Undergraduate Course: Mathematics of Data Assimilation (MATH11170)
Course Outline
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 
SCQF Credits  10 
ECTS Credits  5 
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. 
Course description 
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 wellposedness.
3. Probabilistic formulation of data assimilation and the role of model error.
4. Discretetime data assimilation algorithms Kalman filter and conditions for its optimality, approximate Gaussian filters, finitedimensional nonGaussian 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, realtime 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
Prerequisites  None 
High Demand Course? 
Yes 
Course Delivery Information

Academic year 2018/19, Available to all students (SV1)

Quota: None 
Course Start 
Semester 1 
Timetable 
Timetable 
Learning and Teaching activities (Further Info) 
Total Hours:
100
(
Lecture Hours 22,
Seminar/Tutorial Hours 5,
Summative Assessment Hours 2,
Programme Level Learning and Teaching Hours 2,
Directed Learning and Independent Learning Hours
69 )

Assessment (Further Info) 
Written Exam
80 %,
Coursework
20 %,
Practical Exam
0 %

Additional Information (Assessment) 
Coursework : 20%
Examination : 80% 
Feedback 
Not entered 
Exam Information 
Exam Diet 
Paper Name 
Hours & Minutes 

Main Exam Diet S1 (December)  Mathematics of Data Assimilation (MATH11170)  2:00  
Learning Outcomes
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, wellposedness 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.

Reading List
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

Additional Information
Graduate Attributes and Skills 
Not entered 
Keywords  MoDA 
Contacts
Course organiser  Dr Michal Branicki
Tel: (0131 6)50 4878
Email: M.Branicki@ed.ac.uk 
Course secretary  Mr Martin Delaney
Tel: (0131 6)50 6427
Email: Martin.Delaney@ed.ac.uk 

