Statistical Inference for Dynamical Systems
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
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)
Content, Learning Outcome and Preconditions
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)
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.
Basic MATLAB programming skills.
Courses, Learning and Teaching Methods and Literature
Courses and Schedule
|Statistical Inference for Dynamical Systems [MA5612]
Wed, 10:15–11:45, MI 02.08.011
|Exercises for Statistical Inference for Dynamical Systems [MA5612]
Wed, 16:00–18:00, MI 03.06.011
Learning and Teaching Methods
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.
Description of exams and course work
The exam may be repeated at the end of the semester.