Mathematical models are important tools for supporting our understanding and predicting the behavior of environmental systems. However, uncertainties in data, model structure, and parameters are inevitable. The Eawag Summer School provides guidance to mathematical techniques treating such uncertainties quantitatively. It starts with elementary statistical analyses and proceeds to state of the art Bayesian computation. The summer school briefly covers model construction and sensitivity analysis and then focuses on concepts, implementation and application of Bayesian techniques for statistical inference, model prediction and uncertainty estimation.
The course is targeted at researchers who are interested in analyzing their data with mathematical models and/or in predicting future behavior of environmental systems. This includes PhD students, post-doctoral researchers, and senior research scientists working in this field.
The course consists of lectures covering the underlying theory, practice sessions based on didactical exercises, and discussion of problems of the participants. The participants are encouraged to bring their data sets and models to start working on their own problems during the course.
Emphasis is on sound statistical techniques with a focus on concepts and applications, not on mathematical derivations. Still, basic knowledge in statistics and R is required. We strongly recommend participants without a solid knowledge of probability calculus to attend the introductory lectures on Sunday.
The course will be very intense to optimize the benefit of the participants.
- Provide an overview and understanding of systems analytic techniques relevant for model-based data analysis in the environmental sciences.
- Get practice in applying these techniques with the statistics and graphics software package R and selected more specific data analysis programs.
- Get advice and do first steps in analyzing the data sets of the participants.
- Learn from the approaches chosen by the other participants for analyzing their data.
- Models in the Environmental Sciences: Importance of models, causes of uncertainty in model predictions, description of uncertainty, mathematical representation of models.
- Identification of Models: Construction of models, preliminary analysis, sensitivity analysis, Bayesian inference (formulation of prior knowledge, combining prior knowledge with data, input uncertainty, numerical techniques such as Importance Sampling and Markov Chain Monte Carlo Simulation).
- Model Predictions: Estimation of the uncertainty of model predictions in the Bayesian framework.
The participants are expected to have a basic understanding of probability calculus and statistics and some knowledge of R.
The core part of the course will take place from Monday to Friday and consists of lectures, practice sessions based on didactical exercises, discussion of problems of the participants, and outlooks to techniques not dealt with in detail during the course. On Sunday, there will be the opportunity to attend preparatory lectures and exercises on relevant basic subjects in probability calculus, statistics and a basic introduction to R. This is recommended for those unfamiliar with these concepts and/or this software.
The course will be split into five types of activities:
- Lectures will provide the basic underlying theory of all relevant techniques.
- Exercises will deepen the theoretical knowledge and demonstrate how the techniques can be applied using the statistics and graphics software package R and selected more specific data analysis programs.
- Application sessions will give the participants the chance to start applying the techniques to their own data sets. The participants will be supported in choosing adequate techniques to address the needs for their own data analyses.
- Short presentations of problems of the participants for analyzing their data, and discussion of solution strategies.
- Outlook to techniques not dealt with in detail during the course.
The course will be taught by Peter Reichert, Carlo Albert and Andreas Scheidegger from Eawag Dübendorf and ETH Zurich, Switzerland, and Dmitri Kavetski from the School of Civil, Environmental and Mining Engineering, University of Adelaide, Australia.
The practice sessions will be supported in addition by Lorenz Ammann, Jenny Held, Omar Wani and Max Ramgraber.
PhD students, post-doctoral researchers and senior research scientists interested in applying statistical techniques of model-based data analysis. The course is equivalent to 2 credit points of the European Credit Transfer and Accumulation System (ECTS).
Eawag, Swiss Federal Institute of Aquatic Science and Technology, 8600 Dübendorf, Switzerland (http://www.eawag.ch/en/). Eawag can be reached by a 10 minutes train ride and a 15 minutes walk from Zurich, Switzerland. See here for more details.
A comprehensive manuscript on Environmental Systems Analysis and selected more specific papers will be distributed to the participants.
Reading list (pdf)
The course fee is CHF 800.-- for participants not belonging to an institution of the ETH domain. It includes documentation, coffee and lunches, but it does not include accommodation.
It is the responsibility of the participants to book their hotel. Eawag can be reached by a 5 minutes walk from Hotel ZwiBack (in German), a 10 minutes walk from Hotel Sonnental in Dübendorf or by a 10 minutes train ride and a 15 minutes walk from Zurich, (hotels in Zurich).
Please send your application by email to Karin Ghilardi by February, 28, 2019. 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. The Summer School is fully booked.
This Summer school has been a yearly event since 2009. An overview of previous courses can be found here.