Simon Fraser University
Engaging the World

Course Outlines

Spring 2024 - STAT 460 D100

Bayesian Statistics (3)

Class Number: 2891

Delivery Method: In Person

Overview

  • Course Times + Location:

    Jan 8 – Apr 12, 2024: Tue, 10:30 a.m.–12:20 p.m.
    Burnaby

    Jan 8 – Apr 12, 2024: Fri, 10:30–11:20 a.m.
    Burnaby

  • Exam Times + Location:

    Apr 16, 2024
    Tue, 7:00–10:00 p.m.
    Burnaby

  • Prerequisites:

    STAT 330 and 350, with a minimum grade of C-.

Description

CALENDAR DESCRIPTION:

The Bayesian approach to statistics is an alternative and increasingly popular way of quantifying uncertainty in the presence of data. This course considers comparative statistical inference, prior distributions, Bayesian computation, and applications. Quantitative.

COURSE DETAILS:

Course Outline:

Part 1: Introduction to Bayesian Statistics

  • Motivation for Bayesian Analysis
  • Review of Likelihood-Based Inference
  • Comparison of Likelihood-Based and Bayesian Inference

Part 2: Bayesian Inference for Simple Models

  • Bayesian Analysis in a Nutshell
  • Informative Prior distributions
  • Binomial Models
  • Poisson Models
  • Univariate Normal Models
  • Summarizing Posterior Inference
  • Noninformative and Weakly Informative Prior Distributions
  • Scientific Application: Hardness Ratios in High-Energy Astrophysics

Part 3: Multiparameter Models

  • Marginalization and Monte Carlo
  • Normal Data with Noninformative and Conjugate Priors
  • Scientific Application: Estimating the Speed of Light
  • Multinomial Models
  • Scientific Application: Analysis of a Bioassay Experiment

Part 4: Bayesian Computing

  • Introduction to Bayesian Computing
  • Rejection Sampling
  • Importance Sampling
  • Introduction to Markov Chain Monte Carlo
  • Metropolis and Metropolis-Hastings Algorithms
  • Gibbs Sampler
  • Hybrid and Alternative Algorithms
  • Scientific Application: Inference in High-Energy Astrophysics

Part 5 (time permitting):

  • Bayesian Hierarchical Models
  • Hyperpriors
  • James-Stein Estimators and Shrinkage
  • Scientific Application: Supernova Color Corrections

Grading

  • Assignments 35%
  • Midterm 30%
  • Final Exam 35%

NOTES:

Above grading is subject to change.

REQUIREMENTS:


Sufficient knowledge of R to code Bayesian computing algorithms.

Materials

REQUIRED READING:

Bayesian Data Analysis, 3rd Edition. Authors: Gelman, Carlin, Stern, Dunson, Vehtari, and Rubin

Book is available online for free http://www.stat.columbia.edu/~gelman/book/BDA3.pdf

REQUIRED READING NOTES:

Your personalized Course Material list, including digital and physical textbooks, are available through the SFU Bookstore website by simply entering your Computing ID at: shop.sfu.ca/course-materials/my-personalized-course-materials.

Department Undergraduate Notes:

Students with Disabilities:
Students requiring accommodations as a result of disability must contact the Centre for Accessible Learning 778-782-3112 or caladmin@sfu.ca.  


Tutor Requests:
Students looking for a tutor should visit https://www.sfu.ca/stat-actsci/all-students/other-resources/tutoring.html. We accept no responsibility for the consequences of any actions taken related to tutors.

Registrar Notes:

ACADEMIC INTEGRITY: YOUR WORK, YOUR SUCCESS

SFU’s Academic Integrity website http://www.sfu.ca/students/academicintegrity.html is filled with information on what is meant by academic dishonesty, where you can find resources to help with your studies and the consequences of cheating. Check out the site for more information and videos that help explain the issues in plain English.

Each student is responsible for his or her conduct as it affects the university community. Academic dishonesty, in whatever form, is ultimately destructive of the values of the university. Furthermore, it is unfair and discouraging to the majority of students who pursue their studies honestly. Scholarly integrity is required of all members of the university. http://www.sfu.ca/policies/gazette/student/s10-01.html