Units

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Sample subject outline - Semester 1 2013

Note: Subject outlines often change before the semester begins. Below is a sample outline.

Rationale

Statistical inference is a cornerstone of data analysis, model building, simulation and prediction in a wide range of applications, and hence is an important tool for the mathematical scientist. This unit provides a foundation for your future development whether as a statistical user or a statistician. It also provides the statistical basis for further postgraduate units in statistics.

Aims

The unit is intended to provide you, in a rigorous manner, with the key mathematical concepts and tools for statistical inference and to foster your understanding and skills in statistical inference as a foundation for lifelong learning. Focus is on the development of the theoretical building blocks that are the basis for methodological developments and applications of statistics. Assumed knowledge: exposure to introductory ideas of statistical inference, including parameter estimation, confidence intervals and hypothesis testing, such as provided by a first course in statistics or data analysis.

Objectives

On successful completion of this unit you should be able to:

1. Show theoretical, technical and computational skills in statistical analysis.
2. Demonstrate statistical concepts and skills as part of a problem solving approach to statistical inference and data analysis in real life examples.
3. Deepen skills and sharpen competencies as a statistician for application in a variety of professional circumstances.
4. Critically read published research within the context of the unit.

Content

1. Construction of likelihood function.
2. Maximum likelihood, estimation and properties of maximum likelihood estimates - one, two and many parameter models.
3. Likelihood based confidence intervals, and hypothesis testing using likelihood - one and two sample problems.
4. Principles of Bayesian inference - construction of full probability model and derivation of posterior distribution, marginal and conditional posterior distributions.
5. Bayesian inference for binomial data, Poisson count data and normal data - one and two sample problems.
6. Simulation techniques for sampling from posterior distributions - independent sampling, importance sampling, Gibbs sampling, Markov chain Monte Carlo, sequential Monte Carlo).

The computer packages Matlab and R will be used to implement inference techniques developed throughout the unit.

Approaches to Teaching and Learning

There will be four contact hours per week. This will include 3 hours of lectures and 1 hour practical/computer practical.

Your work will be context-based using a wide variety of examples from many different areas of application. The emphasis will be on enabling your learning through experience, on providing opportunities to enhance your written and oral communication, and on honing skills and attitudes to promote your lifelong learning.

A combination of discussions, use of purpose-written lecture notes, working through small and larger real world problems, using computer-based materials, and expressing solutions individually and in groups, will promote your creativity in problem-solving, critical assessment skills, and intellectual debate. You will be encouraged to engage in aspects of professionalism and ethics in the practice of statistics.

This unit is being taught concurrently with an undergraduate offering of the same subject. University policy permits that postgraduate and undergraduate students attend the same lectures. Separate practical/discussion groups will be provided for postgraduate student where numbers allow. As a postgraduate student you will be required to complete separate or additional assessment. For this unit this means that you will write a report reviewing a statistical journal paper.

Assessment

Formative assessment will take place throughout the semester primarily in practicals but also in lectures and outside class.You will receive regular feedback in practicals.

Assessment name: Problem Solving Task
Description: Continuous assessment: This will consist of two sets of exercises based on class and laboratory work.
Relates to objectives: 1, 2 and 3
Weight: 30%
Internal or external: Internal
Group or individual: Individual
Due date: Weeks 6 & 12

Assessment name: Literature Review
Description: A recent statistical journal paper of your choice, which employs either likelihood based or Bayesian inference, is to be reviewed and a report written..
Relates to objectives: 3 and 4
Weight: 10%
Internal or external: Internal
Group or individual: Individual
Due date: Week 13

Assessment name: Examination (Theory)
Description: End-semester examination: This will consist of a written School-based exam based on the material presented related to the content specified above.
Relates to objectives: 1, 2 and 3
Weight: 60%
Internal or external: Internal
Group or individual: Individual
Due date: End Semester

Academic Honesty

QUT is committed to maintaining high academic standards to protect the value of its qualifications. To assist you in assuring the academic integrity of your assessment you are encouraged to make use of the support materials and services available to help you consider and check your assessment items. Important information about the university's approach to academic integrity of assessment is on your unit Blackboard site.

A breach of academic integrity is regarded as Student Misconduct and can lead to the imposition of penalties.

Resource materials

There is no required text


References:

Most books on mathematical statistics and statistical inference are useful as reference material. Some examples are:
1. Davison, AC (2003). Statistical Models, Cambridge.

2. Lee PM (2004). Bayesian Statistics: An introduction, 3rd edition, Arnold

3. Albert J (2007). Bayesian Computation with R, Springer

Risk assessment statement

There are no out of the ordinary risks associated with this unit. Further information on health and safety at QUT can be found at http://hrd.qut.edu.au/healthsafety/healthsafe/index.jsp

Disclaimer - Offer of some units is subject to viability, and information in these Unit Outlines is subject to change prior to commencement of semester.

Last modified: 19-Oct-2012