Methods of Mathematical Statistics (MAST90105)

Graduate courseworkPoints: 25On Campus (Parkville)

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Overview

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Semester 1
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This subject introduces probability and the theory underlying modern statistical inference. Properties of probability are reviewed, univariate and multivariate random variables are introduced, and their properties are developed. It demonstrates that many commonly used statistical procedures arise as applications of a common theory. Both classical and Bayesian statistical methods are developed. Basic statistical concepts including maximum likelihood, sufficiency, unbiased estimation, confidence intervals, hypothesis testing and significance levels are discussed. Computer packages are used for numerical and theoretical calculations.

Intended learning outcomes

  • Develop a systematic understanding of probability, random variables, probability distributions and probability models, and their relevance to statistical inference;
  • Be able to formulate standard probability models from real world applications and critically assess them;
  • Be able to apply the properties of probability distributions, moment generating functions, variable transformations and conditional expectations to analyse common random variables and probability models;
  • Be able to use a computer package to perform algebraic and computational tasks in probability analyses.
  • Be familiar with the basic ideas of estimation and hypothesis testing
  • Be able to carry out many standard statistical procedures using a statistical computing package.
  • Develop the ability to fit probability models to data by both estimating and testing hypotheses about model parameters.

Generic skills

In addition to learning specific skills that will assist students in their future careers in science, they should progressively acquire generic skills from this subject that will assist them in any future career path. These include

  • problem-solving skills: the ability to engage with unfamiliar problems and identify relevant solution strategies;
  • analytical skills: the ability to construct and express logical arguments and to work in abstract or general terms to increase the clarity and efficiency of analysis;
  • collaborative skills: the ability to work in a team;
  • time management skills: the ability to meet regular deadlines while balancing competing commitments.
  • computer skills: the ability to use statistical computing packages

Last updated: 4 March 2025