Department Systems Analysis, Integrated Assessment and Modelling

13th Summer School in Environmental Systems Analysis 2022

Mathematical models are important tools to understand environmental systems and to predict their behavior. However, uncertainties in data, model structure, and parameters are inevitable. In this Summer School we provide guidance how to treat such uncertainties quantitatively with Bayesian techniques.

The course is targeted at  PhD students, post-doctoral researchers, and senior research scientists working with mathematical models. The presented methods can be applied to models from all disciplines, however, the presented examples are mostly from hydrology and ecology. The course consists of lectures and practice sessions with didactical exercises. We will also have time to discuss your individual modeling challenges.

Emphasis is on the concepts and applications of methods, not on mathematical derivations. Nevertheless, to profit most from the course, you should feel comfortable with basic probability calculus and reading and writing simple code. We offer optional introductory lectures on Sunday to refresh probability calculus and give a brief introduction to R.

We will allow for remote participation by streaming the lectures and virtual working groups. However, interactions are limited and the risk of outage is real. Therefore we highly recommend to participate in person.

The course is equivalent to 2 ECTS points.


We cover the following topics:

  • Model representation and Philosophy: Importance of models, sources of uncertainty in models, description of uncertainty, mathematical representation of models.
  • Model Inference: Sensitivity analysis, model calibration, likelihood construction, prior formulations, Bayesian inference and required numerical algorithm such as Importance Sampling and Markov Chain Monte Carlo Simulation.
  • Model Predictions: Estimation of the uncertainty of model predictions in the Bayesian framework.

For details please have a look at the Program 2021 (Program 2022 will follow).


The participants should be familiar with basic probability calculus and have some a knowledge of R (if you feel comfortable with another programming language, you should do fine too). The probability calculus exercises and R exercises  from the optional introductory lectures on Sunday should help to gauge your level.  If you have any doubts, please do not hesitate to contact us.


The course is at Eawag (Swiss Federal Institute of Aquatic Science and Technology) in Dübendorf, Switzerland. Eawag can be reached by a 10 minutes train ride and a 15 minutes walk from Zurich, Switzerland. See here for more details.

Course Fee

The course fee is CHF 800.- for participants not belonging to an institution of the ETH domain. It includes documentation, coffee and lunch, but not accommodation.
The fee for remote participation is CHF 400.- (the number of remote participants is also limited).


Please send your application by email to Carlo Albert by April 15, 2022. Please include your affiliation, billing address, and a short description of your working area. The number of participants is limited to 30. The participants will be considered according to the time of their application.


Eawag can be reached by a 5 minutes walk from Hotel ZwiBack, a 10 minutes walk from Hotel Sonnental and Hotel harry's home  or by a 10 minutes train ride and a 15 minutes walk from Zurich, (hotels in Zurich).


The course will be taught by Carlo Albert, Peter Reichert, Andreas Scheidegger and Marco Baity Jesi from Eawag Dübendorf and ETH Zurich, Switzerland, and Dmitri Kavetski  from the School of Civil, Environmental and Mining Engineering, University of Adelaide, Australia.