Statistical Inference: Theory and Practice - 2023 entry

Statistical models help us to describe and predict the real world, and are used in sectors as diverse as finance, insurance, economics, marketing, pharmaceuticals, sport, environment and government to name only a few. Statistical inference is the way that we use data and other information to learn about and apply our models. This module introduces you to some of the main approaches to statistical inference and explains their associated procedures. It is designed for students who want to understand the ideas and mathematical theory that lie behind many modern statistical methods. The module establishes key theoretical concepts and results alongside explanations of their practical purpose and application. We will use computer simulations to illustrate basic concepts and as a tool for comparing procedures. You will gain practical experience with the methods through a series of worked examples and exercises.

Prerequisite module: MTH2006 Statistical Modelling and Inference or equivalent

This module aims to help you to develop a thorough understanding of statistical inference from a frequentist perspective. This includes understanding the underlying concepts, the mathematical theory, and how to apply the inferential methods to a range of statistical models. Such understanding is important for any job that involves conducting statistical investigations.

On successful completion of this module, you should be able to:

Module Specific Skills and Knowledge:

1 demonstrate an understanding of the purpose of statistical inference, different approaches to statistical inference, and the key theoretical results and inferential procedures associated with these approaches;

2 apply these procedures to draw inferences about parametric statistical models, and compare different procedures critically.

Discipline Specific Skills and Knowledge:

3 demonstrate an understanding of the ways in which statistical inferential procedures and their performances may differ;

4 demonstrate an understanding of inferential concepts integral to statistical science;

5 progress to study a wider range of statistical inferential approaches in more detail.

Personal and Key Transferable/ Employment Skills and  Knowledge:

6 demonstrate an understanding of key mathematical arguments, statistical concepts and practical issues important for advanced study, application and development of statistical science;

7 use the statistical programming environment 'R' to implement generic inferential procedures and to conduct simulation studies.

1. Classical Inference:

- The principles and methods of classical frequentist inference are explained. These include point estimators, bias and efficiency; hypothesis tests, the Neyman-Pearson Theorem and uniformly most powerful tests; confidence sets and their construction from hypothesis tests; prediction intervals and their construction from ancillary statistics.

2. Likelihood Inference:

- Inferential approaches based on the likelihood are introduced. These include maximum likelihood estimators and their asymptotic properties; likelihood-based hypothesis tests and confidence sets; and pseudo-likelihoods.

3. Computational Inference:

- Inferential approaches based on resampling are introduced. These include Monte Carlo and bootstrap tests; the jackknife and bootstrap estimates of bias and variance; bootstrap confidence sets; and bootstrap prediction intervals.

*Please refer to reassessment notes for details on deferral vs. Referral reassessment

Deferrals: Reassessment will be by coursework and/or written exam in the deferred element only. For deferred candidates, the module mark will be uncapped.  

Referrals: Reassessment will be by a single written exam worth 100% of the module only. As it is a referral, the mark will be capped at 40%.  

ELE – http://vle.exeter.ac.uk

Reading list for this module: