Each module contains 3 ECTS. You choose a total of 10 modules/30 ECTS in the following module categories:
- 12-15 ECTS in technical scientific modules (TSM)
TSM modules teach profile-specific specialist skills and supplement the decentralised specialisation modules. - 9-12 ECTS in fundamental theoretical principles modules (FTP)
FTP modules deal with theoretical fundamentals such as higher mathematics, physics, information theory, chemistry, etc. They will teach more detailed, abstract scientific knowledge and help you to bridge the gap between abstraction and application that is so important for innovation. - 6-9 ECTS in context modules (CM)
CM modules will impart additional skills in areas such as technology management, business administration, communication, project management, patent law, contract law, etc.
In the module description (download pdf) you find the entire language information per module divided into the following categories:
- instruction
- documentation
- examination
Bayesian statistics provides an alternative viewpoint to the classical ‘frequentist’ statistics by using a different, more subjective interpretation of probability. This brings various advantages in solving typical industry problems, such as the inclusion of prior knowledge, more intuitive hypothesis tests or modeling uncertainty given small amounts of data. With increasing computational power, the popularity of Bayesian statistics and machine learning has grown significantly over the past decade. This course provides students with a solid understanding of the fundamental concepts of Bayesian statistics, introduces various computational methods required in Bayesian statistics and Bayesian machine learning, and discusses numerous examples and applications of Bayesian machine learning. Bayesian as well as Gaussian process regression models are introduced and explored, with a particular focus on graphical models and Bayesian networks to model relationships and to infer causality. In addition, advanced topics and their applications are covered, such as Bayesian optimisation, non-parametric mixture models for clustering, and Bayesian neural networks.
Prerequisites
Basic probability and statistics, basic programming skills (R and/or Python), linear algebra and multivariate calculus, basic concepts of machine learning.
Learning Objectives
Students are able to formulate their problem setting on the basis of Bayesian models and to include their prior understanding. They are able to explain how Bayesian models balance between prior understanding and data towards a posterior understanding of a problem. They are aware of the advantages and disadvantages of the Bayesian approach and know in which situation it is better suited than standard frequency statistics. Since Bayesian models can rarely be computed in closed form, they are experienced in approximating posterior distributions by means of sampling-based approaches
Contents of Module
Fundamental concepts of Bayesian statistics: Reasoning under uncertainty, probability theory, Bayes theorem, prior, likelihood, posterior, conjugate families (beta-binomial, gamma-poisson, normal-normal), sequential learning, inference, prediction
Sampling methods: Markov chains, Metropolis algorithm, Gibbs sampling, Hamiltonian MC, sequential MC
Bayesian and Gaussian Process regression: kernels, model selection, state-space models, variational inference
Bayesian networks: graphical models, causality
Selection of advanced topics: Bayesian optimisation, Bayesian non-parametric mixture modeling, Bayesian neural networks, physics-informed ML models
Teaching and Learning Methods
Lecture and practical work on computer.
Literature
Lecture notes and notebooks will be available in addition to recommended book chapters.
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