Tentative Class Schedule

Tentative Class Schedule

Week 1: Introductions

  • Monday August 26:
  • Wednesday August 28:
    • Mechanics of Bayesian Statistics
  • Friday August 30:
    • Philosophy of Bayesian Statistics (Confidence vs. Probability)

Week 2: Bayesian Foundations

Week 3: One-Parameter Models

Week 4: Computational Statistics

Week 5: Normal Model

Week 6: Markov Chain Monte Carlo

Week 7: Midterm Week

Week 8: Multivariate Normal

  • Monday October 14: Multivariate Normal Distribution
  • Wednesday October 16: Multivariate Normal Distribution
  • Friday October 18: Wishart distribution and Gibbs Sampling

Week 9: Hierarchical Modeling

Week 10: Regression Introduction

Week 11: Regression

Week 12: GLMs and Metropolis-Hastings

Week 13: Hierarchical Regression

Week 14:

  • Monday November 25: In Class Final
  • Wednesday November 27: Thanksgiving Break NO CLASS
  • Friday November 29: Thanksgiving Break NO CLASS

Week 15:

Week 15: Final Exam Week

  • Monday December 9: Take Home Exam due
  • Friday December 13: 8 AM - 9:50 Final Exam (Presentations)

Course Description

Fundamentals of Bayesian inference, methods of Bayesian data analysis, computational methods for posterior simulation, fundamentals of hierarchical modeling.

Learning Outcomes:

At the end of the course students will be able to:

  • Demonstrate a basic understanding of the fundamental concepts underlying Bayesian inference
  • Demonstrate connections and make comparisons among frequentist, likelihood, and Bayesian methods, both from a practical and philosophical perspective
  • Demonstrate an understanding of the complex issues involved in specifying prior distributions and recognize there is no default prior
  • Demonstrate ability to program methods for taking samples from posterior distributions, including rejection sampling, Metropolis-Hastings algorithm, and Gibbs sampling
  • Understand the concepts underlying the computation approaches, including Hamiltonian Monte Carlo techniques
  • Demonstrate ability to use available and common software to carry out Bayesian data analysis
  • Demonstrate ability to write about conceptual issues, describe and justify assumptions and decisions, and interpret results
  • Demonstrate ability to use creative and appropriate graphics to display raw data and results from statistical models
  • Demonstrate ability to write down sophisticated models with standard notation, recognizing there are multiple ways to write the same analysis
  • Explain the idea behind multi-level, or hierarchical, models and how they relate to models used in traditional linear models classes
  • Demonstrate an understanding of posterior predictive checks, as well as the ability to use them meaningfully in practice
  • Demonstrate a willingness to think about and discuss the foundations of statistical inference

    Prerequisites

  • Required: STAT 422 or STAT 502, and STAT 506
  • Preferred: extensive experience with R

Textbooks

  • A First Course in Bayesian Statistical Methods, by Peter Hoff
  • Bayesian Data Analysis (3rd Edition), by Gelman, Carlin, Stern, & Rubin (Optional)

Additional Resources

Analysis, data visualization, and version control procedures will be implemented with:

  • R / R Studio
  • JAGS
  • Stan
  • Git / Github

Course Policies

Grading Policy

  • 10% of your grade will be determined by weekly quizzes to be completed prior to class on Mondays.

  • 30% of your grade will be determined by weekly homework assignments. Students are allowed and encouraged to work with classmates on homework assignments, but each student is required to complete their own homework.

  • 20% of your grade will be determined by a midterm exam. The midterm exam will have two parts: an in class exam and a take home portion. The in class portions will be largely conceptual including some short mathematical derivations. The take home portions will focus on analysis of data and implementation of Bayesian computational methods.

  • 20% of your grade will be determined by a final exam. The final exam will have two parts: an in class exam and a take home portion. The in class portions will be largely conceptual including some short mathematical derivations. The take home portions will focus on analysis of data and implementation of Bayesian computational methods.

  • 20% of your grade will be determined by a project. The project will be a case study where students will apply Bayesian methods to a data set agreed upon by the instructor and student.

Collaboration

University policy states that, unless otherwise specified, students may not collaborate on graded material. Any exceptions to this policy will be stated explicitly for individual assignments. If you have any questions about the limits of collaboration, you are expected to ask for clarification.

In this class students are encouraged to collaborate on homework assignments, but quizzes should be completed without collaboration.

Academic Misconduct

Section 420 of the Student Conduct Code describes academic misconduct as including but not limited to plagiarism, cheating, multiple submissions, or facilitating others’ misconduct. Possible sanctions for academic misconduct range from an oral reprimand to expulsion from the university.

Disabilities Policy

Federal law mandates the provision of services at the university-level to qualified students with disabilities. Make sure to include all that relevant information here.