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STAT354 Distribution Theory and Inference

Updated: 15 January 2013
Credit Points 6
Offering
Responsible Campus Teaching Period Mode of Study
Armidale Trimester 1 Off Campus
Armidale Trimester 1 On Campus
Intensive School(s) None
Supervised Exam There is a UNE Supervised Examination held at the end of the teaching period in which you are enrolled.
Pre-requisites STAT261 and PMTH212
Co-requisites None
Restrictions None
Notes None
Combined Units None
Coordinator(s) Robert Murison (rmurison@une.edu.au)
Unit Description

Distribution theory includes indicator functions; bivariate and multivariate transformations of variables; the multivariate normal distribution; distribution of quadratic forms and order statistics. Inference includes data reduction; properties of estimators; evaluation of and construction of tests of hypotheses; and likelihood ratio tests. Students should have access to the statistical package R.
Important Information

Where calculators are permitted in examinations, it must be selected from an approved list, which can be accessed from the Further Information link below.

Further information
Recommended Material
Optional 		Text(s):

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

Statistical Inference
ISBN: 9780534243128
Casella, G. and Berger, R.L., Duxbury 2nd ed. 2002
Text refers to: Trimester 1 , On and Off Campus
Introduction to Mathematical Statistics
ISBN: 9780321795434
Hogg, R.V., McKean, J.W. and Craig, A.T., Pearson 7th ed. 2012
Text refers to: Trimester 1 , On and Off Campus
Referenced Material
Optional 		Text(s):

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

Encyclopedia of Statistical Sciences
ISBN: 9780471667193
Kotz, S., Vidakovic, B. and Balakrishnan, N., John Wiley & Sons 2006
Note: Available online through the Dixson Library, UNE
Text refers to: Trimester 1 , On and 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 8%
Assessment Notes
Distribution Theory
Relates to Learning Outcomes (LO) and Graduate Attributes (GA)
LO: 1, 6 GA: 1, 2, 4, 6
Assignment 2 8%
Assessment Notes
Transformations and Multivariate Normal
Relates to Learning Outcomes (LO) and Graduate Attributes (GA)
LO: 1, 2, 6 GA: 1, 2, 4, 6
Assignment 3 8%
Assessment Notes
Order Statistics
Relates to Learning Outcomes (LO) and Graduate Attributes (GA)
LO: 1, 3, 6 GA: 1, 2, 4, 6
Assignment 4 8%
Assessment Notes
Sufficiency, Likelihood
Relates to Learning Outcomes (LO) and Graduate Attributes (GA)
LO: 1, 4, 6 GA: 1, 2, 4, 6
Assignment 5 8%
Assessment Notes
Cramer Rao Lower Bound
Relates to Learning Outcomes (LO) and Graduate Attributes (GA)
LO: 1, 4, 6 GA: 1, 2, 4, 6
Assignment 6 10%
Assessment Notes
Bayesian Inference
Relates to Learning Outcomes (LO) and Graduate Attributes (GA)
LO: 1, 4, 6 GA: 1, 2, 4, 6
Final Examination 2 hrs 50%
Relates to Learning Outcomes (LO) and Graduate Attributes (GA)
LO: 1, 2, 3, 4, 5, 6 GA: 1, 2, 6

Learning Outcomes (LO) Upon completion of this unit, students will be able to:
  1. develop the frameworks for drawing inference from data by applying calculus to summarise the data with optimum estimates;
  2. develop the theory of the multivariate normal distribution and quadratic forms;
  3. use order statistics as a sufficient set of statistics which yield properties about the quantiles of the population;
  4. evaluate estimators and construct tests of hypotheses, including the likelihood ratio test;
  5. compare the classical statistical inference with Bayesian inference; and
  6. develop skill in setting out solutions formally to preserve neatness and convey logic in development and practise calculus and algebra.

Graduate Attributes (GA)
Attribute Taught Assessed Practised
1 Knowledge of a Discipline
Through learning statistical inference, graduates will recognise the scope of statistical analysis and be able to distil properties in a data set and apply the appropriate statistical models. 		True True True
2 Communication Skills
Graduates will communicate their results with formal setting out of solutions, augmented by clear sentences which explain the results and the meanings and importances of terms in the algebra. The explanation has to be relatively free of technical jargon and where such is necessary, its meaning be fully explained. Students will develop skills in drawing pen-pictures that explain features of graphs. 		True True True
3 Global Perspectives
Graduates will appreciate that statistics is ubiquitous by learning how statistical techniques are generic and are driven by properties of the data rather than the application. 		True
4 Information Literacy
Graduates will know the classical papers and books upon which statistical inference is founded. They will be equipped with terminology so that they can recognise statistical inference in diverse settings such as science, business, social science, humanities, etc 		True True True
5 Life-Long Learning
Solid foundations in statistical inference principles and the requisite mathematics will allow graduates to adopt new methods of inference which will arise with new sources of information, eg. Bioinformatics. Statistics graduates will carry the responsibility of interpreting new information. 		True
6 Problem Solving
Graduates will be proficient in translating problems expressed in words to an algebraic formulation which allows analysis, performing the analysis mathematically, and expressing the solution in words in the context of the original problem. 		True True True
   

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