Probability for Inference
Subject 620618 (2009)
Note: This is an archived Handbook entry from 2009. Search for this in the current handbook
Credit Points:  12.50  

Level:  9 (Graduate/Postgraduate)  
Dates & Locations:  This subject has the following teaching availabilities in 2009: Semester 1,  Taught on campus.
Timetable can be viewed here. For information about these dates, click here.  
Time Commitment:  Contact Hours: 36 hours comprising two onehour lectures per week and one onehour practical class per weeek. Total Time Commitment: Not available  
Prerequisites:  None  
Corequisites:  None  
Recommended Background Knowledge: 
It is recommended that students have completed a subject in probability theory (such as 620201 [2008] Probability or 620205 [2008] Probability for Statistics), or their equivalent, and a third year stochastic modelling subject (equivalent to 620301 [2008] Stochastic Modelling) or its equivalent.
 
Non Allowed Subjects:  None  
Core Participation Requirements: 
It is University policy to take all reasonable steps to minimise the impact of disability upon academic study and reasonable steps will be made to enhance a student's participation in the University's programs. Students who feel their disability may impact upon their participation are encouraged to discuss this with the subject coordinator and the Disability Liaison Unit. 
Coordinator
Assoc Prof Aihua XiaSubject Overview: 
This is an advanced level presenting probability theory from the measure theoretic viewpoint. Topics covered include probability spaces and random variables, the properties of probability measures, Lebesgue decomposition, probability measures on finite dimensional Euclidean spaces, integration and the properties of integrals, the monotone convergence theorem, uniform integrability, the dominated convergence theorem, moments and inequalities, the general notions of absolute continuity and singularity, RadonNikodym theorem and conditional expectation given a sigma algebra. The subject will also discuss generating functions (moment, characteristic), modes of convergence and limit theorems with applications to estimation and hypothesis testing. The presented material will be illustrated by applications to Statistics. 

Objectives: 
After completing this subject students should:

Assessment:  Up to 40 pages of written assignments (30%: two assignments worth 15% each, due mid and late in semester), a threehour written examination (70%, in the examination period). 
Prescribed Texts:  Shiryayev (1984), Probability, Graduate Texts in Mathematics, SpringerVerlag. 
Recommended Texts: 
Billingsley (1995), Probability and Measure, Wiley Series in Probability and Mathematical Statistics. 
Breadth Options:  This subject is not available as a breadth subject. 
Fees Information:  Subject EFTSL, Level, Discipline & Census Date 
Generic Skills: 
Upon completion of this subject, students should gain:

Related Majors/Minors/Specialisations: 
R05 RM Master of Science  Mathematics and Statistics 
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