STA 376: Advanced Modelling and Scientific Computing
Office Hours
TBA
Prerequisites
Basic statistical theory, linear models, and Bayesian modelling at the level of STA214, STA215 and STA244. Some experience in a lower level programming language such as C or FORTRAN and familiarity with UNIX workstations is assummed.
Course Description
An introduction to advanced statistical modelling and modern numerical
methods useful in data analysis, model exploration, inference, and
prediction, with particular emphasis on Bayesian analysis. Topics
include: approximate methods of integration (Normal approximations,
Laplace), random variable generation, Monte Carlo methods of
integration, methods of obtaining samples from posterior distributions
(Gibbs sampling and other MCMC methods), diagnostics, variance
reduction techniques, and optimization methods. Methods will be
illustrated on examples from hierarchical models, linear and
generalized linear (additive) models, variable selection, outliers,
missing data, nonconjugate problems, and experimental design.
Students are expected to develop analyses using high level languages
such as S-plus and BUGS, as well as low level languages such as C and
Fortran using functions available in standand libraries.
References
- Tools for Statistical Inference, (3rd Edition) Tanner
- Markov Chain Monte Carlo in Practice, Gilks, Richardson, and Spiegelhalter
- Stochastic Simulation, Ripley
- Numerical Computation Using C Glassey
In addition to these books, material will be drawn from the current
literature as this is a rapidly developing field.
Grading
The course grade is based on periodic assignments and
a project. By the end of Fall Break, students should have identified
a topic for the course project. The project should use techniques
developed in the course applied to a problem of scientific interest,
using real data (of course). A classroom presentation and a written report on the project is due on December (dates TBA).
clyde@stat.duke.edu - 9/1/97