Module Content

Methods of Estimation: Method of Moments, Method of Maximum Likelihood, Bayes Estimation. 

Estimation: Efficient and Sufficient Statistics, Unbiased Estimators, Exponential Families of Distributions, Cramer-Rao lower bound, Minimum Variance Unbiased Estimators, Rao-Blackwell Theorem. 

Confidence Intervals: Confidence interval for the mean of a normal distribution, Confidence interval for the difference of means of two normal distributions, Confidence interval for the variance of a normal distribution, Confidence interval for the ratio of variances of two normal distributions. 

Testing of Hypothesis: Tests for the mean and the variance of a normal distribution, Tests for proportions, Neyman-Pearson Lemma, Likelihood ratio tests, Link between confidence interval and hypothesis testing. 

One and two sample statistical inference using R. 

Teaching Methods

The module will be delivered on campus, with weekly lecture and tutorial sessions. 

Printed notes will be provided in advance for each section of the course to support and enhance students’ preparation and engagement during class sessions. Lectures will follow the notes, with discussions of the main theoretical topics, and study of examples of the applications of the theory. There will be a strong emphasis on student involvement in discussions in lectures, to encourage a more active approach to learning the material, and to allow the delivery to be tailored to build on the students’ current understanding. 

Regular formative work in tutorial sessions will allow students to internalise the mathematical ideas and methods developed in the lectures, and lead to the development of problem-solving skills. This formative work will also feed back into the delivery of lectures and tutorials. 

Assessment Methods

The module is assessed through a portfolio of exercises and an examination.