STATS/DATASCI 551/651 Fall 2026

Bayesian Modeling

Overview

This course provides basic concepts and several modern techniques of Bayesian modeling and computation. They include basic models, conjugate priors, and posterior computation, as well as techniques associated with complex models, such as hierarchical models, spatiotemporal models, and dynamical models. A substantial part of the course is devoted to computational algorithms based on Markov Chain Monte Carlo sampling for complex models. If time permits, we will also introduce advanced topics such as nonparametric Bayes, variational inference, and Hamiltonian Monte Carlo techniques. Foundational topics will be discussed when appropriate, although they are not our primary focus in this course; such topics may include decision theoretic characterization of Bayesian inference and its relation to frequentist methods, de Finetti-type theorems and the existence of priors, objective prior distributions, and Bayesian model selection.

Syllabus

For course policies, course requirements, and grading policies, please see the syllabus [link].

Piazza

Students can join Piazza through Canvas to participate in course discussions.

All communications with the teaching team (the instructor and the GSIs) should be conducted over Piazza; please do not email. If you'd like to reach the instructor or the GSIs for private questions, please post a private note on Piazza that is only visible to the instructor and the GSIs. See here for detailed instructions. The GSIs and the instructor will be monitoring Piazza, endorsing correct student answers, and answering questions that remain after a discussion.

As a bonus, up to 3 percentage points will be added to your final course grade based on Piazza participation. You will receive (3x) bonus percentage points if the number of your total Piazza contributions is (x * 100)% of the maximum number of contributions among all students. The number of Piazza contributions will be determined by Piazza class statistics.

Teaching Team and Office Hours

  • Instructor: Yixin Wang — weekly Office Hours.
  • GSI: Filippo Michelis — office hour TBD.

Please refer to the course calendar for details.

Course Calendar

  • Lecture: Tue/Thur 4:00pm-5:20pm
  • Location: 170 WEISER
  • Google Calendar: The Google Calendar below ideally contains all events and deadlines for student's convenience. Please feel free to add this calendar to your Google Calendar by clicking on the plus (+) button on the bottom right corner of the calendar below. Any adhoc changes to the schedule will be visible on the calendar first.

Lecture Schedule

The Schedule is subject to change.

By each date, please read about the topic at hand; please choose one reading from the list for the topic.

FBSM = A first course in Bayesian statistical methods [link]
BDA = Bayesian Data Analysis by Gelman [link]
PML = Probabilistic Machine Learning: Advanced Topics by Murphy [link]
PRML = Pattern Recognition and Machine Learning by Bishop [link]
Date Topic Readings Assignments

Lecture 1

09/01

Introduction I

BDA ch. 1
FBSM ch. 1
"Bayesian data analysis for newcomers" (Kruschke and Liddel, 2018)
"Review of Probability" (Blei, 2016)
"R Basics with Google Colab" Notebook Video

 

Lecture 2

09/03

Introduction II

''

 

Lecture 3

09/08

Introduction III

''

 

Lecture 4

09/10

Interpretation of probabilities and Bayes' formulas I

FBSM ch. 2

 

Lecture 5

09/15

Interpretation of probabilities and Bayes' formulas II

''

Quiz 1

Lecture 6

09/17

Interpretation of probabilities and Bayes' formulas III

''

 

Lecture 7

09/22

One-parameter models I

BDA ch. 2
FBSM ch. 3

 

Lecture 8

09/24

One-parameter models II

''

 

Lecture 9

09/29

One-parameter models III

''

Quiz 2

Lecture 10

10/01

One-parameter models IV

''

 

Lecture 11

10/06

Monte Carlo Approximation I

FBSM ch. 4

 

Lecture 12

10/08

Monte Carlo Approximation II

''

 

Lecture 13

10/13

Monte Carlo Approximation III

''

 

Lecture 14

10/15

Midterm Exam

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Fall break

10/20

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Lecture 15

10/22

Monte Carlo Approximation IV

''

 

Lecture 16

10/27

The Normal Model I

''

 

Lecture 17

10/29

The Normal Model II

''

 

Lecture 18

11/03

Bayesian Computation and Introduction to Stan I

FBSM ch. 6
BDA ch. 10-12

Quiz 3

Lecture 19

11/05

Bayesian Computation and Introduction to Stan II

''
BDA ch. 5

 

Lecture 20

11/10

Group comparisons and hierarchical modeling I

FBSM ch. 8
BDA ch. 5

 

Lecture 21

11/12

Group comparisons and hierarchical modeling II

''

 

Lecture 22

11/17

Regression Models I

FBSM ch. 9
BDA ch. 14-16

Quiz 4

Lecture 23

11/19

Regression Models II

''

 

Lecture 24

11/24

Regression Models III

''

 

Thanksgiving Break

11/26

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Lecture 25

12/01

Regression Models IV

''

Quiz 5

Lecture 26

12/03

Finite mixture models

BDA, Chap. 22
"Bayesian Mixture Models and the Gibbs Sampler" (Blei, 2016)

 

Lecture 27

12/08

Guest lecture

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Lecture 28

12/10

Guest lecture

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Acknowledgements

The course materials are adapted from the related courses offered by David Blei, Yang Chen, Andrew Gelman, Long Nguyen, and Scott Linderman.