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Statistical Inference for Dynamical Systems

Module MA5612

This Module is offered by Department of Mathematics.

This module handbook serves to describe contents, learning outcome, methods and examination type as well as linking to current dates for courses and module examination in the respective sections.

Module version of SS 2016 (current)

There are historic module descriptions of this module. A module description is valid until replaced by a newer one.

Whether the module’s courses are offered during a specific semester is listed in the section Courses, Learning and Teaching Methods and Literature below.

available module versions
SS 2016WS 2013/4SS 2013

Basic Information

MA5612 is a semester module in English language at Master’s level which is offered irregular.

This Module is included in the following catalogues within the study programs in physics.

  • Specialization Modules in Elite-Master Program Theoretical and Mathematical Physics (TMP)
Total workloadContact hoursCredits (ECTS)
180 h 60 h 6 CP

Content, Learning Outcome and Preconditions


Mathematical models are nowadays essential for the quantitative assessment of technical, physical, chemical, and biological processes. While a broad class of models is used in the different field, almost all models share one common property: the need for accurate parameter values. Due to experimental constraints, many parameters cannot be measured directly, but have to be estimated from the available experimental data.
In this course, we will introduce deterministic modeling approaches for biochemical reaction networks. These modeling approaches can be used to describe, e.g., signal transduction and metabolic processes. For these models the respective parameter estimation problem will be formulated and methods will be presented to solve these problems. As parameter estimates carry uncertainties due to limited amounts of data and measurement noise, we furthermore provide methods for a rigorous analysis of parameter uncertainties. This is crucial to evaluate the model uncertainties as well as the predictive power of models.
The participants will gather hands-on experiences with parameter estimation and uncertainty analysis, including the implementation of own models and estimation procedures in MATLAB. The estimation methods are presented in the context of biological processes, but the approaches are applicable in many other fields.

1) Modeling of biochemical reaction networks in a nutshell ( 2 lectures)
1.1) Introduction of biochemical reaction networks (including several examples)
1.2) Mass action and Michaelis-Menten kinetics
1.3) Reaction rate equation (RRE)
(The RRE is a system of ordinary differential equations which can be used describe the dynamics of reaction networks. It is widely used in chemistry, biochemistry and biology. In this lecture we develop methods for systems of ordinary differential equations and illustrate them using different RRE models.)

2) Maximum likelihood estimation for RREs (4 lectures)
2.1) Likelihood function
2.2) Maximum likelihood estimation as optimization problem
2.3) Local and global optimization
a. Gradient descent and interior point methods
b. Multi-start optimization

3) Identifiability and uncertainty analysis for RREs (3 lectures)
3.1) Structural and practical identifiability
3.2) Uncertainty analysis of and confidence intervals for parameters
a. Asymptotic confidence intervals
b. Bootstrapping confidence intervals
c. Profile likelihoods

4) Bayesian parameter estimation for RREs (3 lectures)
1) Bayes theorem and Bayesian statistics
2) Markov chain Monte-Carlo sampling
3) Bayesian confidence intervals for parameter estimates and predictions

5) Properties of estimators (e.g. bias and variance) (1 lectures)

6) Summary and Outlook (1 lectures)

Learning Outcome

After successful completion of the module, the participants can:
1. model biochemical reaction networks using ODEs.
2. solve parameter estimation problems for ODEs using MATLAB.
3. analyze the uncertainty of parameter estimates using MATLAB.
4. critically evaluate parameter estimation procedures.


Bachelor in mathematics, bioinformatics, statistics or related fields.
Basic MATLAB programming skills.

Courses, Learning and Teaching Methods and Literature

Courses and Schedule

Learning and Teaching Methods

lecture + exercise module
The module is offered as lectures with accompanying practice sessions. In the lectures, the contents will be presented in a talk with demonstrative examples, as well as through discussion with the students. The lectures should motivate the students to carry out their own analysis of the themes presented and to independently study the relevant literature. Corresponding to each lecture, practice sessions will be offered, in which exercise sheets and solutions will be available. In this way, students can deepen their understanding of the methods and concepts taught in the lectures and independently check their progress.


blackboard and slides


Will be announced during the course.

Module Exam

Description of exams and course work

The exam will be in written form (90 min) if more than 15 students participate, otherwise the exam will be in oral form (20 min). The students will be asked to apply parameter optimization and uncertainty analysis techniques discussed in the course. In addition, the students will be expected to be able to analyze estimation results (e.g. check the plausibility and consistency) and to transfer the acquired knowledge to similar problems. To evaluate the programming skills, the students will be asked to write pseudo code for the implementation of an algorithm / a method. The students will be allowed to use any printed material (lecture notes, books, etc.)

Exam Repetition

The exam may be repeated at the end of the semester.

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