Monash University Handbook

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

Outcomes

On completion of this unit students will be able to:

Explain the central role of likelihood models in statistics
Construct likelihood models for stochastic processes using graphical models
Develop and apply likelihood ratio tests for model comparison and selection
Use the principle of maximum likelihood to estimate parameters of a model
Apply Bayesian alternatives for model comparison and estimation
Assess whether an estimator has desirable properties
Describe the asymptotic behaviour of time averages for stationary processes
Perform model selection and estimation tasks for stationary, ARMA and diffusion processes.

Assessment

NOTE: From 1 July 2019, the duration of all exams is changing to combine reading and writing time. The new exam duration for this unit is 3 hours and 10 minutes.

End of semester examination (3 hours): 60% (Hurdle)

Continuous assessment: 40% (Hurdle)

Hurdle requirement: To pass this unit a student must achieve at least 50% overall and at least 40% for both the end-of-semester examination and continuous assessment components.