STA 214 PROBABILITY & STATISTICAL MODELS

Spring 1997

Classes:

Tue/Thu 9:10-10:25am, room 025 Old Chemistry Bldg

STA 214: Syllabus and course details

Synopsis of course content:


The 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.

The second half of the course will consider application of themes developed in the first part of the course to a variety of important statistical problems. We will discuss in some detail Bayesian inference in nonlinear models for repeated measurements and case control studies. Besides introducing the basic problem formulation and inference in commonly used models the discussion will include the application of mixtures based on models introduced in the first part of the course. Other topics to be covered include graphical representation of probability models and decision problems (influence diagrams, optimal design), and, if time permits, alternative mixture models and approaches to nonparametric Bayesian inference.

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.

Additional material will be available at a later date in support of the second half of the course, including important reference papers and some selected current research papers on the covered topics. Gelman et al. will serve as a reference to standard methods and models.

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.
One in class mid-term for Part 1, and one take-home mid-term for Part 2.
Assessment will be equally split between homeworks and mid-term on Part 1, and TBA for Part 2.

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.