Course details
- It is a 2 credit course running in segments 3-6 of Jan-Apr '2025-26
- Schedule and venue: Slot-G in segments 3 and 4 (in BT/BM010) and Slot-A in segments 5 and 6 (BT/BM-118)
- Discussion hour: Thursday, 13h00-14h00, BM305
- Evaluation: (4E+1P)- 26th Feb at 5 PM (17%), 20th Mar (17%), 09th Apr (17%), 28th Apr (29%), Project (20%)
Course contents
This course is designed for students with a background in mathematical modelling and statistical inference (preferably with BM5033 under their belt) and an interest in physiology, medicine, and bioengineering. Students will learn how to incorporate prior knowledge with emerging data to refine predictions and inform decision-making in both research and clinical settings. Practical sessions will introduce computational methods like Markov Chain Monte Carlo (MCMC) and Gibbs Sampling, allowing students to implement these techniques using Python/R. In doing so, students will see first hand how these methods can be applied to problems ranging from parameter estimation in physiological modeling and diagnostics. The course will broadly follow following trajectory
- Recap of frequentist inference, p-values, hypothesis testig, power analysis
- Basic probability concepts and Bayes’ Theorem, priors, likelihoods, and posteriors in a biological context
- Prior and Posterior Distributions, Bayesian inference, hypothesis testing
- MCMC sampling, Metropolis-Hastings algorithm, Gibbs sampler
- Examples from bioengineering- bioassays, survival analysis, longitudinal studies
References
- Bayesian Biostatistics by Lesaffre and Lawson
- Bayesian Biostatistics and Diagnostic Medicine by Broemeling
Problem sets
- Problem set 0
- Problem set 1(uploaded on Feb 23rd 2026)
- Problem set 2(uploaded on Feb 24th 2026)
Problem sets from 2025
- Problem set 0 (uploaded on Feb 09th 2025)
- Problem set 1 (uploaded on Feb 18th 2025)
- Problem set 2 (uploaded on Feb 20th 2025)
- Problem set 3 (uploaded on Apr 01st 2025)
- Problem set 4 (uploaded on Apr 14th 2025)
- Project problems (uploaded on Apr 21st 2025)
Reading materials
- Why Most Published Research Findings Are False by John P. A. Ioannidis, 2005, PLOS Med.
- Bayes' theorem by Puga et al., 2015, nature methods
- Bayesian statistics by Puga et al., 2015, nature methods
- Using Bayes factor hypothesis testing in neuroscience to establish evidence of absence by Keysers et al., 2020, nature neuro
- Gibbs Sampling
R scripts and other source codes
Course logistics and policies
- Assignments: The course has no assignments. Instead, practice problems will be given at regular intervals. Students are not expected to submit the answers to these problems
- Answers/solutions to the practice problems will not be provided. Students are encouraged to utilise the discussion hour to discuss the problems if they want to.
- Exams: There are 4 exams scheduled (roughly) at the end of each segment. See above for dates.
- Attendance: Attendance is not mandatory in the classes.
- Missing exams: On missing an exam due to a medical emergency you are expected to produce a medical certificate from the institute health center. At the end of the course, a Bayesian method will be followed to reward marks for the missed exam. Missing the exam due to any other reason will result in no marks.
- Use of unfair means (e.g. plagiarism, copying etc.) is unacceptable in the course. Any sign of it will result in a severe penalty.
Some suggestions
- The best way to follow the course is to work out the details of the topics discussed in each class by yourself after the class.
- There will be one discussion hour each week for clarification of doubts and practice problems. Take advantage of that.
- You have to take the practice problems seriously and solve them on your own. In case you are facing difficulty, you can come and meet the instructor during the discussion hour