MTH4089 · Computational statistical inference

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 of computational statistical inference and introduce advanced computational methods used in this emerging field. 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.

Areas of study: Master of Mathematics

Offerings

Assessment

The Handbook lists an examination for this unit.

Assessment details may change. Please refer to the assessment information in Moodle closer to the start of the teaching period.

Requisites

The Handbook lists no prerequisite, corequisite or prohibition for this unit.

Learning outcomes

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.

Workload

• Two 1.5 -hour seminars; • One 1-hour applied class (in weeks 2-12) and • 8 hours of independent study per week.

Student experience, not official rules. Nothing here changes what the Handbook says.