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| Title |
Parameter Estimation
|
| Semester |
E2025
|
| Master programme in |
Mathematical Bioscience / Physics and Scientific Modelling
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| Type of activity |
Course |
| Mandatory or elective |
Mandatory/Elective Mandatory: Mathematical Bioscience. Physics and Scientific Modelling - Thematic profile 1 Elective: Physics and Scientific Modelling - General profile |
| Teaching language |
English
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| 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 |
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| 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 |
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| ASSESSMENT | |
| Overall learning outcomes |
The student will be able to
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| Prerequisites |
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| Form of examination |
Individual written portfolio and oral exam The character limit of the portfolio is 12,000-312,000 characters, including spaces. Examples of written products are exercise responses, talking points for presentations, written feedback, reflections, written assignments. The preparation of the products may be subject to time limits. The character limits include the cover, table of contents, bibliography, figures and other illustrations, but exclude appendices. Time allowed for the exam including time used for assessment: 40 minutes. The assessment is an overall assessment of the written product(s) and the subsequent oral examination. Permitted support and preparation materials for the oral exam: All. Assessment: 7-point grading scale Moderation: Internal co-assessor |
| Form of Re-examination |
Samme som ordinær eksamen / same form as ordinary exam
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| Type of examination in special cases |
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| Examination and assessment criteria (implemented) |
The portfolio consists of 4-5 mini project done during the class. Oral exam: The student draws an individual mini project from own portfolio. The student will have approximately 10 minutes to present the mini project. Afterwards the exam will take form as a dialogue focusing on data, ODE model, Bayesian inference, and results and conclusions related to the mini project. Examinator and co-assessor may pose questions at any time during your presentation and most likely will pose several questions after your short presentation. The students are allowed to use their report on the mini project, their notes and computer, and the device in the room (projector, blackboard, etc.). The use of GAI is not allowed during the oral exam. Assessment criteria: The student will be assessed by their ability to: • present the data, • present the statistical model, • present the Bayesian approach, • demonstrate hability to use software / programming to estimate parameters and uncertainties for ODE models • present the results of the mini project, • link the practical case and the method to the theoretical background for Bayesian inferences • apply mathematical analysis and linear algebra in differential geometry. The assessment of the oral exam is based on the student’s ability to meet the criteria mentioned above and their ability to • clearly present and communicate the scientific content of the course • engage in a scientific dialogue and discussion with the assessors Regarding the use of generative AI at the exam In this course, generative AI tools (GAI) are allowed in the work on the exam if their use is declared. You must clearly indicate how you have used generative artificial intelligence (GAI). This can, for example, be included as part of a methodology section or as a brief statement at the end of your exam paper or submitted as an appendix to your assignment. This means that you must describe how you have used GAI, for example, for preparatory work on the assignment, to ask questions, search and process information, receive feedback and critique on your text, perform proofreading, or improve language and readability. It is important that you actively consider your choice of tools in this way, as it is part of the entire creation process of the assignment and thus part of your scientific method and academic communication. The use of any specific text that is GAI-generated requires citation, just like the use of any other sources from which direct quotes are taken. In the library's guide, you can see more about how to cite AI and how you can declare your use of GAI - find the guide here. Regular spell check and other language suggestions, as known from Word or other word processing programs, as well as programs for writing minutes and transcription, are allowed in all written exams and do not need to be declared. |
| Exam code(s) | |
| Last changed | 23/10/2025 |
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