140.724.41
Probability Theory IV
- Location:
- Internet
- Term:
- 4th term
- Department:
- Biostatistics
- Credits:
- 3 credits
- Academic Year:
- 2022 - 2023
- Instruction Method:
- Synchronous Online
- Class Times:
-
- Tu Th, 3:30 - 4:50pm
- Auditors Allowed:
- No
- Undergrads Allowed:
- No
- Grading Restriction:
- Letter Grade or Pass/Fail
- Course Instructor:
- Contact:
- Abhirup Datta
- Resources:
- Prerequisite:
Calculus, real analysis; 140.721-3
- Description:
-
Covers basic stochastic processes including martingales and Markov chains, followed by consideration of Markov Chain Monte Carlo (MCMC) methods.
- Learning Objectives:
-
Upon successfully completing this course, students will be able to:
- Identify foundational concepts of probability theory
- Assess the convergence of a sequence or series of random variables using martingale theory
- Classify the states and derive the transition probabilities of a Markov chain
- Derive the stationary distribution of certain Markov chains
- Identify the principles of MCMC algorithms like Gibbs sampler and Metropolis-Hastings
- Methods of Assessment:
This course is evaluated as follows:
- 30% Homework
- 30% In-class midterm exam
- 40% In-class final exam
- Instructor Consent:
Consent required for some students
- Consent Note:
Consent required for students who are not in the Biostatistics PhD program
- For consent, contact:
- Special Comments:
Please note: This is the virtual/online section of a course that is also offered onsite. Students will need to commit to the modality for which they register. The course may include one or two lab sessions scheduled for the corresponding lecture periods.