MTH4260 - Statistics of stochastic processes

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

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 Jonathan Keith

Unit Coordinator(s)

Associate Professor Jonathan Keith

Notes

This Level 4 unit and its Level 3 counterpart MTH3260 share the same core content and learning activities such as seminars and applied classes. However, studies at Level 4 are distinguished from those at Level 3 by a deeper understanding of mathematical theories and their applications, higher levels of critical thinking, and greater autonomy in learning.

Learning outcomes

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

Critically evaluate and articulate the central role of likelihood models in statistics

Design and construct likelihood models for complex stochastic processes using graphical modelling techniques

Develop and apply likelihood ratio tests for model comparison and selection, demonstrating a deep understanding of statistical methodologies.

Utilise the principle of maximum likelihood to estimate parameters of complex models, showcasing proficiency in theoretical and practical applications.

Integrate and apply Bayesian alternatives for model comparison and estimation.

Assess and evaluate the desirable properties of estimators, employing advanced statistical criteria and techniques

Analyse and describe the asymptotic behaviour of time averages for stationary processes

Teaching approach

Active learning

Assessment

1 - Continuous assessment

2 - Final assessment - Exam (3 hours and 10 minutes)

Scheduled and non-scheduled teaching activities

Applied sessions

Seminars

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