Lesson Plan: Markov Chain Monte Carlo (MCMC)

Class 1: Introduction to MCMC Methods

Objective: Students will understand the basics of MCMC methods, including their importance and key concepts.

Materials: Presentation slides, whiteboard, markers

Agenda: 1. Introduction (10 mins) - Welcome students and introduce the topic. - Explain the importance of MCMC methods in statistical and probabilistic modeling.

  1. Key Concepts (20 mins)
    • Define Monte Carlo methods and Markov chains.
    • Explain the principles of MCMC and how it combines these two concepts.
    • Discuss the role of MCMC in sampling from complex distributions.
  2. Metropolis-Hastings Algorithm (20 mins)
    • Explain the Metropolis-Hastings algorithm.
    • Walk through a simple example.
  3. Q&A and Discussion (10 mins)
    • Encourage questions and clarify any doubts.

Homework: - Read assigned sections from a textbook or paper on MCMC.

Class 2: Implementing MCMC Algorithms in Julia

Objective: Students will learn how to implement basic MCMC algorithms in Julia.

Materials: Laptops with Julia installed, sample code snippets

Agenda: 1. Recap of Previous Class (5 mins) - Briefly review the key points from the last class.

  1. Introduction to Julia (10 mins)
    • Overview of Julia language and its benefits for numerical computations.
    • Basic syntax and setup.
  2. Implementing Metropolis-Hastings Algorithm (35 mins)
    • Step-by-step implementation of the Metropolis-Hastings algorithm.
    • Code walkthrough and explanation.
    • Hands-on coding exercise for students.
  3. Q&A and Troubleshooting (10 mins)
    • Address any issues students face during implementation.

Homework: - Complete the implementation of the Metropolis-Hastings algorithm. - Write a short reflection on the coding experience.

Class 3: Applications of MCMC in Bayesian Statistics

Objective: Students will explore the applications of MCMC methods in Bayesian statistics.

Materials: Presentation slides, case studies, statistical software

Agenda: 1. Recap of Previous Class (5 mins) - Briefly review the key points from the last class.

  1. Introduction to Bayesian Statistics (15 mins)
    • Explain the basics of Bayesian inference.
    • Discuss the importance of prior and posterior distributions.
  2. Role of MCMC in Bayesian Inference (20 mins)
    • Explain how MCMC methods are used to approximate posterior distributions.
    • Walk through a case study illustrating the use of MCMC in a Bayesian context.
  3. Hands-on Exercise (15 mins)
    • Provide students with a dataset and guide them through applying MCMC methods to perform Bayesian inference.
  4. Q&A and Discussion (5 mins)
    • Address any questions and facilitate a discussion on the applications.

Homework: - Analyze a dataset using MCMC methods and write a report on the findings.

Class 4: Using the Turing Package for Advanced MCMC Simulations

Objective: Students will learn how to use the Turing package in Julia for advanced MCMC simulations.

Materials: Laptops with Julia and Turing installed, sample code snippets

Agenda: 1. Recap of Previous Class (5 mins) - Briefly review the key points from the last class.

  1. Introduction to the Turing Package (10 mins)
    • Overview of the Turing package and its capabilities.
  2. Setting Up and Using Turing (35 mins)
    • Guide students through the installation and setup of Turing.
    • Provide examples of implementing MCMC models using Turing.
    • Hands-on coding exercise for students.
  3. Q&A and Troubleshooting (10 mins)
    • Address any issues students face during implementation.

Homework: - Develop a complex MCMC model using Turing and prepare a presentation on the results.