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STAT503 Stochastic Processes

Updated: 06 November 2012
Credit Points 6
Offering
Responsible Campus Teaching Period Mode of Study
Armidale Trimester 1 Off Campus
Intensive School(s) None
Supervised Exam There is no UNE Supervised Examination.
Pre-requisites candidature in a postgraduate award and permission of head of school
Co-requisites None
Restrictions None
Notes None
Combined Units None
Coordinator(s) Robert Murison (rmurison@une.edu.au)
Unit Description

Spectral methods in statistics. The unit will provide theory and practice in analysing signals using Fourier and wavelet transforms. Statistical package R will be used. Topics are stochastic integrals, filtering, stochastic d.e.'s, non-stationary signals.
Referenced Material
Optional 		Text(s):

Note: Reference material is held in the University Library - purchase is optional

Wavelet Methods for Time Series Analysis
ISBN: 9780521685085
Percival, D. and Walden, A., CUP 2006
Note: Available from the Dixson Library, UNE
Text refers to: Trimester 1 , Off Campus
Encyclopedia of Statistical Sciences
ISBN: 9780471667193
Kotz, S., Vidakovic, B. and Balakrishnan, N., John Wiley & Sons 2006
Note: This book is available online through Dixson Library, UNE
Text refers to: Trimester 1 , Off Campus
Disclaimer Unit information may be subject to change prior to commencement of the teaching period.
Assessment
Title Exam Length Weight Mode No. Words
Assignment 1 10%
Assessment Notes
Write a program to calculate the discrete Fourier transform of a tie series.
Relates to Learning Outcomes (LO) and Graduate Attributes (GA)
LO: 1, 5, 6 GA: 1, 2, 3, 4, 5, 6
Assignment 2 20%
Assessment Notes
Find the covariance of a Poisson process and use this to get the solution to a first order stochastic d.e.
Relates to Learning Outcomes (LO) and Graduate Attributes (GA)
LO: 2, 6 GA: 1, 2, 4, 6
Assignment 3 10%
Assessment Notes
Filter a time series and analyse the periodogram.
Relates to Learning Outcomes (LO) and Graduate Attributes (GA)
LO: 2, 5 GA: 1, 2, 4, 6
Assignment 4 10%
Assessment Notes
Use the wavelet transform to identify the abrupt frequency change in a dense signal.
Relates to Learning Outcomes (LO) and Graduate Attributes (GA)
LO: 3, 5, 6 GA: 1, 2, 4, 6
Take Home Exam 50%
Relates to Learning Outcomes (LO) and Graduate Attributes (GA)
LO: 1, 2, 3, 4, 5, 6 GA: 1, 2, 3, 4, 5, 6

Learning Outcomes (LO) Upon completion of this unit, students will be able to:
  1. learn the properties of stochastic integrals in order to make inference about the signal using estimates;
  2. use Fourier analysis for 2nd order stationary stochastic processes;
  3. appreciate the fractal nature of some signals and use wavelets to analyse these;
  4. learn introductory material on stochastic differential equations;
  5. acquire skill in applying filters to signals; and
  6. know the mathematical theory that underpin signal analyses.

Graduate Attributes (GA)
Attribute Taught Assessed Practised
1 Knowledge of a Discipline
Knowledge of the discipline is imparted by lecture, on-line material and by notes, and it is assessed by practical computer workshops, tutorials, as well as by written assignments and written examination. 		True True True
2 Communication Skills
Communication skills are addressed primarily in the tutorial but are assessed in the quality of written work, where typeset assignment solutions are required. These skills are also tested in the computer practical sessions. 		True True True
3 Global Perspectives
The historical and modern development of spectral methods is mainly addressed in the lecture stream of this unit. 		True True True
4 Information Literacy
All students doing this unit are required to submit assignment solutions using a mathematical typesetting package. 		True True True
5 Life-Long Learning
The content of this unit will need to be used frequently by all students who wish to pursue a career in statistics or its application. 		True True True
6 Problem Solving
As this is essentially the reason for statistics being a discipline, problem solving is not only covered in lectures, but forms the basis of tutorials, practical and assignment activities. 		True True True
   

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