University of Galway

Course Module Information

Course Modules

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
  1. Derive a likelihood function for random samples from a probability model and under more complex sampling schemes, eg mixed populations, censoring;
  2. Calculate simple unbiased estimators and calculate optimal combinations of estimators;
  3. Find maximum likelihood estimators by solving the score equation and obtain an estimate of precision based on observed and expected information;
  4. Find confidence intervals for simple problems using pivotal quantities;
  5. Calculate the size and power function for a given test procedure;
  6. 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;
  7. Use the likelihood ratio procedure to derive a test of nested hypotheses for some simple statistical models.
  8. Explain the fundamental concepts of Bayesian statistics and use these concepts to calculate Bayesian estimators.
Assessments
  • Written Assessment (75%)
  • Continuous Assessment (25%)
Teachers
Reading List
  1. "mathematical statistics with applications" by John E. Freund
    ISBN: ISBN013142706.
  2. "Statistical Inference" by Casella & Berger, Duxbury.
  3. "Introduction to the Theory of Statistics" by Mood, Graybill & Boes
    Publisher: McGraw Hill
  4. "Probability and statistical inference" by Robert V. Hogg Elliot A Tanis
    Publisher: MacMillan
The above information outlines module ST2004: "Statistical Inference" and is valid from 2019 onwards.
Note: Module offerings and details may be subject to change.