# ST220 Introduction to Mathematical Statistics

###### Lecturer(s): Prof Wilfrid Kendall

**Prerequisite(s):** ST111/2 Probability A&B

**Commitment: **3 lectures/week, 5 hours tutorials (and 2 revision lectures in Term 3). This module runs in Term 1.

**Aims:
**This module is designed for students in the Maths Dept (and other non Statistics dept students). It serves as a prerequisite, replacing ST218/219 Mathematical Statistics A&B, for many of the 3rd year statistics modules.

It will introduce the main ideas of statistical inference emphasising the use of likelihood for estimation and testing. These ideas are fundamental to the use of statistics in modern applications such as mathematical finance, telecommunications, bioinformatics as well as more traditional areas such as insurance, engineering and the social sciences.

**Content:**

1. Standard families of Probability distributions: Binomial, Geometric, Poisson, Exponential, Gamma, Gaussian.

2. The weak law of large numbers and central limit theorem.

3. The Multivariate Gaussian distribution. Orthogonality and Independence for jointly Gaussian random variables.

Distributions derived from the Gaussian: Chi-squared, t and F.

4. The notion of a parametrized Statistical model, and examples.

5. Likelihood including maximum likelihood estimates and use of likelihood ratios to compare hypotheses.

6. The repeated sampling principle: bias and MSE, confidence intervals and p-values.

7. Fisher's theorem on Gaussian sampling, and its extension to linear regression.

**Books:**

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

**Assessment: **100% by examination in June.

**Deadlines for handing in assessments:**

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

* Examination Period:* Summer

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