General Information
This is an intermediate level subject in the theory and practice of statistical inference. It extends STAT11-112 in the areas of probability and distribution theory, discrete and continuous random variables and joint distributional behaviour, as well as introducing principles of likelihood theory, estimation, confidence intervals and hypothesis tests. In addition, topics such as moment and cumulant generating functions are introduced, as well as an introduction to random sums and Central Limit Theorem based large-sample distributional approximations.
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Details
Academic unit: Bond Business School Subject code: ACSC71-200 Subject title: Mathematical Statistics Subject level: Postgraduate Semester/Year: May 2021 Credit points: 10.000 -
Delivery & attendance
Timetable: https://bond.edu.au/timetable Delivery mode: Standard Workload items: - Lecture: x12 (Total hours: 24) - Lecture
- Workshop: x12 (Total hours: 24) - Workshop
- Personal Study Hours: x12 (Total hours: 72) - Study time and reviewing materials
Attendance and learning activities: Attendance at all class sessions is expected. Students are expected to notify the instructor of any absences with as much advance notice as possible. -
Resources
Prescribed resources: Books
- Dennis Wackerly, William Mendenhall, and Richard Scheaer. (2007). Mathematical statistics with applications.. 7th, Cengage Learning
- Mendenhall, W., Beaver, R. J. and Beaver, B. M Introduction to Probability and Statistics. 14th, Cengage
iLearn@Bond & Email: iLearn@Bond is the online learning environment at Bond University and is used to provide access to subject materials, lecture recordings and detailed subject information regarding the subject curriculum, assessment and timing. Both iLearn and the Student Email facility are used to provide important subject notifications. Additionally, official correspondence from the University will be forwarded to students’ Bond email account and must be monitored by the student. To access these services, log on to the Student Portal from the Bond University website as www.bond.edu.au
| Academic unit: | Bond Business School |
|---|---|
| Subject code: | ACSC71-200 |
| Subject title: | Mathematical Statistics |
| Subject level: | Postgraduate |
| Semester/Year: | May 2021 |
| Credit points: | 10.000 |
| Timetable: | https://bond.edu.au/timetable |
|---|---|
| Delivery mode: | Standard |
| Workload items: |
|
| Attendance and learning activities: | Attendance at all class sessions is expected. Students are expected to notify the instructor of any absences with as much advance notice as possible. |
| Prescribed resources: | Books
|
|---|---|
| iLearn@Bond & Email: | iLearn@Bond is the online learning environment at Bond University and is used to provide access to subject materials, lecture recordings and detailed subject information regarding the subject curriculum, assessment and timing. Both iLearn and the Student Email facility are used to provide important subject notifications. Additionally, official correspondence from the University will be forwarded to students’ Bond email account and must be monitored by the student. To access these services, log on to the Student Portal from the Bond University website as www.bond.edu.au |
Enrolment requirements
| Requisites: |
Nil |
|---|---|
| Assumed knowledge: |
Assumed knowledge is the minimum level of knowledge of a subject area that students are assumed to have acquired through previous study. It is the responsibility of students to ensure they meet the assumed knowledge expectations of the subject. Students who do not possess this prior knowledge are strongly recommended against enrolling and do so at their own risk. No concessions will be made for students’ lack of prior knowledge. Possess demonstrable knowledge in elementary probability theory, statistics, elementary calculus and linear algebra to the level of a unit such as STAT11-112 Quantitative Methods. |
| Restrictions: |
Nil |
Assurance of learning
Assurance of Learning means that universities take responsibility for creating, monitoring and updating curriculum, teaching and assessment so that students graduate with the knowledge, skills and attributes they need for employability and/or further study.
At Bond University, we carefully develop subject and program outcomes to ensure that student learning in each subject contributes to the whole student experience. Students are encouraged to carefully read and consider subject and program outcomes as combined elements.
Program Learning Outcomes (PLOs)
Program Learning Outcomes provide a broad and measurable set of standards that incorporate a range of knowledge and skills that will be achieved on completion of the program. If you are undertaking this subject as part of a degree program, you should refer to the relevant degree program outcomes and graduate attributes as they relate to this subject.
Subject Learning Outcomes (SLOs)
On successful completion of this subject the learner will be able to:
- Explain the concepts of probability and calculate probabilities in a variety of scenarios.
- Define and derive probability generating functions, moment generating functions and cumulant generating functions and use them to evaluate moments and cumulants and recognise distributions.
- Define, apply and undertake calculations relating to basic discrete and continuous distributions.
- Explain and apply the concepts of multivariate random variables, and their joint probability distributions.
- Describe and apply the main methods of estimation and the main properties of estimators.
- Construct and interpret a variety of confidence intervals and test a variety of hypotheses.
Generative Artificial Intelligence in Assessment
The University acknowledges that Generative Artificial Intelligence (Gen-AI) tools are an important facet of contemporary life. Their use in assessment is considered in line with students’ development of the skills and knowledge which demonstrate learning outcomes and underpin study and career success. Instructions on the use of Gen-AI are given for each assessment task; it is your responsibility to adhere to these instructions.
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Assessment details
Type Task % Timing* Outcomes assessed Computer-Aided Examination (Open) Comprehensive Final Examination – Short answer and quantitative calculation problems utilising techniques introduced in the unit (emphasis on those presented after Mid-semester) 45% Final Examination Period 1,2,3,4,5,6 Computer-Aided Examination (Open) Mid-semester Examination – Short answer and quantitative calculation problems utilising techniques presented to date 25% Week 7 (Mid-Semester Examination Period) 1,2,3,4 Skills Assignment Assignment 1 – Short answer and quantitative calculation problems utilising techniques presented to date 15% Week 4 1,2,3,4 Skills Assignment Assignment 2 – Short answer and quantitative calculation problems utilising techniques presented after Mid-semester 15% Week 10 5,6 - * Assessment timing is indicative of the week that the assessment is due or begins (where conducted over multiple weeks), and is based on the standard University academic calendar
- C = Students must reach a level of competency to successfully complete this assessment.
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Assessment criteria
Assessment criteria
High Distinction 85-100 Outstanding or exemplary performance in the following areas: interpretative ability; intellectual initiative in response to questions; mastery of the skills required by the subject, general levels of knowledge and analytic ability or clear thinking. Distinction 75-84 Usually awarded to students whose performance goes well beyond the minimum requirements set for tasks required in assessment, and who perform well in most of the above areas. Credit 65-74 Usually awarded to students whose performance is considered to go beyond the minimum requirements for work set for assessment. Assessable work is typically characterised by a strong performance in some of the capacities listed above. Pass 50-64 Usually awarded to students whose performance meets the requirements set for work provided for assessment. Fail 0-49 Usually awarded to students whose performance is not considered to meet the minimum requirements set for particular tasks. The fail grade may be a result of insufficient preparation, of inattention to assignment guidelines or lack of academic ability. A frequent cause of failure is lack of attention to subject or assignment guidelines. Quality assurance
For the purposes of quality assurance, Bond University conducts an evaluation process to measure and document student assessment as evidence of the extent to which program and subject learning outcomes are achieved. Some examples of student work will be retained for potential research and quality auditing purposes only. Any student work used will be treated confidentially and no student grades will be affected.
| Type | Task | % | Timing* | Outcomes assessed |
|---|---|---|---|---|
| Computer-Aided Examination (Open) | Comprehensive Final Examination – Short answer and quantitative calculation problems utilising techniques introduced in the unit (emphasis on those presented after Mid-semester) | 45% | Final Examination Period | 1,2,3,4,5,6 |
| Computer-Aided Examination (Open) | Mid-semester Examination – Short answer and quantitative calculation problems utilising techniques presented to date | 25% | Week 7 (Mid-Semester Examination Period) | 1,2,3,4 |
| Skills Assignment | Assignment 1 – Short answer and quantitative calculation problems utilising techniques presented to date | 15% | Week 4 | 1,2,3,4 |
| Skills Assignment | Assignment 2 – Short answer and quantitative calculation problems utilising techniques presented after Mid-semester | 15% | Week 10 | 5,6 |
- * Assessment timing is indicative of the week that the assessment is due or begins (where conducted over multiple weeks), and is based on the standard University academic calendar
- C = Students must reach a level of competency to successfully complete this assessment.
Assessment criteria
| High Distinction | 85-100 | Outstanding or exemplary performance in the following areas: interpretative ability; intellectual initiative in response to questions; mastery of the skills required by the subject, general levels of knowledge and analytic ability or clear thinking. |
|---|---|---|
| Distinction | 75-84 | Usually awarded to students whose performance goes well beyond the minimum requirements set for tasks required in assessment, and who perform well in most of the above areas. |
| Credit | 65-74 | Usually awarded to students whose performance is considered to go beyond the minimum requirements for work set for assessment. Assessable work is typically characterised by a strong performance in some of the capacities listed above. |
| Pass | 50-64 | Usually awarded to students whose performance meets the requirements set for work provided for assessment. |
| Fail | 0-49 | Usually awarded to students whose performance is not considered to meet the minimum requirements set for particular tasks. The fail grade may be a result of insufficient preparation, of inattention to assignment guidelines or lack of academic ability. A frequent cause of failure is lack of attention to subject or assignment guidelines. |
Quality assurance
For the purposes of quality assurance, Bond University conducts an evaluation process to measure and document student assessment as evidence of the extent to which program and subject learning outcomes are achieved. Some examples of student work will be retained for potential research and quality auditing purposes only. Any student work used will be treated confidentially and no student grades will be affected.
Study Information
Submission procedures
Students must check the iLearn@Bond subject site for detailed assessment information and submission procedures.
Policy on late submission and extensions
A late penalty will be applied to all overdue assessment tasks unless an extension is granted by the subject coordinator. The standard penalty will be 10% of marks awarded to that assessment per day late with no assessment to be accepted seven days after the due date. Where a student is granted an extension, the penalty of 10% per day late starts from the new due date.
Academic Integrity
University’s Academic Integrity Policy defines plagiarism as the act of misrepresenting as one’s own original work: another’s ideas, interpretations, words, or creative works; and/or one’s own previous ideas, interpretations, words, or creative work without acknowledging that it was used previously (i.e., self-plagiarism). The University considers the act of plagiarising to be a breach of the Student Conduct Code and, therefore, subject to the Discipline Regulations which provide for a range of penalties including the reduction of marks or grades, fines and suspension from the University.
Bond University utilises Originality Reporting software to inform academic integrity.Feedback on assessment
Feedback on assessment will be provided to students within two weeks of the assessment submission due date, as per the Assessment Policy.
Accessibility and Inclusion Support
If you have a disability, illness, injury or health condition that impacts your capacity to complete studies, exams or assessment tasks, it is important you let us know your special requirements, early in the semester. Students will need to make an application for support and submit it with recent, comprehensive documentation at an appointment with a Disability Officer. Students with a disability are encouraged to contact the Disability Office at the earliest possible time, to meet staff and learn about the services available to meet your specific needs. Please note that late notification or failure to disclose your disability can be to your disadvantage as the University cannot guarantee support under such circumstances.
Additional subject information
As part of the requirements for Business School quality accreditation, the Bond Business School employs an evaluation process to measure and document student assessment as evidence of the extent to which program and subject learning outcomes are achieved. Some examples of student work will be retained for potential research and quality auditing purposes only. Any student work used will be treated confidentially and no student grades will be affected.
Subject curriculum
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Introduction to mathematical statistics and exploratory data analysis
A review of descriptive statistics, including numerical and graphical summaries of location, spread and symmetry. Also includes the definition and structure of probability models.
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Probability theory
A review of basic probability rules, including conditional probability and Bayes theorem, joint events and independence. The importance and usage of the Law of Total Probability is introduced.
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Advanced probability and random variables
An introduction to random variables, including distributions, moments, percentiles and various generating functions.
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Discrete random variables
Introduces the properties and relationships of common discrete random variables, including binomial, Poisson, negative binomial and hypergeometric.
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Continuous random variables
An exploration of the properties and relationships of common continuous random variables, including normal, log-normal, Cauchy, Student’s t, uniform, exponential, gamma, Weibull, Pareto, beta, Fisher F and Burr. The change of variable method is introduced to facilitate calculations regarding the relationships between various distribution and density functions.
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Joint and conditional distributions
Introduces the structure, definition and properties of joint distributions, marginal distributions and conditional distributions.
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Functions of random variables
Basic distribution theory, including the use of convolutions, is introduced. Derivation of the density functions of the Student’s t-distribution, beta distribution and Fisher’s F-distribution are also covered. In addition, definition and discussion of the properties of random sums and compound distributions is presented.
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The Central Limit Theorem and extensions
Various distributional properties of multivariate normal random variables are presented and the Central Limit Theorem is introduced first via the normal approximation to the binomial distribution with continuity correction and then more generally using cumulant generating functions. In addition, Cochran’s Theorem is introduced.
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Likelihood and estimation
The concepts of point estimation, including the method of moments and maximum likelihood are explained. The likelihood function is introduced as are the concepts of mean-squared error and loss functions. In addition, the principles of sufficiency and optimality in constructing estimators are introduced and discussed, and lead to presentation of Bayesian and resampling-based frameworks for estimator construction and assessment.
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Interval estimation and confidence region construction
Definition and principles of construction of interval estimates are introduced and investigated. These include standard pivot-based intervals as well as both Bayesian highest posterior density regions and bootstrap-based non-parametric confidence intervals.
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Hypothesis testing
The structure and properties of hypothesis tests including definitions of size, power, one-sided versus two-sided testing and optimal test structure are considered. These principles are applied to the case of maximum likelihood. In addition, the Pearson chi-squared goodness of fit test for a categorical response variable is introduced.