo, M. L., Statistical computing with R
Morgan, B.J.T., Elements of Simulation
Robert, C. P., Casella, G. Monte Carlo Statistical Methods
Martine W. L. Computational Statistics Handbook with MATLAB Second Edition