STA 214 PROBABILITY & STATISTICAL MODELS

Spring 1997

Classes:

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

Part 2: Peter Mueller



Assignments:

Assignment 6 Answers 6 (not yet there)
Assignment 7
Due Tuesday 4/22/97
Question 1: Splus program
Data: X , Y , day , ni , 214.dta qnorm ,
Answers 7
Assignment 8
Due Thursday April 24 (last class).
Data and Splus code (you don't need either for the homework - just in case you want to experiment..).

Midterm 2:

Click here for the problems.
Data: Y .
Due: We, May 7, 12pm

.


Synopsis of course content:


This 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.

Papers and additional material will be available 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.
Assessment will be equally split between homeworks and exam on 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.


DETAILED SYLLABUS:


PART 2: Tentative schedule of lectures

Mar 13:
Graphical representations of probability models and decision problems; influence diagrams; solving influence diagrams.
Mar 25, 27:
Alternatives to the MDP model: flexible mixture models for density estimation with partially improper priors. Polya trees and their uses
Apr 1, 3:
Nonlinear models for repeated measurements
(Mixed effects models, longitudinal data models, population models, pharmacokinetic/pharmacodynamic models, ...); models, MCMC with normal population distributions.
Apr 8, 10:
Mixtures in mixed effects models
Case-control studies
Apr 15,17
Bayesian models for case-control studies: Mixtures of normal exposure models, relationship to logistic prospective models. Error in variables, meta-analysis, categorical covariates, ...
Apr 22,24
Additional topics: maybe Neural network models
Wrap-up and review.