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ST219: Mathematical Statistics Part B

Lecturer(s): Dr Anastasia Papavasiliou

Important: This module is for students from the Statistics department only. Students from other departments should take ST220 Introduction to Mathematical Statistics.

Prerequisite(s): ST218 Mathematical Statistics Part A

Commitment: 3 lectures/week, 1 tutorial/fortnight. This module runs in Term 2.

Aims: To introduce the major ideas of statistical inference with an emphasis on likelihood methods of estimation and testing.

Content:

  1. The notion of a parametrized statistical model for data.
  2. The definition of likelihood and examples of using it compare possible parameter values.
  3. Parameter estimates and in particular maximum likelihood estimates. Examples including estimated means and variances for Gaussian variables.
  4. The repeated sampling principle: the notion of estimator and its sampling distribution. Bias and MSE. Examples of calculating sampling distributions. Fisher's theorem on Gaussian sampling.
  5. Construction of confidence intervals.
  6. Notion of a hypothesis test. Likelihood ratio tests. Neyman-Pearson Lemma. P-value. Examples including classic t-test, F-test.
  7. Principle of data reduction: sufficient statistics, and applications to point estimation and hypothesis testing.
  8. Linear models. Estimators and associated tests.
  9. Asymptotic normality of MLEs. Examples.
  10. Chi-squared goodness of fit test. Contingency tables.

Books:

  • Suhov and Kelbert: Probability and Statistics by Example: Basic Probability and Statistics
  • Casella and Berger: Statistical Inference.

Assessment: 90% by 2 hour examination, 10% by coursework.

Deadlines: Assignment 1: week 3, Assignment 2: week 5 Assignment 3: week 7 and Assignment 4: week 9.

Feedback: You will hand in answers to selected questions on the fortnightly exercise sheets. Your work will be marked and returned to you in the tutorial taking place the following week when you will have the opportunity to discuss it.

Resources for Current Students
(restricted access)