Bayesian Methods - Exercise class

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• SIS page: NMST431
• Schedule: on Monday 14:00-15:30 in classroom K4 and 15:40-17:10 in K4 and K5
• Language: materials in English, instructed in Czech (unless anybody requires English)
• Instructor e-mail: vavraj@karlin.mff.cuni.cz
• Lecture web page: https://www.karlin.mff.cuni.cz/~komarek/vyuka/2026_27/nmst431-2026.html
• Note: Division into “lecture” and “exercise class” is just formal. The style of teaching (“lecture”/“exercise class”) will change dynamically over the semester. At the beginning of the semester exercises will become lectures. The first exercise will probably be by the end of October.

Credit

• Satisfactory solution to given assignments by the prescribed deadline.
  If your solution will not be satisfactory enough, you might be asked for revision.
  Two revisions or late deliveries are tolerated. Early communication increases my tolerance for late deliveries.
  Send your solution via email to address vavraj@karlin.mff.cuni.cz.
  Recommended form: Rmarkdown output (PDF or HTML) or Sweave for the software part, theoretical derivations can be written by hand and scanned

Overview

Exercise 1 (26 October)

• Topic: Bayesian approach when the posterior is known
• Assignment: Discover the true posterior distribution, construct credible intervals and compare them with approximation via Monte Carlo approach. Full assignment in PDF
• Deadline: Monday 2 November 9:00

Exercise 2 (9 November)

• Topic: How to use JAGS (Just Another Gibbs Sampler) for estimating hierarchical models
• Assignment: Using Gibbs sampling approximate the posterior distribution of model parameters of logistic regression with random intercepts. The intercepts are treated as additional secondary parameters. Full assignment in PDF and Diagram of hierarchical model
• Data: toenail.txt
• Deadline: None - solved together during exercise class, but there is Exercise 2.5

Homework (9-23 November)

• Topic: Try JAGS for yourself on a simple regression model
• Assignment: Full assignment in PDF
• Data: chicago.csv
• Deadline: Monday 23 November 9:00

Exercise 3a (23 November)

• Topic: Implement and fit LME with random intercept and slope using JAGS.
• Assignment: Full assignment in PDF
• Data: aids from library(JM)
• Deadline: Monday 14 December 9:00

Exercise 3b (23 November)

• Topic: Implement and fit parametric proportional hazards model (under Weibull assumption) for right-censored time to death using JAGS.
• Assignment: Full assignment in PDF
• Data: aggregated aids from library(JM)
• Deadline: Monday 14 December 9:00

Exercise 3c (30 November)

• Topic: Implement and fit joint model of LME and parametric proportional hazards model using JAGS.
• Assignment: Full assignment in PDF
• Data: aids from library(JM)
• Deadline: Monday 14 December 9:00

Exercise 3d (14 December)

• Topic: Joint model with more flexible baseline hazard function using library(JMbayes).
• Data: aids from library(JM)
• Deadline: None - solved together during exercise class

Exercise 4 (14 December)

• Topic: Exam project (Poisson mixture model) + Discussion
• Assignment: Full assignment in PDF
• Data: velibCount from library(MBCbook)
• Deadline: 2 days before exam

Exercise 5a (4 January)

• Topic: Metropolis-Hastings algorithm for \(\mathsf{AR}(1)\)-\(\mathsf{GARCH}(1,1)\) model.

Exercise 5b (4 January)

• Topic: Introduction of RStan on \(\mathsf{AR}(1)\)-\(\mathsf{GARCH}(1,1)\) model.