Bayesian density estimation programs that sit in
the MDP ftp directory
Assignments:
Synopsis of course content:
This first half of the course will focus on mixture models in statistical work.
Statistical models with mixture structure and components are very widely used in
research and application. We will explore the development of theory, models and
computational methods in various mixture contexts, and use this framework to introduce
new distributions and distribution theory, simulation methods, graphical representations
and other ideas and methods as necessary. Iterative simulation methods (Markov chain Monte
Carlo methods, or MCMC) are fundamental to modern applied statistics and will be used throughout
the course.
Textbooks:
There is no required text. However,
"Bayesian Data Analysis", by A Gelman, J B Carlin, H S Stern and D B Rubin (Chapman & Hall)
is strongly recommended. It covers a lot of basic Bayesian statistical theory, methodology, and
computation, and has useful review and reference material on elements of Bayesian inference,
distribution theory, and so forth. For anyone interested in further statistics courses at Duke,
or future research, this is a great book in any case. It is also a text for STA 215 this semester.
A course-pack will be available for the first half of the course on mixture modelling,
with much of the course will be based around selected sections from other texts and
published papers from the research literature.
An earlier announcement listed the book "Markov Chain Monte Carlo in Practice" by Gilks et al.
This will be a very useful book for anyone interested in Bayesian statistics beyond this course,
but is not really central for the revised version of this course.
Assignments etc:
Regular homeworks and weekly readings will be required, and there will be
one in class mid-term for Part 1
Assessment will be equally split between homeworks and mid-term on Part 1.
Prerequisites:
Math 103 and 104, and STA 213 and 244 or equivalent. A background in statistics
at a more advanced level, such as STA 215 and 216, is desirable. Co-registration in either
STA 215 or 216 would be beneficial. Computing will be part of the course. Students will be expected
to develop statistical and graphical programs using S-Plus on unix, or similar tools such as BUGS or Matlab,
with minimal guidance from the instructor.
DETAILED SYLLABUS:
PART 1: Schedule of lectures
Jan 16,21:
Introduction: Basic review of Bayesian inference and methods, including posterior simulation.
Basic structure of mixtures and mixture models: Data models and mixed populations, and mixtures
arising in other areas.
Jan 23:
NO CLASS. Reading and modelling assignments
Jan 28,30:
Mixtures of data distributions: Structure and model fitting via MCMC
Some specific discrete mixtures of normals in application
Problems of identification, posterior summarisattion, prediction
Feb 4,6:
Multivariate models and distribution theory: Multinormal distribution and random sampling context
Wishart distributions, posterior and predictive inference in normal models
Feb 11,13:
Multivariate normal mixture models: Classification and related problems
MCMC methods in multivariate normal mixtures
Feb 18
Mixture priors and Bayes's factors/likelihood ratios in
hypothesis testing
Feb 20,25:
Dirichlet process and Dirichlet mixtures (or MDPs): Theory of DP and MDPs
Predictive density estimation using mixtures
Feb 27:
NO CLASS. Reading and modelling assignments, or guest lecture (TBA)
Mar 4:
More on MDPs including MCMC methods of model fitting
Mar 6:
Mid-term ("final" for Part 1) in class test