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DRPS : Course Catalogue : School of Mathematics : Mathematics

Undergraduate Course: Mathematics of Data Assimilation (MATH11170)

Course Outline
SchoolSchool of Mathematics CollegeCollege of Science and Engineering
Credit level (Normal year taken)SCQF Level 11 (Year 5 Undergraduate) AvailabilityAvailable to all students
SCQF Credits10 ECTS Credits5
SummaryThe 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 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.
Entry Requirements (not applicable to Visiting Students)
Pre-requisites Students MUST have passed: ( Probability (MATH08066) OR Probability with Applications (MATH08067))
Prohibited Combinations Other requirements None
Information for Visiting Students
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:
  1. Ability to formulate a data assimilation procedure in a Bayesian framework.
  2. Capacity to understand the difference between stochastic filtering, data assimilation, and smoothing.
  3. Understand the issue of optimality, well-posedness of the filtering problem and convergence proof for a particle filter in the large particle number limit.
  4. 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.
  5. 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
Course organiserDr Michal Branicki
Tel: (0131 6)50 4878
Course secretaryMr Martin Delaney
Tel: (0131 6)50 6427
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