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Course Module Information
Course Modules
ST2004: Statistical Inference
Semester 2 | Credits: 5
An introduction to the ideas of statistical inference from a mathematical perspective. Topics covered include: populations and samples, properties of estimators, likelihood functions, principles and methods of point estimation, interval estimates, hypothesis testing and construction of tests.
Learning Outcomes
- Derive a likelihood function for random samples from a probability model and under more complex sampling schemes, eg mixed populations, censoring;
- Calculate simple unbiased estimators and calculate optimal combinations of estimators;
- Find maximum likelihood estimators by solving the score equation and obtain an estimate of precision based on observed and expected information;
- Find confidence intervals for simple problems using pivotal quantities;
- Calculate the size and power function for a given test procedure;
- Obtain a most powerful test of two simple hypotheses using the Neyman Pearson lemma and extend this to a uniformly most powerful test of one-sided alternatives;
- Use the likelihood ratio procedure to derive a test of nested hypotheses for some simple statistical models.
- Explain the fundamental concepts of Bayesian statistics and use these concepts to calculate Bayesian estimators.
Assessments
- Written Assessment (75%)
- Continuous Assessment (25%)
Teachers
- COLLETTE MCLOUGHLIN:
Research Profile |
Email
- JOHN NEWELL:
Research Profile |
Email
- HAIXUAN YANG:
Research Profile |
Email
Reading List
- "mathematical statistics with applications" by John E. Freund
ISBN: ISBN013142706. - "Statistical Inference" by Casella & Berger, Duxbury.
- "Introduction to the Theory of Statistics" by Mood, Graybill & Boes
Publisher: McGraw Hill - "Probability and statistical inference" by Robert V. Hogg Elliot A Tanis
Publisher: MacMillan
Note: Module offerings and details may be subject to change.