EPSE 581C: Bayesian Methods
2019/20, Winter Term 1
See the full syllabus here.
Office hours:
Mondays 4:30 - 5:30 PM in Scarfe 2526.
At most other times, I will be in my office in Scarfe 2526.
Meeting times and locations:
Mondays, 1:00 - 4:00 PM, Scarfe 204A
Course overview:
This course will cover the basics of Bayesian methodology. We will compare and contrast the Bayesian approach to estimation and inference with the traditional frequentist approach you are all familiar with from previous statistics-based courses. The paramount role of prior information in Bayesian methodology will be emphasized throughout. Although you will work on a variety of applied data problems, this course is about concepts and methodology, not computation. There will also be regular emphasis on practical applications for applied researchers in a variety of disciplines.
Download RStudio here:
https://www.rstudio.com/products/rstudio/download/
Recommended textbooks:
- Bayesian Data Analysis, Andrew Gelman, John B. Carlin, Hal S. Stern, David B. Dunson, Aki Vehtari, and Donald B. Rubin. This is an excellent textbook written by a swath of luminaries in the field. It contains much of the relevant mathematics of the subject, is full of applied examples (with R code), and is relatively easy to read. Available online through UBC Library.
- Statistical Rethinking, Richard McElreath. A soft textbook written for applied scientists. A softer textbook (in terms of mathematics), full of applied examples (with R code). Available online through UBC Library.
Class Notes:
-Week 1: Introduction: Bayes' Theorem, posteriors, likelihoods, priors, normalizing factors
-Week 2: Mathematical foundations of Bayesian methodology
-Week 3: Single parameter models: basic estimation and inference
-Week 4: Multi-parameter models: basic linear model, nuisance parameters
-Week 5: Basic linear model; model building and checking
-Week 6: More on linear models, prediction
-Week 7: The problem of computation: a closer look at how we approximate the posterior
-Week 8: More on computation and model selection
-Week 10: Measurement error, missing data, types of priors
-Week 1: Introduction: Bayes' Theorem, posteriors, likelihoods, priors, normalizing factors
- Reading from McElreath: Chapter 1
- Reading from Gelman et al.: Chapter 1
-Week 2: Mathematical foundations of Bayesian methodology
- Reading from McElreath: Chapter 1
- Reading from Gelman et al.: Chapter 1
-Week 3: Single parameter models: basic estimation and inference
- Reading from McElreath: Chapter 2
- Reading from Gelman et al.: Chapter 2
-Week 4: Multi-parameter models: basic linear model, nuisance parameters
- Reading from McElreath: Chapters 4 & 5
- Reading from Gelman et al.: Chapter 3
-Week 5: Basic linear model; model building and checking
- Reading from McElreath: Chapter 6
- Reading from Gelman et al.: Chapters 6 & 7
-Week 6: More on linear models, prediction
- Case study: Tsutakawa 1985
-Week 7: The problem of computation: a closer look at how we approximate the posterior
- Reading from McElreath: Chapter 3 & 8
- Reading from Gelman et al.: Chapters 10, 11 & 12 (depending on how deeply you want to go!)
-Week 8: More on computation and model selection
-Week 10: Measurement error, missing data, types of priors
Homeworks:
-Week 1, 2 & 3 problems: due in-class Oct. 7th
-Final problems: due Dec. 20th
-Week 1, 2 & 3 problems: due in-class Oct. 7th
-Final problems: due Dec. 20th
- Garthwaite, Kadane, & O'Hagan: Statistical methods for eliciting probability distributions (2005)
- Final dataset
- Final R code