PhD Courses in Denmark

Welcome to Bayesian Statistics Simulation and Software (2025)

Description: During the last decades, Bayesian statistics has gained enormous popularity as an elegant and powerful computational tool to perform statistical analysis in complex stochastic models as applied in engineering, science and medicine. Bayesian statistics offers an alternative approach to traditional data analysis by including prior knowledge about the model parameters in form of a prior distribution. Using Bayes formula the prior distribution is updated from the posterior distribution by incorporating the observed data by means of the likelihood. Subsequently statistical inference about the unknown model parameters is derived from the posterior distribution. However, the posterior distribution is often intractable due to high-dimensional complex integrals implying that approximate stochastic simulation techniques such as Markov Chain Monte Carlo (MCMC) methods become crucial. This course reviews the basics ideas behind Bayesian statistics and Markov chain Monte Carlo (MCMC) methods. Background on Markov chains will be provided and subjects such as Metropolis and Metropolis-Hastings algorithms, Gibbs sampling and output analysis will be discussed. Furthermore, graphical models will be introduced as a convenient tool to model complex dependency structures within a stochastic model.

Prerequisites: In principle the course is accessible to those new to these subjects, however, some mathematical training will be an advantage and a basic knowledge of statistics and probability theory as obtained through engineering studies at Aalborg University is definitely expected.

Learning objectives: The course aims at providing fundamental knowledge about complex Bayesian models which require MCMC methods. The participants are expected to gain experience with Bayesian methods (prior and posterior distributions, confidence regions, prediction, sensitivity analysis, model criticism), MCMC algorithms (Gibbs sampling, Metropolis-Hastings algorithm, Gibbs within Metropolis-Hastings algorithm) and practical data examples. The course will not be a "a black box approach" to the subject as there will be some mathematical abstraction which is needed in order to construct meaningful Bayesian models and simulation procedures.

Teaching methods: A mixture of lectures and exercises. The theory will be demonstrated through different examples of applications and exercises, partly based on the software package R.

Criteria for assessment: Assessment of the course through active participation and a larger hand-in exercise after the completion of the course.  

Key literature: The course does not follow any particular text book, but rather the course slides and a few notes (referred to in the plan) will be the main course material. However, a few pointers to relevant literature can be found in the following. We do not recommend or endorse any of these books in particular, and it is impossible to recommend a book for everyone taking the course given the very diverse background of the participants.    

Two introductory level books:  

- Peter D. Hoff (2009). A First Course in Bayesian Statistical Methods. Springer.   

- Peter M. Lee (2004). Bayesian Statistics: an introduction, 3rd ed. Arnold.    

Additional useful textbooks:    

- Andrew Gelman, et al. (2014). Bayesian Data Analysis, 3rd ed. CRC Press.  

- Jean-Michel Marin and Christian Robert (2007) Bayesian Core: A Practical Approach to Computational Bayesian Statistics. Springer.   

- Jean-Michel Marin and Christian Robert (2014) Bayesian Essentials with R. Springer.   

- Olle Häggström (2002). Finite Markov Chains and Algorithmic Applications. Cambridge University Press.  

- Christian P. Robert and George Casella (2004). Monte Carlo Statistical Methods, 2nd ed. Springer.  

- Maria Rizzo (2007). Statistical Computing with R. Chapman & Hall/CRC.  

- Ioannis Ntzoufras (2009). Bayesian Modeling Using WinBUGS. Wiley.

Organizer: Jesper Møller

Lecturers: Jesper Møller

ECTS: 5

Time: 10 - 11, 13 - 14, 17 - 18 November 2025

Place: Aalborg University

Zip code: 9220

City: Aalborg

Maximal number of participants: 40

Deadline: 22 October 2025