MTH4260 Statistics of stochastic processes
Faculty of Science
MTH4260 Statistics of stochastic processes is a level 4, 6-credit-point, undergraduate and postgraduate unit from the Faculty of Science, offered in 2027 in Semester 2 at Clayton. It has no prerequisites and unlocks 3 units.
- Credit points
- 6
- Offered in 2027
- Semester 2
- Clayton
- Assessment
- Exam 50%
- and 1 other task
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Requisites
Before MTH4260
No prerequisites or corequisites besides the enrolment rules below.
After MTH4260
3 units list MTH4260 as a prerequisite or corequisite.
Enrolment rules
Prohibition:MTH3260
You must be enrolled in the Graduate Certificate in Mathematics or the Master of Mathematics
Overview
Many practical experiments involve repeated measurements made over a period of time, where the individuals or systems being observed are evolving during the study period. Examples of this kind of data arise in signal processing, financial modelling and mathematical biology. For experiments of this kind, standard statistical methods that assume data points are independent and identically distributed (iid) are of limited value, due to dependencies among measurements. This unit will introduce statistical methods for such processes.
Topics: Review of fundamental statistics: their distributions, properties and limitations; Stochastic processes: Markov, ARMA, Stationary and diffusion processes; Likelihood models, Graphical models, Bayesian models; Decision theory, Likelihood ratio tests, Bayesian model comparison; Sufficient statistics, Maximum likelihood estimation, Bayesian estimation; Exponential families; Convergence of random variables and measures; Properties of estimators: bias, consistency, efficiency; Laws of large numbers and ergodic theorems, Central limit theorems; Statistics for stationary processes; Statistics for ARMA processes; Statistics for diffusion processes
Offerings in 2027
| Teaching period | Campus | Mode |
|---|---|---|
| Second semester | Clayton | On campus |
Assessment
- Continuous assessmentDemonstration50%
- Final assessment - Exam (3 hours and 10 minutes)Examination50%
Assessment details may change. Please refer to the assessment information in Moodle closer to the start of the teaching period.
Learning outcomes
When you finish this unit, you should be able to:
- 1
Apply likelihood-based methods to construct, estimate, and compare models for stochastic processes, including maximum likelihood and Bayesian approaches;
- 2
Analyse and evaluate the properties of estimators, including bias, consistency, efficiency, and asymptotic behaviour, with applications to stationary, ARMA, and diffusion processes;
- 3
Interpret and apply statistical results from stochastic process models to real-world problems in areas such as signal processing, finance, and mathematical biology;
- 4
Communicate statistical reasoning and results effectively, both orally and in writing, and collaborate in small groups to solve problems in the statistics of stochastic processes;
- 5
Extend and deepen understanding of statistical methods for stochastic processes through advanced model synthesis, rigorous analysis, and independent application to complex or novel datasets.
Workload and teaching
- Applied sessions22 hours
- Seminars36 hours
- Teaching approachActive learning
Three 1-hour seminars
One 2-hour applied class (in weeks 2-12) and
7 hours of independent study per week
Contacts
- Unit Coordinators
- Associate Professor Jonathan Keith
- Chief Examiners
- Associate Professor Jonathan Keith
Common questions
What are the prerequisites for MTH4260?
MTH4260 has no prerequisites, but enrolment rules apply.
What can I take after MTH4260?
MTH4260 is a prerequisite or corequisite for 3 units, including MTH5210, MTH5510 and MTH5520.
When is MTH4260 offered?
In 2027, MTH4260 runs in Semester 2 at Clayton.
Does MTH4260 have an exam?
Yes. The exam is worth 50% of the final mark, alongside 1 other task.