PDF for print
Find calendar
| Title |
Parameter Estimation
|
| Semester |
E2024
|
| Master programme in |
Mathematical Bioscience / Physics and Scientific Modelling
|
| Type of activity |
Course |
| Teaching language |
English
|
| Study regulation | |
| REGISTRATION AND STUDY ADMINISTRATIVE | |
| Registration |
Sign up for study activities at stads selvbetjeningwithin the announced registration period, as you can see on the Studyadministration homepage. When signing up for study activities, please be aware of potential conflicts between study activities or exam dates. The planning of activities at Roskilde University is based on the recommended study programs which do not overlap. However, if you choose optional courses and/or study plans that goes beyond the recommended study programs, an overlap of lectures or exam dates may occur depending on which courses you choose. |
| Number of participants |
The Master Programme/Institute reserves the right to cancel the course if fewer than 8 studentes are registered for the course. |
| ECTS |
5
|
| Responsible for the activity |
Johnny T. Ottesen (johnny@ruc.dk)
|
| Head of study |
Jesper Schmidt Hansen (jschmidt@ruc.dk)
|
| Teachers |
|
| Study administration |
INM Registration & Exams (inm-exams@ruc.dk)
|
| Exam code(s) |
U60168
|
| ACADEMIC CONTENT | |
| Overall objective |
The overall objective of the course is to provide students with a fundamental understanding of selected methods in the field of parameter estimation. Students will learn to apply parameter estimation critically in various biological applications, by working with empirical data and mathematical models. |
| Detailed description of content |
Assessing parameter values for models described by non-linear ordinary differential equations is a serious challenge in all fields of science. Often the challenge is divided into two challenges. Ones regard the possibility of estimating the parameters values if perfect data was available assuming the model is correct, i.e., if pseudo-data was generated from the model, can all parameter values be uniquely obtained then? Whenever, such structural identifiability is established, the challenge of estimating the parameters from real measurement occur. This is done by specifying a criterion for obtaining the best estimates e.g., a least square cost or another way of addressing the best (optimal) estimates. Often this is considered as a statistical problem. Given noisy data and an underlying mathematical model predicting the data, pose a statistical model describing the deviation between data and model prediction and use this to estimate the underlying model parameters and the parameters of the statistical model. Such an approach is often denoted Bayesian interference. This second challenge is very diverse: Often data are given to the mathematicians, and we have not been involved in deciding which measurements are obtained. The practical limitation of what can be measured is another challenge. However, parameter estimation frequently allows us to access otherwise inaccessible parts of the system, a strategy sometimes referred to as the mathematical microscope. Moreover, data may be noisy, which leads to uncertainties on the estimated parameters. In the process of estimating parameter values mathematical methods from classical optimization or Bayesian interference is often used. Furthermore, parameter estimation comes with computational challenges such as robustness of the method and computational costs. The estimates and their uncertainties need to be interpreted in relation to the actual modeling challenge. The course deals with these topics. The theoretical foundation needed to understand methods and related practical challenges will be addressed. Moreover, the state of the art of mathematical models will be applied to these real-world challenges. The course will require good skills in linear algebra, analysis, dynamical systems, probability theory, statistics, and knowledge of Python (or similar) programming. |
| Course material and Reading list |
The course will require good skills in linear algebra, analysis, dynamical systems, probability theory, statistics, and in Python (or similar) programming. The pensum will be parameter estimation in dynamical system models i.e., models specified by ODEs. Equal weight is on the theoretical foundation and the application to real-world problems in mini-project. |
| Overall plan and expected work effort |
The course is a 5 ETCS credit course, corresponding to an expected student work-load of 135 hours.
The 100 hours preparation time means that students on average should expect to use at least 4 hours of preparation time for each double-lecture throughout the semester. In addition, there will be six mini-projects during the course where the student uses the theory in practice on real-world challenges. In the periods with mini-projects more preparation time may be needed compared to the remaining period. The students are expected to use at least 10 hours extra per mini-project distributed over the project period (1-2 weeks). |
| Format |
|
| Evaluation and feedback |
The course includes formative evaluation based on dialogue between the students and the teacher(s). Students are expected to be active and provide constructive critique, feedback and viewpoints during the course. The teaching switch between classical lectures and ‘flip the classroom’ controlled activities. The last being more pronounced during the PPL oriented mini-projects. Every other year at the end of the course, there will also be an evaluation through a questionnaire in SurveyXact. The Study Board will handle all evaluations along with any comments from the course responsible teacher. Furthermore, students can, in accordance with RUCs ‘feel free to state your views’ strategy through their representatives at the study board, send evaluations, comments or insights form the course to the study board during or after the course. |
| Programme |
|
| ASSESSMENT | |
| Overall learning outcomes |
The student will be able to
|
| Form of examination |
Individual written take-home assignment.
The character limit of the assignment is: 1,200-120,000 characters, including spaces. The character limit includes the cover, table of contents, bibliography, figures and other illustrations, but exclude any appendices. The duration of the take-home assignment is 24 hours. Assessment: 7-point grading scale. |
| Form of Re-examination |
Individual oral exam without time for preparation.
Time allowed for exam including time used for assessment: 30 minutes. Permitted support and preparation materials: Course material and own notes. Assessment: 7-point grading scale. Moderation: Internal co-assessor. |
| Type of examination in special cases |
|
| Examination and assessment criteria |
|
| Exam code(s) | |
| Last changed | 11/11/2024 |
Find calendar (1)
PDF for print (1)