## MAMCDTU-Data & Uncertainty

Module Provider: Mathematics and Statistics
Number of credits: 12 [6 ECTS credits]
Level:7
Terms in which taught: Autumn term module
Pre-requisites:
Non-modular pre-requisites:
Co-requisites: MAMCDTE Partial Differential Equations and MAMCDTS Dynamical Systems and MAMCDTN Numerical Methods
Modules excluded:
Module version for: 2017/8

Module Convenor: Dr Jochen Broecker

Summary module description:
Note: As this module is part of a joint programme with Imperial College London, the academic regulations for this module might differ from standard academic regulations usually applied at the University of Reading. The relevant document is the Joint Degree Programme Agreement between Imperial College London and University of Reading.

Aims:
This module develops the theoretical foundations of methods to infer both dynamic and static models from complex data. Classical and Bayesian inference is discussed, followed by and introduction to discrete time stochastic processes, in particular Markov processes. Data assimilation and optimal filtering as well as identification in dynamical models are considered. The asymptotic properties of Monte Carlo methods are analysed, both as an important statistical tool as well as an application of the methods taught in the concurrent course on Dynamical Systems. Brownian motion and functional limit theorems are discussed as an example of an advanced statistical methodology, but also as an introduction to diffusion processes and general continuous time stochastic processes.

Assessable learning outcomes:

On completion of this module students will have acquired:

• familiarity with a variety of mathematical techniques used in statistical inference in both static and dynamic models;

• familiarity with hypothesis testing, confidence intervals, and estimators and their asymptotic distributions;

• familiarity with stochastic processes in discrete time, in particular Markov processes;

• an appreciation of data assimilation and optimal filtering as well as identification in dynamical models;

• an appreciation of Brownian motion and functional limit theorems, e.g. as used in the proof of the Kolmogorov--Smirnov statistics.

Outline content:
Definitions and examples, Review of probability theory, Classical and Bayesian inference, Stochastic processes in discrete time, Data assimilation, filtering, identification of dynamical models, Monte Carlo methods, Brownian motion, Functional limit theorems.

Brief description of teaching and learning methods:
Lectures and tutorials.

Contact hours:
 Autumn Spring Summer Lectures 20 Tutorials 6 Guided independent study 94 Total hours by term 120.00 Total hours for module 120.00

Summative Assessment Methods:
 Method Percentage Set exercise 50 Class test administered by School 50

Other information on summative assessment:

Formative assessment methods:

Peer marked tutorial questions.

Penalties for late submission:

Where the piece of work is submitted after the original deadline (or any formally agreed extension to the deadline): a mark of zero will be recorded.
You are strongly advised to ensure that coursework is submitted by the relevant deadline. You should note that it is advisable to submit work in an unfinished state rather than to fail to submit any work.

Penalties for late submission on this module are in accordance with the University policy. Please refer to page 5 of the Postgraduate Guide to Assessment for further information: http://www.reading.ac.uk/internal/exams/student/exa-guidePG.aspx

Length of examination:

Requirements for a pass:
An average of 50% across the whole module.

Reassessment arrangements:
Via a written resit exam. Coursework will be carried forward if it received 40% or more, otherwise it must be resubmitted before the resit exam.