Module Code ST3453 Module Name Stochastic models in space ...

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Module Descriptor 2012/13

School of Computer Science and Statistics.

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1

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Module Code

ST
3453


Module Name

Stochastic models in space and time I


Module Short
Title


Stochastic models


ECTS weighting

?


Semester/term
taught


Michaelmas




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:

36


Module
Personnel


Lecturing
staff:

Prof J Haslett


Learning
Outcomes


Students will have a
bility t
o 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



an
d to extend the application of

Poisson and Gaussian processes to space


Module
Learning
Aims



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




Module
Content


Specific
topics addressed in this module include:



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

Module Descriptor 2012/13

School of Computer Science and Statistics.

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Gaussian processes in discrete time including

o

AR and MA processes used in forecasting

o

Noisy observations of GPs and HMMs



Gaussian proce
sses 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 w
hich I will give a brief re
-
introduction. The key concepts are those of marginal, joint and conditional probability
distributions. We will use simple discrete Markov chains to embed these elementary
concepts.


Recommended
Reading List


The central text is

Ross, S. M. Introduction to Probability Models, Academic Press.8
th

ed 2003 519.2 M94*7

;
7
th

ed 519.2 M94*6

; 6
th

ed 2002 PL
-
403
-
442

; 5
th

ed 1993 PL
-
224
-
947. In the 6
th

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 H
L
-
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 Ti
me 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.


Module

Pre
Requisite


ST2351 and ST2352
.




Module Co
Requisite




Assessment
Details


Exam,
one

optional

projects 25%


The final grade will be max( exam/100, exam/75 + project/25)


Module
N/a

Module Descriptor 2012/13

School of Computer Science and Statistics.

Page
3

of
3


approval date



Approved By


N/a


Academic
Start Year


2012
-
2013


Academic Year
of Data


2012