STAT 532 Overview:

  • Meeting Time: Monday, Wednesday, Friday -  1:10 - 2:00 
  • Classroom: Wilson Hall 1-147
  • Office Hours: Monday/Wednesday 2  -  3 or my appointment

Course Description

This course will introduce the basic ideas of Bayesian statistics with emphasis on both philosophical foundations and practical implementation. The goal of this course is to provide a theoretical overview of Bayesian statistics and relevant computational tools along with the knowledge and experience to use them in a research setting.

Prerequisites

One of: STAT 422 or STAT 502 and STAT 506

Course Objectives

At the completion of this course, students will be able to:

  1. Describe fundamental differences between Bayesian and classical inference,
  2. Select appropriate models and priors, write likelihoods, and derive posterior distributions given a research question and dataset,
  3. Make inferences from posterior distributions,
  4. Implement Markov Chain Monte Carlo (MCMC) algorithms, and 
  5. Read, understand, and explain techniques in scientific journals implementing Bayesian methods.

Textbook:

  1. A First Course in Bayesian Methods, by Peter Hoff.

Course Evaluation:

  • Quizzes: 10% of final grade:
    • There is no formal attendance policy, but there will be weekly quizzes. 

  • Homework: 30% of final grade
    • Homework problems will be assigned every week. Students are allowed and encouraged to work with classmates on homework assignments, but each student is required to write their own homework.
  • Midterm Exam 20% & Final Exam 20%  of final grade
    • Exams will have two components: an in-class exam and a take home portion. The in-class portions will be largely conceptual including some short mathematical derivations. The take home portions will focus on the analysis of data and implementation of Bayesian computational methods.
  • Project 20% of final grade
    • The project will be a case study where students will apply Bayesian methods to a dataset agreed upon by the instructor and student.

Course Schedule:

Week Content

 Week 1: Aug 27  

 Week 1: Aug 29

 Week 1: Aug 31

 Week 1 notes

 Mon. Quiz 1: Introduction & Course Overview

 Wed. Mechanics of Bayesian Statistics

 Fri. Philosophy of Bayesian Statistics: (Read Gelman's Philosophy and Practice of Bayesian Statistics)

 Week 2: Sept 3  

 Week 2: Sept 5

 Week 2: Sept 7

 Week 2 notes

 Mon. No Class (Labor Day)

 Wed. HW 1 due, (LaTex) (PDF) Quiz 2: Belief, Probability, and Exchangeability

 Fri. Belief, Probability, and Exchangeability

 Week 3: Sept 10  

 Week 3: Sept 12

 Week 3: Sept 14

 Week 3 notes

 Mon. Quiz 3, HW 2 due (LaTex) (PDF). Binomial Models

 Wed. Poisson and Exponential Family Models

 Fri. Priors

 Week 4: Sept 17  

 Week 4: Sept 19

 Week 4: Sept 21

 Week 4 notes

 Mon. Quiz 4, HW 3 due (LaTex) (PDF). Posterior Sampling and Intro to Monte Carlo

 Wed. Normal Model

 Fri. No class: MT ASA Chapter Meeting in Missoula, MT 

 Week 5: Sept 24

 Week 5: Sept 26

 Week 5: Sept 28 

 Week 5 notes

 Mon. Quiz 5, HW 4 due (LaTex) (PDF). Normal Model (cont). R code: (MonteCarlo Normal)

 Wed. MCMC with Normal Model. R code: (Gibbs Sampler)

 Fri. Demo: Intro to MCMC (HTML) (R Markdown)

 Week 6: Oct 1

 Week 6: Oct 3

 Week 6: Oct 5

 Week 6 notes

 Mon. Quiz 6, HW 5 due (LaTex) (PDF). Demo: Intro to MCMC (HTML) (R Markdown)

 Wed. MCMC

 Fri. Demo: MCMC/JAGS/Stan (HTML) (R Markdown)

 Week 7: Oct 8

 Week 7: Oct 10

 Week 7: Oct 12

 

 Mon. Quiz 7, HW 6 due (LaTex) (PDF). Demo2: MCMC/JAGS/Stan

 Wed. In class exam (2016 in class exam) (2016 take-home exam) (midtermbikes.csv) (bozemanhousing.csv)

 Fri. No class - work on midterm take-home (2017 take-home exam) (BozemanHousing2017exam.csv)

 Week 8: Oct 15

 Week 8: Oct 17

 Week 8: Oct 19

 MonMidterm take-home due Multivariate Normal Distribution

 Wed. Inverse Wishart Distribution

 Fri.  Hierarchical Modeling.

 Week 9: Oct 22

 Week 9: Oct 24

 Week 9: Oct 26 

 Mon. HW 7 due (LaTex) (PDF) Quiz 9. Hierarchical Modeling.

 Wed. Lab: Shrinkage and Stein's Paradox (LaTex) (PDF) (SteinData.csv)

 Fri.  Bayesian Regression

 Week 10: Oct 29

 Week 10: Oct 31

 Week 10: Nov 2

 Mon. Quiz 10, HW 8 due (LaTex) (PDF). 

 Wed. Bayesian Regression

 Fri. Bayesian Regression

 Week 11: Nov 5

 Week 11: Nov 7

 Week 11: Nov 9 

 Mon. Quiz 11, HW 9 due (LaTex) (PDF). (SeattleHousing.csv) Bayesian Regression + Non conjugate priors and Metropolis-Hastings 

 Wed. Metropolis-Hastings (Advanced MCMC)

 Fri. Metropolis-Hastings. Final Description Due, write 1/2 page summary of data set + proposed methods or paper. 

 Week 12: Nov 12

 Week 12: Nov 14

 Week 12: Nov 16 

 Mon. Quiz 12, No Class (Veteran's Day)

 Wed. Hierarchical Regression.

 Fri. Hierarchical Regression.

 Week 13: Nov 19

 Week 13: Nov 21

 Week 13: Nov 23

 Mon. Quiz 13, HW 10 due (LaTex) (PDF) (SeattleBinaryHousing.csv). Latent Variable Models.

 Wed. No Class (Thanksgiving Break)

 Fri. No Class (Thanksgiving Break)

 Week 14: Nov 26

 Week 14: Nov 28

 Week 14: Nov 30

 

 Mon. Quiz 14. Bayesian testing and point mass priors.

 Wed. 

 Fri. 

 Week 15: Dec 3

 Week 15: Dec 5

 Week 15: Dec 7 

 Mon. In Class Final. Take home final due (PDF). Course Lecture Notes (PDF)

 Wed. Class Presentations 

 Fri. Class Presentations 

  Finals Week: 

 Class Presentations. 

Project Rubric (PDF)