Module description
Syllabus:
Estimation: unbiasedness, consistency, Cramér–Rao bound. Fisher information. Sufficiency. Robustness.
Methods of estimation: maximum likelihood estimators, asymptotic properties. Confidence intervals. Method of least squares. Generalised method of moments. Prior and posterior distributions. Bayesian estimators and Bayesian intervals.
Hypothesis testing: Likelihood ratio. Neyman-Pearson lemma. Power function. Two-sided tests. Composite hypothesis. Bayesian testing.
Prerequisites:
Before taking this module you must take 5CCM241A (or 6CCM241B) Probability and Statistics II
Assessment details
Written examination.
Educational aims & objectives
This module develops the principles of estimation and hypothesis testing at a general level. Frequentist and Bayesian methods are explored, with an emphasis on likelihood-based methods.
Learning outcomes
On successful completion of this modules students will
- be able to calculate the Cramer-Rao lower bound for general estimation problems
- understand the concepts of consistency, sufficiency and robustness
- be able to find maximum likelihood estimators and confidence intervals for parameters of general distributions
- develop and apply various types of hypothesis test for general situations
- use Bayesian methods in simple cases and interpret the results
Teaching pattern
Three hours of lectures and one hour of tutorial per week throughout the term
Suggested reading list
Indicative reading list - link to Leganto system where you can search with module code for lists