STAT:7400 Computer Intensive Statistics
Week 15
Topics
- Markov Chain Monte Carlo
Notes
Reading and Computing
We will continue to look at Markov chain Monte Carlo methods. You should read reading Monahan’s Chapter 13 and Chapter 7 in Givens and Hoeting. Also explore the R packages related to Markov chain Monte Carlo that are available on the Linux systems and on CRAN. In particular, look at the coda and boa packages for output analysis.
Week 14
Topics
- Markov Chain Monte Carlo
Notes
Reading and Computing
We will continue to look at Markov chain Monte Carlo methods. You should read reading Monahan’s Chapter 13 and Chapter 7 in Givens and Hoeting. Also explore the R packages related to Markov chain Monte Carlo that are available on the Linux systems and on CRAN. In particular, look at the coda and boa packages for output analysis.
Week 13
Topics
- Variance reduction
- Markov Chain Monte Carlo
Reading and Computing
We will continue look at variance reduction ideas. Givens and Hoeting discuss these in Section 7.3.
We will also start discussing Markov chain Monte Carlo methods. You should read reading Monahan’s Chapter 13 and Chapter 7 in Givens and Hoeting. Also explore the R packages related to Markov chain Monte Carlo that are available on the Linux systems and on CRAN. In particular, look at the coda and boa packages for output analysis.
Week 12
Topics
- Generating random variables and random vectors
- Variance reduction
Notes
Reading and Computing
We continue to look at methods of generating random variables from non-uniform distributions. Monahan discusses this in Chapter 11. You should also read Chapter 6 in Givens and Hoeting through 6.2.3.
You should look at the facilities R provides for generating variates from standard distributions (rnorm, rgamma, etc.). Also look at the control provided by RNGkind over the underlying method for generating uniform pseudo-random numbers.
We will then look at variance reduction ideas. Givens and Hoeting discuss these in Section 7.3.
Week 11
Topics
- Brief introduction to uniform pseudo-random variables
- Generating random variables and random vectors
Notes
Reading and Computing
We will look at methods of generating random variables from non-uniform distributions. Monahan discusses this in Chapter 11. You should also read Chapter 6 in Givens and Hoeting through 6.2.3.
You should look at the facilities R provides for generating variates from standard distributions (rnorm, rgamma, etc.). Also look at the control provided by RNGkind and RNGversion over the underlying method for generating uniform pseudo-random numbers.
Week 10
Topics
- Some Machine Learning
- Brief introduction to uniform pseudo-random variables
Notes
Reading and Computing
We will briefly review methods for and issues in generating uniform pseudo-random numbers.
Week 7
Topics
- Density estimation and smoothing.
Reading and Computing
You should read Chapters 10 and 11 in Givens and Hoeting. Monahan also discusses density estimation on pages 344–349 and curve fitting on 159–163. You should also explore the function density, the KernSmooth package and the functions gam, loess, and other methods based on smoothing.
You should also read Chapters 12 in Givens and Hoeting and explore some of the packages and functions implementing related methods in R. These include SemiPar, mgcv, acepack, among others. Package MASS also implements several relevant functions.
Week 6
Topics
- Brief introduction to optimization.
- Density estimation and smoothing.
Week 5
Topics
- Brief introduction to optimization.
Notes
Reading and Computing
You should read Chapters 8 and 9 in Monahan and Chapters 2 and 4 in Givens and Hoeting. You should also explore the optim and optimize functions and the Optimization task view.
Week 4
Topics
- Matrices with special structure.
- Iterative methods for solving linear equations.
- Linear algebra software.
Week 3
Topics
- Brief introduction to numerical linear algebra.
Notes
Reading and Computing
This week we will start a brief review of numerical linear algebra, very briefly covering the material in Monahan’s Chapters 3–6. You should start to read these chapters now and continue next week. The objective is not to understand every detail, but to get a general sense of the issues and the methods available.
As you read, explore which methods are available in R and how they can be used. Some functions to examine are lm.fit, solve, and qr.
Week 1
Topics
- Review of syllabus and course outline.
- Brief overview of tools.
- Outline of computer architecture.
- Overview of computer arithmetic.
Reading and Computing
To brush up on prerequisites you should read the first chapter of Givens and Hoeting.
Read the web pages