- Fall 2020
- Instructor: David B. Dahl
- Email: dahl@stat.byu.edu
- Virtual office hours:
- Via Zoom: https://byu.zoom.us/j/92679630337
- Note: Ping Dr. Dahl at 1-801-422-9222, if waiting more than 2 minutes.
- Tuesdays, 4:30-5:30pm
- Thursdays, Noon-1pm

- Teaching Assistant: Brianne Gurney
- Email: brianne.gurney@gmail.com

- Website: https://dahl.byu.edu/651
- Check for course announcements, lecture materials, and assignments.

- Quotes:
- “I never teach my pupils, I only attempt to provide the conditions in which they can learn.” — Albert Einstein
- “One learns by doing the thing; for though you think you know it, you have no certainty until you try.” — Sophocles

#### 2020-09-01

- Topic: Foundations
- Introduction based on Hoff
- Homework 1 is assigned
- Class project is assigned

#### 2020-09-03

- Topic: Foundations
- Read Gelman Chapter 1, Berger & Berry (1998) [free when accessed via BYU’s network]
- Single-parameter, conjugate exampole
- Predictive distributions in general
- Binomial-beta example model: model, code
- Calculations for Berger & Berry (1988): notes, code

#### 2020-09-08

- Topic: Basic single-parameter models
- Read Gelman Chapter 2
- Homework 2 is assigned
- Notes on “noninformative” priors: flat prior, Jefferys’ prior
- Variance decomposition
- Bayes estimation and decision theory (Notes by Jonathan Pillow)

#### 2020-09-10

- Topic: Introduction to Black-box software for Bayesian analysis
- Read: Bayesian Basics
- Stan: A state-of-the-art platform for statistical modeling and high-performance statistical computation
- Stan documentation
- JAGS: Just Another Gibbs Sampler
- JAGS User Manual
- Binomial-beta example model, revisited:

#### 2020-09-15

- Topic: Basic multiparameter models
- Read Gelman Chapter 3
- Homework 3 is assigned
- Logistic regression, extending the binomial-beta model with a covariate:
- Mixture distributions: examples, Student t as a mixture of normals

#### 2020-09-17

- Topic: Basic multiparameter models
- Read Gelman Chapter 3
- Bioassay example

#### 2020-09-22

#### 2020-09-24

- Topic: Hierarchical Models
- Read Gelman Chapter 5
- Homework 5 is assigned
- Homework 6 is assigned
- Introduction to hierarchical models
- Discussion on exchangeability, independence, and de Finetti theorem.
- Ingot example:
- Data
- Model with a mistake
- Model
- Code “by hand”
- Using Stan: R file, Stan file
- Using JAGS (under different model specifications): R file, JAGS file

- Change-point model

#### 2020-09-29

#### 2020-10-01

#### 2020-10-06

#### 2020-10-08

- Topic: Catch-up and review.
- No reading assignment.

#### 2020-10-13

- Topic: More MCMC and Convergence Diagnostics
- Read both articles and, for one of them, comment and suggest a question of discussion:

#### 2020-10-15

- Topic: Advanced MCMC Computations
- Read Gelman Chapter 12
- Overview of advanced MCMC techniques
- Discussion of commonly used methods among the faculty
- Adaptive MCMC
- Article: Examples of Adaptive MCMC
- Revisit the random walk for beta: code

- Article: Bayesian auxiliary variable models for binary and multinomial regression
- Article: A Conceptual Introduction to Hamiltonian Monte Carlo

#### 2020-10-20

#### 2020-10-22

- No reading quiz (that would have been due yesterday)
- Midterm Exam I
- Released at 8am and is due at the start of our next class period
- Covers all material to date

- In class, we will answer clarify questions about Midterm Exam I

#### 2020-10-27

- Topic: Model Checking
- Read Gelman Chapter 6
- Homework 8 is assigned
- Examples:
- Model checking in the airlines example

#### 2020-10-29

- Topic: Model Checking
- Read Gelman Chapter 6
- Discussion of Midterm Exam I.

#### 2020-11-03

- Topic: Model Selection and Comparison
- Read Gelman Chapter 7
- Big picture notes
- AIC, DIC, and WAIC…. and BIC
- Article: Bayesian measures of model complexity and fit (with discussion)
- Article: A widely applicable Bayesian information criterion
- Article: Practical Bayesian model evaluation using leave-one-out cross-validation and WAIC
- Model comparison in the airlines example
- Leave-one-out and k-fold cross validation.
- loo CRAN package implementing this article
- Log pseudo marginal likelihood (LPML) and the conditional predictive ordinate (CPO):

#### 2020-11-05

- Topic: Hypothesis Testing
- Read Gelman Chapter 7
- Wikipedia page on Bayes factor
- Article: Computing the Bayes Factor from a Markov Chain Monte Carlo Simulation of the Posterior Distribution
- Notes on Bayesian hypothesis testing by David Hitchcock
- Examples of Bayesian hypothesis testing: code

#### 2020-11-10

- Topic: Regression Models and Variable Selection
- Read Gelman Chapter 14 and this article: A review of Bayesian variable selection methods: what, how and which
- Bayesian linear regression: From Bernardo & Smith, From Wikipedia
- Zellner’s g-prior
- Variable selection example: code

#### 2020-11-12

- Project workday
- Topic: Bayesian nonparametrics
- Read Gelman 23
- Recommended reading
- Talk at BYU on November 12, 2020
- Notes on clusterings/partitions
- ‘pumpkin’ package in R
- Notes on Dirichlet process
- Samples from Dirichlet process
- Posterior simulation for partitions
- Posterior simulation for random measure
- DPpackage: Bayesian Nonparametric Modeling in R
- Density estimation for galaxy data

#### 2020-11-19

- Topic: Bayesian nonparametrics
- Read Gelman 23

#### 2020-12-01

- Student project presentations over class Zoom link.
- 10 minutes presentations, plus 1 minute for questions, plus 1 minute for transition.
- Order: aott20, brimei96, angela77, jense42, dsheansh, mlouder, sorgill7

- Student project presentations over class Zoom link.
#### 2020-12-03

- Student project presentations over class Zoom link.
- 10 minutes presentations, plus 1 minute for questions, plus 1 minute for transition.
- Order: mjaxx, wightc2, lynsiew, djj1229, mwassom, bc383

- Student project presentations over class Zoom link.
#### 2020-12-08

- No reading quiz (that would have been due yesterday)
- Midterm Exam II
- Covers all material to date
- Released at 8am and is due at the start of our next class period
- Due at the start of class on Thursday, December 12
- Submit your solutions in the save Box folder as the where you got the exam.

- In class, we will answer clarify questions about Midterm Exam II

#### 2020-12-10

- Topic: Gaussian process (GP) modeling
- Read Gelman 21
- Example of GP model
- Useful functions for GPs
- Sampling from GPs
- Simple posterior inference

Basic Bayesian inference; conjugate and nonconjugate analyses; Markov chain Monte Carlo methods; hierarchical modeling; convergence diagnostics

- Apply, Implement, and Interpret
- Apply, implement, and interpret a fully Bayesian approach to relevant statistical problems, including design, model selection, and model fitting steps.

- Generate Analysis
- Generate their own Bayesian analysis in R.

- Understand, Explain, and Demonstrate
- Understand, explain, and demonstrate basic Bayesian theory and its usefulness in real-world applications.

Bayesian Data Analysis, Third Edition by Andrew Gelman, John Carlin, Hal Stern, David Dunson, Aki Vehtari, and Donald Rubin. It is available for download from the BYU library. The book website contains a lot of resources, including datasets for examples and homework.

A First Course in Bayesian Statistics by Peter Hoff. This is gentle introduction to Bayesian statistics. It is available for download from the BYU library.

Bayesian Ideas and Data Analysis by Ronald Christensen, Wesley Johnson, Adam Branscum, and Timothy E. Hanson. This is more advanced than Hoff, but less voluminous than Gelman, et al. It is available for download from the BYU library.

Grades will be assigned according to the standard grading scale, or a more generous scale as determined by Dr. Dahl. Class attendance, participation, citizenship, and improvement over the course may be used in determining final grades in some situations.

- Reading: 10%
- Homework: 20%
- Midterm Exam 1: 15%
- Midterm Exam 2: 20%
- Class Project: 15%
- Final Exam: 20%

Instructions for submitting your work will be provided. Paper submissions must be stapled with your name and assignment name clearly indicated. Unless otherwise indicated, assignments are due at the start of lecture on the prescribed day.

Please read the assigned material prior to the lecture in which it is covered. If a lecture is missed, you can obtain copies of notes from fellow students.

In keeping with the principles of the BYU Honor Code, students are expected to be honest in all of their academic work. Academic honesty means, most fundamentally, that any work you present as your own must in fact be your own work and not that of another. Violations of this principle may result in a failing grade in the course and additional disciplinary action by the university. Students are also expected to adhere to the Dress and Grooming Standards. Adherence demonstrates respect for yourself and others and ensures an effective learning and working environment. It is the university’s expectation, and every instructor’s expectation in class, that each student will abide by all Honor Code standards. Please call the Honor Code Office at 422-2847 if you have questions about those standards.

In accordance with Title IX of the Education Amendments of 1972, Brigham Young University prohibits unlawful sex discrimination against any participant in its education programs or activities. The university also prohibits sexual harassment-including sexual violence-committed by or against students, university employees, and visitors to campus. As outlined in university policy, sexual harassment, dating violence, domestic violence, sexual assault, and stalking are considered forms of “Sexual Misconduct” prohibited by the university.

University policy requires all university employees in a teaching, managerial, or supervisory role to report all incidents of Sexual Misconduct that come to their attention in any way, including but not limited to face-to-face conversations, a written class assignment or paper, class discussion, email, text, or social media post. Incidents of Sexual Misconduct should be reported to the Title IX Coordinator at t9coordinator@byu.edu or (801) 422-8692. Reports may also be submitted through EthicsPoint at https://titleix.byu.edu/report or 1-888-238-1062 (24-hours a day).

BYU offers confidential resources for those affected by Sexual Misconduct, including the university’s Victim Advocate, as well as a number of non-confidential resources and services that may be helpful. Additional information about Title IX, the university’s Sexual Misconduct Policy, reporting requirements, and resources can be found at http://titleix.byu.edu or by contacting the university’s Title IX Coordinator.

Brigham Young University is committed to providing a working and learning atmosphere that reasonably accommodates qualified persons with disabilities. A disability is a physical or mental impairment that substantially limits one or more major life activities. Whether an impairment is substantially limiting depends on its nature and severity, its duration or expected duration, and its permanent or expected permanent or long-term impact. Examples include vision or hearing impairments, physical disabilities, chronic illnesses, emotional disorders (e.g., depression, anxiety), learning disorders, and attention disorders (e.g., ADHD). If you have a disability which impairs your ability to complete this course successfully, please contact the University Accessibility Center (UAC), 2170 WSC or 801-422-2767 to request a reasonable accommodation. The UAC can also assess students for learning, attention, and emotional concerns. If you feel you have been unlawfully discriminated against on the basis of disability, please contact the Equal Employment Office at 801-422-5895, D-285 ASB for help. Academic Honesty

The first injunction of the Honor Code is the call to “be honest.” Students come to the university not only to improve their minds, gain knowledge, and develop skills that will assist them in their life’s work, but also to build character. “President David O. McKay taught that character is the highest aim of education” (The Aims of a BYU Education, p.6). It is the purpose of the BYU Academic Honesty Policy to assist in fulfilling that aim. BYU students should seek to be totally honest in their dealings with others. They should complete their own work and be evaluated based upon that work. They should avoid academic dishonesty and misconduct in all its forms, including but not limited to plagiarism, fabrication or falsification, cheating, and other academic misconduct.