Module Descriptor 2012/13
School of Computer Science and Statistics.
Module Code
ST3453
Module Name
Stochastic models in space and time I
Module Short
Title
Stochastic models
ECTS weighting
?
Michaelmas
Semester/term
taught
Contact Hours
Lecture hours: 36
There will no formal tutorials, but several of the hours will be used for problem solving.
Students will be encouraged to use Monte Carlo simulation as a means of assimilating the
material
Total hours:
Module
Personnel
36
Lecturing staff: Prof J Haslett
Learning
Outcomes

Module
Learning Aims
Students will have ability to discuss and model simple versions of the following processes in
time:
o Markov chains, with particular emphasis on binary chains
o Counting processes in continuous time, with particular emphasis on Poisson
processes
o Discrete and continuous time Gaussian processes
o Hidden Markov models, with particular emphasis on noisy observations of binary
chains
and to extend the application of Poisson and Gaussian processes to space
Stochastic processes and in particular Gaussian, Poisson and Markov Models are the central
examples of “stochastic processes”. Gaussian processes, in combination with Hidden
Markov have become central tools in statistics and machine learning. They are used for
smoothing, de-noising; and generally for determining structure in noisy signals and using
this for prediction. This course will provide simple examples, some of which will be
extended and applied in ST3454
Specific topics addressed in this module include:
Module
Content




Examples by Monte Carlo simulation
Binary Markov Chains in time,
o revision of joint, marginal and conditional distributions; and
o application to missing or noisy observation
Simple examples of more general Markov chains
Poisson processes in continuous time, application to simple examples including
o Thinning
o Inhomogeneous processes
Page 1 of 3
Module Descriptor 2012/13
School of Computer Science and Statistics.



Gaussian processes in discrete time including
o AR and MA processes used in forecasting
o Noisy observations of GPs and HMMs
Gaussian processes in continuous time, characterised by covariance functions
Brief extension of GPs to 2D space.
The treatment of Gaussian stochastic processes will be at an introductory level. The basic
mathematics is that of the multivariate normal distribution on which I will give a brief reintroduction. The key concepts are those of marginal, joint and conditional probability
distributions. We will use simple discrete Markov chains to embed these elementary
concepts.
The central text is
Recommended Ross, S. M. Introduction to Probability Models, Academic Press.8 th ed 2003 519.2 M94*7 ;
Reading List
th
th
th
th
7 ed 519.2 M94*6 ; 6 ed 2002 PL-403-442 ; 5 ed 1993 PL-224-947. In the 6 ed, Ch 1-4,
6, 10 are relevant
Aspects of the following are relevant for deeper study
Christensen, R. Linear Models for Multivariate, Time Series and Spatial Data, (Springer Texts
in Statistics) 1996 Ch 5 and 6 are relevant
Christensen, Ronald Advanced Linear Modeling: Multivariate, Time Series and Spatial Data Nonparametric Regression and Response Surface Maximization (Springer Texts in Statistics)
2001 (updated and extended version of above)
MacDonald I. L. and Zucchini W. Hidden Markov and other models for discrete-valued time
series. 1997 Chapman and Hall HL-195-718 Good book for advanced applications. For
introductory work Sections 1.2, 1.3
Chatfield , C. The Analysis of Time Series, Chapman and Hall, 6th ed 2004. 519.5 M0996*5 ;
5th ed 1996 ARTS 330.18 M98*4. Chapter 3 (5th ed) on Probability Models for Time Series
is directly relevant for that part of the course dealing with Gaussian processes in discrete
time.
Ripley, B.D. Spatial Statistics, 1981, 519.5 M192. Chapter 4 and Section 5.2 are directly
relevant to our treatment of spatial processes.
ST2351 and ST2352.
Module Pre
Requisite
Module Co
Requisite
Assessment
Details
Module
Exam, one optional projects 25%
The final grade will be max( exam/100, exam/75 + project/25)
N/a
Page 2 of 3
Module Descriptor 2012/13
School of Computer Science and Statistics.
approval date
Approved By
N/a
Academic
Start Year
2012-2013
Academic Year
2012
of Data
Page 3 of 3