Math459: Bayesian Statistics (Spring 2010)

Instructor

Nan Lin

Office

Cupples I, Room 205

Phone

935-5703

Email

Time and location

TBA

Office hours

TBA

Textbook

Carlin, B. P. And Louis, T. A. (2008) Bayesian Methods for Data Analysis, 3rd Edition, Chapman & Hall/CRC. ISBN : 1584886978

Reference Books

Jim, Albert (2008), Bayesian Computation with R, Springer. ISBN: 0387713840 Online R codes

Description

This course introduces the Bayesian approach to statistical inference for data analysis in a variety of applications. The topics include: comparison of Bayesian and frequentist methods, Bayesian model specification, prior specification, basics of decision theory, Markov chain Monte Carlo, Bayes factor, empirical Bayes, hierarchical models, Bayesian data analysis using R and WinBUGS.

Prerequisite

Math493 or equivalent.

Computing

Real statistical analysis is practical only in the context of computer statistical packages.  During this course, students will learn how to use statistical software R and WinBugs to perform Bayesian analysis. Both R and WinBugs are free software. You can access these software on the computers in the Computing Center in Eads Hall.

Grading

Your course grade depends on your performance on the homework and final term project. Your percentage grade is first calculated using the following formula.

 

Percentage grade = 60% * Homework + 40% * Term Project

 

Then your letter grade is determined as follows. The A range will be 90 to 100, the B range will be 80 to 90, the C range will be 70 to 80, and the D range will be 60 to 70, with plus and minus grades at the tops and bottoms of each of these ranges. (If you are registered pass/fail, you must average at least 70 to pass.)

Term project

Students need to independently complete a term project with a written report. Your project objective can be either methodological studies on Bayesian inference or applications of Bayesian analysis to real-world data not discussed in class. (Please see a list of examples here). Projects will be carried out in three phases.

1. Project proposal ()

This is a detailed description of what you plan to do, including question(s) to be addressed, dataset to be used (if any), methods to be applied. This should not exceed 1 page.

2. Project interim report ()

This is an informal report that includes results obtained thus far and a brief summary of what they mean and what remains to be done. The purpose of this report is to make sure your project is on track.

3. Project presentation (Written report)

Each student needs to give a 15 min oral presentation about her/his project in class during the final week (). The written report should not exceed 10 pages (not including source codes and plots).

 

Calendar

Week

Lecture

Reading

Homework

Lab

Remark

Week 1

(Jan12 - Jan16)

Introduction to Bayesian statistics, comparison of frequentist and Bayesian methods

1.1-1.4 (CL)

1.1-1.2 (A)

 

Basics of R

 

Week 2

(Jan 19 - Jan 23)

One-parameter models

1.5,2.1 (CL)

1.3 (A)

HW1

Solution

 

No class on Jan 19

 

Week 3

(Jan 26 - Jan30)

Prior Specification

2.2 (CL)

HW2

Solution

Writing a function; simulation

 

Week 4

(Feb 2 - Feb 6)

Multi-parameter and multivariate models

Appendix A (CL)

Chapters 2-4 (A)

 

Example 1: dose-response data

Example 2: mixture of conjugate prior

 

Week 5

(Feb 9 – Feb 13)

Basics of Decision Theory, Hierarchical models

Appendix B.1,

2.3, 2.4.1 (CL)

Chapter 7 (A)

HW3

Solution

A hierarchical model

 

Week 6

(Feb 16 – Feb 20)

Laplace Approximation, Random number generation, Monte Carlo methods

3.1-3.3 (CL)

HW4

Solution

 

 

Week 7

(Feb 23 – Feb 27)

Metropolis-Hastings algorithm, Gibbs sampler, convergence diagnostic

3.4 (CL)

6.7-6.9 (A)

HW5

Solution

An example of using the M-H algorithm

Introduction to the boa package (manual)

 

Week 8

(Mar 2 – Mar 6)

Review

 

 

 

An old exam

Week 9

(Mar 9 – Mar 13)

Spring Break

 

 

 

No class

Week 10

(Mar 16 – Mar 20)

Bayes Factor and DIC

2.4.2,4.6.1 (CL)

 

 

 

Week 11

(Mar 23 – Mar 27)

Linear models

9.2 (A)

 

WinBUGS example: simple linear regression

WinBUGS FAQs

Project proposal due Monday, Mar 23

Week 12

(Mar 30 – Apr 3)

Linear hierarchical models, Generalized linear models

7.3 (CL)

Chapter 7 (A)

 

Hooker data, R code, WinBUGS code

 

Week 13

(Apr 6 – Apr 10)

ANOVA, Robust models

 

 

BRugs manual, example

link

Project interim report due Monday, Apr 6

Week 14

(Apr 13 – Apr 17)

Mixture models, spatial-temporal modeling of extreme events, computing Bayes Factor, SSVS

 

 

 

 

Week 15

(Apr 20 – Apr 24)

Student oral presentation schedule

 

 

 

Written report due at 5pm, Monday, May 5