Bayesian Data Assimilation - Interactive curriculae of TU Ilmenau

fundamentals of analysis, linear algebra, probability theory, Python programming or Matlab programming

Upon completion of this course, students will be able to thoroughly comprehend the fundamentals of Bayesian Sequential State and Parameter Estimation. This encompasses not only a clear understanding of the mathematical derivations of common standard methods such as filters and smoothers in Data Assimilation, but also the ability to analyze their stability and long-term behavior.

Furthermore, students will be equipped to independently implement prevalent sequential filtering algorithms. They can subsequently apply these skills to simplified example scenarios from domains such as meteorology, personalized medicine, and space weather.

By the end of the course, students will not only grasp the theory but also have developed practical skills to apply these concepts in real-world applications. As such, this course offers comprehensive preparation for independent research in the realm of Bayesian Inverse Problems.

1. Introduction to Data Assimilation and Filtering Methods in Diverse Application Areas
Data assimilation is a fascinating interdisciplinary field that enables the fusion of models and observational data to achieve accurate estimations of states or processes. In this course, we will commence with captivating examples from various application domains such as medicine, climate research, and space weather forecasting. We will delve into refreshing the essential fundamentals in areas including statistics, stochastic processes, numerical methods, and dynamic systems. Subsequently, we will explore the mathematical derivation of standard filters such as the Kalman filter, particle filter, ensemble Kalman filter, variational methods, and smoothers.

2. Comprehensive Algorithmic Studies and Implementation Using Toy Models
We will thoroughly engage in the implementation of methods and independently create toy models of various kinds. This will enable us to develop a deeper understanding of the functioning of these methods and practically apply them in a controlled environment.

3. Analyses of Stability and Long-Term Behavior of Presented Methods
We will conduct thorough analyses of the stability and long-term behavior of the introduced methods. This is of paramount importance in comprehending the behavior of the methods across different timeframes and under various conditions.

4. Extensions of Standard Filters, Such as Hierarchical Algorithms or Hybrid Filter Methods
Moreover, we will delve into extensions of standard filters, including hierarchical algorithms or hybrid filter methods. These advancements allow for further optimization of the filters' performance in complex scenarios.

projector, assignments, slides, jupyter notebooks, personal computer with Python or Matlab to work on the programming part of the exercises

Sebastian Reich und Colin Cotter: Probabilistic Forecasting and Bayesian Data Assimilation, Cambridge University Press

Kody Law, Andrew Stuart und Konstantinos Zygalakis: Data Assimilation: A Mathematical Introduction, Springer

Simo Särkkä: Bayesian Filtering and Smoothing, Cambridge University Press

Nicolas Chopin und Omiros Papaspiliopoulos: An Introduction to Sequential Monte Carlo, Springer