Spring 2023 - STAT 460 D100
Bayesian Statistics (3)
Class Number: 5880
Delivery Method: In Person
Course Times + Location:
Tu 10:30 AM – 12:20 PM
SWH 10051, Burnaby
Fr 10:30 AM – 11:20 AM
SWH 10051, Burnaby
Exam Times + Location:
Apr 19, 2023
12:00 PM – 3:00 PM
WMC 3220, Burnaby
Prerequisites:STAT 330 and 350, with a minimum grade of C-.
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.
Part 1: Introduction to Bayesian Statistics
- Motivation for Bayesian Analysis
- Review of Likelihood-Based Inference
- Comparison of Likelihood-Based and Bayesian Inference
- Bayesian Analysis in a Nutshell
Part 2: Bayesian Inference for Simple Models
- Exchangeability and deFinetti’s Representation Theorem
- 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
- Multivariate Normal 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
- James-Stein Estimators and Shrinkage
- Scientific Application: Supernova Color Corrections
- Assignments 30%
- Midterm 30%
- Final Exam 40%
Above grading is subject to change.
Sufficient knowledge of R to code Bayesian computing algorithms.
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 firstname.lastname@example.org.
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