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Bayesian Statistics

Course Materials

(Subject to minor change; make sure to check out the latest version)

  1. August 26
    Introducing Bayesian Inference
  2. September 2
    Linear Model Theory Review
  3. September 9
    Multilevel Structures and Multilevel Linear Models: the Basics
  4. September 16
    Multilevel Linear Models: Varying Slopes, Non-Nested Models and Other Complexities
  5. September 23
    Multilevel Logistic Regression, Multilevel Generalized Linear Models
  6. September 30
    Multilevel Modeling in Bugs and R: the Basics, MCMC Theory. Part 1
  7. October 7
    Causal Inference. Guest lecture by Dr. Ryan Moore
  8. October 14
    Multilevel Modeling in Bugs and R: the Basics, MCMC Theory. Part 2
  9. October 21
    Fitting Multilevel Linear and Generalized Linear Models in Bugs and R, MCMC Coding
  10. October 28
    Understanding and Summarizing the Fitted Models, Multilevel Analysis of Variance
  11. November 4
    Model Checking and Comparison
  12. November 11
    Treatment of Missing Data
  13. November 18
    Sample Size and Power Calculations
  14. November 25
    Bayesian Nonparametrics
  15. December 2
    Online Wrap Up and Presentation of Projects

Calendar

August 26
Introducing Bayesian Inference


Reading:

Code/Data: Intro code

Slides: Introduction to Bayesian methods (This is the slides for the lecture.); Bayesian mechanics slides; Preview of multilevel models.

Exercise: Exercise 1

September 2
Linear Model Theory Review


Exercise 1 dues.

Reading:

  • Gelman & Hill, Chapters 3 and 4

Code/Data: Chapter 3-4 code, Binomial PMF likelihood grid search, Anaemia data, Tweed data, clx.R

Slides: Linear model

Exercise: Exercise 2

September 9
Multilevel Structures and Multilevel Linear Models: the Basics


Exercise 2 dues.

Reading:

  • Gelman & Hill, Chapters 11 and 12
  • Introductory Chapter (Gill and Womack, from the SAGE Handbook of Multilevel Modeling)

Code/Data: chapter 11-12 code, Radon data, Uranium data, Smoking data

Slides: Intro to hierarchical modelling

Exercise: Exercise 3

September 16
Multilevel Linear Models: Varying Slopes, Non-Nested Models and Other Complexities


Exercise 3 dues.

Reading:

  • Gelman & Hill, Chapter 13

Code/Data: Chapter 13 code

Slides: Multilevel linear models

Exercise: Exercise 4

September 23
Multilevel Logistic Regression, Multilevel Generalized Linear Models


Exercise 4 dues.

Reading:

  • Gelman & Hill, Chapter 14 (skip Section 14.3), Chapter 15

Code/Data: Chapter 14 code, polls.dta file (remove .txt appendix, load with foreign library), cheney.asia.sub.txt, police_stops_data.txt.

Slides: Multilevel logistic regression

Exercise: Exercise 5 (see data inside)

September 30
Multilevel Modeling in Bugs and R: the Basics, MCMC Theory. Part 1


Exercise 5 dues.

Reading:

Code/Data: R to JAGS code, data

Slides: MCMC methods

Exercise: Exercise 6

October 7
Causal Inference. Guest lecture by Dr. Ryan Moore


Exercise 6 dues.

Reading:

  • Gelman & Hill Chapters 9 and 10

Code/Data:

Slides:

Exercise: Exercise 7

October 14
Multilevel Modeling in Bugs and R: the Basics, MCMC Theory. Part 2


Exercise 7 dues.

Reading:

  • Gelman & Hill Chapter 16

Code/Data: Chapter 16 code

Slides: BUGS Modeling Language

Exercise: Exercise 8

October 21
Fitting Multilevel Linear and Generalized Linear Models in Bugs and R, MCMC Coding


Exercise 8 dues.

Reading:

  • Gelman & Hill, Chapter 17

Code/Data: Chapter 17 code

Slides: BUGS Modeling Language

Exercise: Exercise 9

October 28
Understanding and Summarizing the Fitted Models, Multilevel Analysis of Variance


Exercise 9 dues.

Reading:

  • Gelman & Hill, Chapter 21

Code/Data: Chapter 21 code, ANOVA, CD4 data, Caesarian data, Bypass data, Depression data.

Slides: Understanding and summarizing models, ANOVA

Exercise: Exercise 10

November 4
Model Checking and Comparison


Exercise 10 dues.

Reading:

  • Gelman & Hill, Chapter 24

Code/Data: Chapter 24 code

Slides: Model checking

Exercise: Exercise 11

November 11
Treatment of Missing Data


Exercise 11 dues.

Reading:

  • Gelman & Hill, Chapter 25
  • Paper by van Buuren and Groothuis-Oudshoorn

Code/Data: Chapter 25 code

Slides: Missing data

Exercise: Exercise 12 (see data inside)

November 18
Sample Size and Power Calculations


Exercise 12 dues.

Reading:

  • Gelman & Hill, Chapter 20

Code/Data: None.

Slides: Sample size

Exercise: Exercise 13

November 25
Bayesian Nonparametrics


Exercise 13 dues.

Reading:

Code/Data: None.

Slides: None.

Exercise: None.

December 2
Online Wrap Up and Presentation of Projects

The project dues today.