MXB341 Statistical Inference
To view more information for this unit, select Unit Outline from the list below. Please note the teaching period for which the Unit Outline is relevant.
| Unit code: | MXB341 |
|---|---|
| Prerequisite(s): | MXB241 or MAB314 |
| Equivalent(s): | MAB524 |
| Credit points: | 12 |
| Timetable | Details in HiQ, if available |
| Availabilities |
|
| CSP student contribution | $555 |
| Domestic tuition unit fee | $3,324 |
| International unit fee | $4,296 |
Unit Outline: Semester 1 2024, Gardens Point, Internal
| Unit code: | MXB341 |
|---|---|
| Credit points: | 12 |
| Pre-requisite: | MXB241 or MAB314 |
| Equivalent: | MAB524 |
| Coordinator: | Gentry White | gentry.white@qut.edu.au |
Overview
This is an advanced unit in mathematical statistics covering the theory of point estimation and inference using both classical and Bayesian methods. Statistical inference is the practice of both estimating probability distribution parameters and using statistical testing to validate these results, and plays a crucial role in research, and many real-world applications. You will use the methods of least squares, moments, and maximum likelihood to construct estimators of probability distribution parameters and evaluate them according to criteria including completeness, sufficiency, and efficiency. Results will be computed both analytically and numerically using software such as R. You will learn and apply the Neyman-Pearson Lemma for the construction of statistical tests, including to real-world applications, and learn Bayesian statistics for finding posterior distributions of parameters and evaluating their performance. Results will be communicated both orally and in written form.
Learning Outcomes
On successful completion of this unit you will be able to:
- Carry out statistical analyses using theoretical, technical and computational skills.
- Use statistical inference and data analysis concepts and skills as part of a problem solving approach to real life problems.
- Apply advanced statistical skills and competencies in a variety of professional circumstances.
Content
Construction of likelihood function, Maximum likelihood estimation and properties of maximum likelihood estimates one, two and many parameter models, Likelihood based confidence intervals, and hypothesis testing using likelihood one and two sample problems. Principles of Bayesian inference- construction of full probability model and derivation of posterior distribution, marginal and conditional posterior distributions. Bayesian inference for binomial data, Poisson count data and normal data. One and two sample problems Simulation techniques for sampling from posterior distributions: independent sampling, importance sampling and Gibbs sampling (dependent sampling using a Markov chain). Graphical models.
Learning Approaches
This unit involves 2 hours of lectures each week (which may be delivered online) where theory and concepts will be presented and discussed, and where you will be exposed to the processes required to solve problems using the methods of this unit. There will also be 2 hours of practical class each week, conducted online, where you will be guided through practical exercises including theoretical and computer-based activities.
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. The standards of the discipline as well as appropriate approaches to the communication of mathematical and statistical information will be conveyed via the examples presented in lectures and workshops.
You are able to partake in any lecture/workshop session times allocated, but also in your own private study time. That is, you are expected to consolidate the material presented during class by working a wide variety of exercises, problems and online learning activities in your own time.
Feedback on Learning and Assessment
Formative feedback will be provided for the in-semester assessment items by way of written comments on the assessment items, student perusal of the marked assessment piece and informal interview as required.
Summative feedback will be provided throughout the semester with progressive posting of results via Canvas.
Assessment
Overview
The assessment items in this unit are designed to determine your level of competency in meeting the unit outcomes while providing you with a range of tasks with varying levels of skill development and difficulty.
Unit Grading Scheme
7- point scale
Assessment Tasks
Assessment: Problem Solving Task
The problem solving task is a continuous assessment item that will consist of exercises based on class and laboratory work, delivered with timing appropriate to the progress of the class. There will be three sets of exercises.
This assignment is eligible for the 48-hour late submission period and assignment extensions.
Assessment: Examination (invigilated)
This assessment is based on the work covered during the semester.
The examination will require attendance at a local testing centre. For students enrolled as internal or on-campus, the local testing centre will be on QUT campus. For students enrolled as online, QUT Examinations will provide local testing centre information.
Academic Integrity
Students are expected to engage in learning and assessment at QUT with honesty, transparency and fairness. Maintaining academic integrity means upholding these principles and demonstrating valuable professional capabilities based on ethical foundations.
Failure to maintain academic integrity can take many forms. It includes cheating in examinations, plagiarism, self-plagiarism, collusion, and submitting an assessment item completed by another person (e.g. contract cheating). It can also include providing your assessment to another entity, such as to a person or website.
You are encouraged to make use of QUT’s learning support services, resources and tools to assure the academic integrity of your assessment. This includes the use of text matching software that may be available to assist with self-assessing your academic integrity as part of the assessment submission process.
Further details of QUT’s approach to academic integrity are outlined in the Academic integrity policy and the Student Code of Conduct. Breaching QUT’s Academic integrity policy is regarded as student misconduct and can lead to the imposition of penalties ranging from a grade reduction to exclusion from QUT.
Resources
There are no set texts for this unit.
There are many reference texts for this unit, many of which can be located in the library. There are also many online resources such as lecture notes and some e-books that can be found online. Most books on mathematical statistics and statistical inference are useful as reference material. Some examples are:
1. Berry DA (1996). Statistics: A Bayesian perspective, Wadsworth
2. Lee PM (2004) Bayesian Statistics: An introduction, 3rd edition, Arnold
3. Pawitan Y (2001) In all likelihood: Statistical Modelling and Inference Using Likelihood, Oxford University Press
4. Albert J (2007) Bayesian Computation with R, Springer
Risk Assessment Statement
There are no out of the ordinary risks associated with this unit, as all classes will be held in ordinary lecture theatres. Emergency exits and assembly areas will be pointed out in the first few lectures. You are referred to the University policy on health and safety.
http://www.mopp.qut.edu.au/A/A_09_01.jsp
Unit Outline: Semester 1 2024, Online
| Unit code: | MXB341 |
|---|---|
| Credit points: | 12 |
| Pre-requisite: | MXB241 or MAB314 |
| Equivalent: | MAB524 |
Overview
This is an advanced unit in mathematical statistics covering the theory of point estimation and inference using both classical and Bayesian methods. Statistical inference is the practice of both estimating probability distribution parameters and using statistical testing to validate these results, and plays a crucial role in research, and many real-world applications. You will use the methods of least squares, moments, and maximum likelihood to construct estimators of probability distribution parameters and evaluate them according to criteria including completeness, sufficiency, and efficiency. Results will be computed both analytically and numerically using software such as R. You will learn and apply the Neyman-Pearson Lemma for the construction of statistical tests, including to real-world applications, and learn Bayesian statistics for finding posterior distributions of parameters and evaluating their performance. Results will be communicated both orally and in written form.
Learning Outcomes
On successful completion of this unit you will be able to:
- Carry out statistical analyses using theoretical, technical and computational skills.
- Use statistical inference and data analysis concepts and skills as part of a problem solving approach to real life problems.
- Apply advanced statistical skills and competencies in a variety of professional circumstances.
Content
Construction of likelihood function, Maximum likelihood estimation and properties of maximum likelihood estimates one, two and many parameter models, Likelihood based confidence intervals, and hypothesis testing using likelihood one and two sample problems. Principles of Bayesian inference- construction of full probability model and derivation of posterior distribution, marginal and conditional posterior distributions. Bayesian inference for binomial data, Poisson count data and normal data. One and two sample problems Simulation techniques for sampling from posterior distributions: independent sampling, importance sampling and Gibbs sampling (dependent sampling using a Markov chain). Graphical models.
Learning Approaches
This unit involves 2 hours of lectures each week (which may be delivered online) where theory and concepts will be presented and discussed, and where you will be exposed to the processes required to solve problems using the methods of this unit. There will also be 2 hours of practical class each week, conducted online, where you will be guided through practical exercises including theoretical and computer-based activities.
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. The standards of the discipline as well as appropriate approaches to the communication of mathematical and statistical information will be conveyed via the examples presented in lectures and workshops.
You are able to partake in any lecture/workshop session times allocated, but also in your own private study time. That is, you are expected to consolidate the material presented during class by working a wide variety of exercises, problems and online learning activities in your own time.
Feedback on Learning and Assessment
Formative feedback will be provided for the in-semester assessment items by way of written comments on the assessment items, student perusal of the marked assessment piece and informal interview as required.
Summative feedback will be provided throughout the semester with progressive posting of results via Canvas.
Assessment
Overview
The assessment items in this unit are designed to determine your level of competency in meeting the unit outcomes while providing you with a range of tasks with varying levels of skill development and difficulty.
Unit Grading Scheme
7- point scale
Assessment Tasks
Assessment: Problem Solving Task
The problem solving task is a continuous assessment item that will consist of exercises based on class and laboratory work, delivered with timing appropriate to the progress of the class. There will be three sets of exercises.
This assignment is eligible for the 48-hour late submission period and assignment extensions.
Assessment: Examination (invigilated)
This assessment is based on the work covered during the semester.
The examination will require attendance at a local testing centre. For students enrolled as internal or on-campus, the local testing centre will be on QUT campus. For students enrolled as online, QUT Examinations will provide local testing centre information.
Academic Integrity
Students are expected to engage in learning and assessment at QUT with honesty, transparency and fairness. Maintaining academic integrity means upholding these principles and demonstrating valuable professional capabilities based on ethical foundations.
Failure to maintain academic integrity can take many forms. It includes cheating in examinations, plagiarism, self-plagiarism, collusion, and submitting an assessment item completed by another person (e.g. contract cheating). It can also include providing your assessment to another entity, such as to a person or website.
You are encouraged to make use of QUT’s learning support services, resources and tools to assure the academic integrity of your assessment. This includes the use of text matching software that may be available to assist with self-assessing your academic integrity as part of the assessment submission process.
Further details of QUT’s approach to academic integrity are outlined in the Academic integrity policy and the Student Code of Conduct. Breaching QUT’s Academic integrity policy is regarded as student misconduct and can lead to the imposition of penalties ranging from a grade reduction to exclusion from QUT.
Resources
There are no set texts for this unit.
There are many reference texts for this unit, many of which can be located in the library. There are also many online resources such as lecture notes and some e-books that can be found online. Most books on mathematical statistics and statistical inference are useful as reference material. Some examples are:
1. Berry DA (1996). Statistics: A Bayesian perspective, Wadsworth
2. Lee PM (2004) Bayesian Statistics: An introduction, 3rd edition, Arnold
3. Pawitan Y (2001) In all likelihood: Statistical Modelling and Inference Using Likelihood, Oxford University Press
4. Albert J (2007) Bayesian Computation with R, Springer
Risk Assessment Statement
There are no out of the ordinary risks associated with this unit, as all classes will be held in ordinary lecture theatres. Emergency exits and assembly areas will be pointed out in the first few lectures. You are referred to the University policy on health and safety.
http://www.mopp.qut.edu.au/A/A_09_01.jsp