Undergraduate Course: Mathematics of Data Assimilation (MATH11170)
|School||School of Mathematics
||College||College of Science and Engineering
|Credit level (Normal year taken)||SCQF Level 11 (Year 5 Undergraduate)
||Availability||Available to all students
|Summary||The main goal of this course is to present a unified framework for data assimilation as a clearly defined mathematical problem in which the Bayesian formulation provides the foundation for derivation and analysis of algorithmic approaches, and for implementing 'informed' approximations which are needed in practical applications.
1. Background material (basics of probability in continuous probability spaces, metrics on spaces of probability measures, probabilistic view on dynamical systems).
2. Filtering problem in R^n in discrete time, filter optimality and well-posedness.
3. Probabilistic formulation of data assimilation and the role of model error.
4. Discrete-time data assimilation algorithms -Kalman filter and conditions for its optimality, approximate Gaussian filters, finite-dimensional non-Gaussian filters.
In many scientific areas there is a growing demand for integration of complex dynamical models with observed data in order to improve the predictive performance of the underlying mathematical techniques. Such strategies have been applied in engineering and weather forecasting for a few decades, though in an often ad hoc fashion. Despite the allure of this approach and the rapidly increasing availability of experimental data (satellite measurements, real-time streams of sensor data, etc.), a seamless and systematic fusion of these noisy data sets and imperfect models remains challenging. Consequently, the ability to fully appreciate the power, limitations, and - importantly - to benefit from a systematic implementation of such a framework requires familiarity with some fundamental principles which will be introduced in this course.
The main theme - data assimilation - is a process of obtaining the best statistical estimate of the state of an evolving dynamical system from imperfect observations and an imperfect dynamical model, and it naturally leads to a Bayesian formulation for the posterior probability distribution of the system state, given the observations.
Information for Visiting Students
|High Demand Course?
Course Delivery Information
|Academic year 2018/19, Available to all students (SV1)
|Learning and Teaching activities (Further Info)
Lecture Hours 22,
Seminar/Tutorial Hours 5,
Summative Assessment Hours 2,
Programme Level Learning and Teaching Hours 2,
Directed Learning and Independent Learning Hours
|Assessment (Further Info)
|Additional Information (Assessment)
||Coursework : 20%
Examination : 80%
||Hours & Minutes
|Main Exam Diet S1 (December)||Mathematics of Data Assimilation (MATH11170)||2:00|
On completion of this course, the student will be able to:
- Ability to formulate a data assimilation procedure in a Bayesian framework.
- Capacity to understand the difference between stochastic filtering, data assimilation, and smoothing.
- Understand the issue of optimality, well-posedness of the filtering problem and convergence proof for a particle filter in the large particle number limit.
- Ability to utilise appropriate metrics to assess the quality of data assimilation algorithms, and familiarity with the impact of modelling errors on the optimality of data assimilation algorithms.
- Ability to apply approximate filtering/data assimilation algorithms to new problems encountered in practice.
|Data assimilation: A mathematical Introduction, A.M. Stuart, K.J.H. Law, K.C. Zygalakis |
Optimal Filtering, B.D.O. Anderson and J.B. Moore
Fundamentals of Stochastic Filtering, A. Bain and D. Crisan
|Graduate Attributes and Skills
|Course organiser||Dr Michal Branicki
Tel: (0131 6)50 4878
|Course secretary||Mr Martin Delaney
Tel: (0131 6)50 6427