Introductory description

This module runs in Term 2 and is core for students with their home department in Statistics. It is not available to other students who should consider ST220: Introduction to Mathematical Statistics as an alternative.

Prerequisite(s): ST218 Mathematical Statistics Part A
Leads To: many ST3 and ST4 modules

Module web page

Module aims

Outline syllabus

This is an indicative module outline only to give an indication of the sort of topics that may be covered. Actual sessions held may differ.

The notion of a parametrized statistical model for data.
The definition of likelihood and examples of using it compare possible parameter values.
Parameter estimates and in particular maximum likelihood estimates. Examples including estimated means and variances for Gaussian variables.
The repeated sampling principle: the notion of estimator and its sampling distribution. Bias and MSE. Examples of calculating sampling distributions.
Construction of confidence intervals.
Notion of a hypothesis test. Likelihood ratio tests. Neyman-Pearson Lemma. P-value.
Principle of data reduction: sufficient statistics, and applications to point estimation and hypothesis testing.
Asymptotic normality of MLEs. Examples.

Learning outcomes

By the end of the module, students should be able to:

• Understand the main notions of statistical inference including a (parametrized) statistical model, an estimator and its sampling distribution, and hypothesis tests.
• Be able to calculate maximum likelihood estimators in a variety of examples.
• Be able to use likelihood ratios to construct hypothesis tests in a variety of examples including the classical t and F tests.
• Be able to derive properties of sampling distributions of estimators in a variety of examples.

Indicative reading list

The main reference books for the course are:

1. Statistical Inference, G. Casella and R. L. Berger.
2. Introduction to the theory of Statistical Inference, H. Liero and S. Zwanzig.

Other possible books that you can refer at:
3. Probability and statistics by example: 1: Basic probability and statistics, Y. M. Suhov, M. Kelbert (available online through Warwick Reading Lists)
4. Introductory Statistics, S.M. Ross.
5. Introduction to Probability and Statistics for Engineers and Scientists, S. M. Ross

Note that 1-3 are already available through "Talis Aspire link"

View reading list on Talis Aspire

Subject specific skills

Among others, ability to recognise sufficient/complete statistics, computing the Fisher information about a parameter of a given statistical model

Transferable skills

Among others, ability to derive methods for standard point estimation, hypothesis tests and confidence intervals in different setting that the statistical models considered in the module, e.g., for linear models or for stochastic processes.