Overview

Computational statistical inference merges statistics with computational mathematics stochastic computation, computational linear algebra, and optimization to fully exploit the power of ever-increasing data sets, sophisticated mathematical models, and cutting-edge computer architectures. Driven by applied problems in finance, biology, geophysics, and data analytics, this unit aims to provide an integrated view … For more content click the Read More button below. This unit covers both practical algorithms and theoretical foundations of statistical inference, with cases studies on a selection of application problems. The main topics are parameter estimation and Bayesian inference, missing data problems and expectation maximisation, advanced Monte Carlo methods including importance sampling and Markov chain Monte Carlo, approximate Bayesian computation, linear and nonlinear filtering methods, classification, Gaussian processes, and kernel methods.

Offerings

S1-01-CLAYTON-ON-CAMPUS
S1-FF-CLAYTON-FLEXIBLE

Rules

Enrolment Rule

Contacts

Chief Examiner(s)

Associate Professor Jonathan Keith

Unit Coordinator(s)

Associate Professor Jonathan Keith

Learning outcomes

On successful completion of this unit, you should be able to:
1.

Apply sophisticated computational statistical inference in a wide range of application problems that require the integration of mathematical modelling with observed data to provide credible interpretation of the underlying system.

2.

Explain the roles of likelihood models, missing data, and Bayesian inference and formalise parameter estimation problems in complex applications using these concepts.

3.

Develop and apply advanced expectation maximization methods to missing data problems.

4.

Use the principle of Bayesian inference and apply expert computational methods to estimate parameters of statistical models and mathematical models.

5.

Implement advanced computational methods used in statistical inference, including importance sampling, filtering, and Markov chain Monte Carlo, and understand the asymptotic behaviour of these methods.

6.

Apply machine learning tools such as classification, Gaussian processes, and kernel methods to analyse and interpret complicate data sets and understand the computational aspects of these tools.

Assessment summary

Examination (3 hours and 10 minutes): 60% (Hurdle)

Continuous assessment: 40%

Hurdle requirement: If you would otherwise have passed the unit but who do not achieve at least 45% of the marks available for the end-of-semester examination will receive a Hurdle Fail (NH) grade and a mark of 45 on your transcript.

This unit is offered at both Level 4 and Level 5, differentiated by the level of the assessment. If you are enrolled in MTH5089 you will be expected to demonstrate a higher level of learning in this subject than those enrolled in MTH4089. The assignments and exam in this unit will use some common items from the MTH4089 assessment tasks, in combination with several higher level questions and tasks.

Workload requirements

Workload

Other unit costs

Costs are indicative and subject to change.
Miscellaneous items required (Printing, Stationery)- $100.

Availability in areas of study

Enrolment in the Master of Mathematics