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 … For more content click the Read More button below.
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
S2-01-CLAYTON-ON-CAMPUS
Rules
Enrolment Rule
Contacts
Chief Examiner(s)
Associate Professor Tianhai Tian
Unit Coordinator(s)
Associate Professor Tianhai Tian
Associate Professor Jonathan Keith
Learning outcomes
On successful completion of this unit, you should be able to:
1.
Explain the central role of likelihood models in statistics
2.
Construct likelihood models for stochastic processes using graphical models
3.
Develop and apply likelihood ratio tests for model comparison and selection
4.
Use the principle of maximum likelihood to estimate parameters of a model
5.
Apply Bayesian alternatives for model comparison and estimation
6.
Assess whether an estimator has desirable properties
7.
Describe the asymptotic behaviour of time averages for stationary processes
8.
Perform model selection and estimation tasks for stationary, ARMA and diffusion processes.
Teaching approach
Active learning
Assessment
1 - In-semester assessment
2 - Examination (3 hours and 10 minutes)
Scheduled and non-scheduled teaching activities
Applied sessions
Lectures
Workload requirements
Workload
Other unit costs
Costs are indicative and subject to change.
Miscellaneous items required (Unit course reader, Printing, Stationery) - $120.
Availability in areas of study
Applied mathematics
Financial and insurance mathematics
Mathematical statistics
Mathematics
Pure mathematics
Financial and insurance mathematics
Mathematical statistics
Mathematics
Pure mathematics