APTS module: Statistical Inference
Module leader: D Firth
Previous module leaders: D R Cox and D Firth (2007–8, 2008–9)
Please see the full Module Specifications 
document for background information relating to all of the APTS modules, including how to interpret the information below.
Aims: This module will provide students with a solid understanding of the main approaches to statistical inference, their strengths and limitations, their similarities and differences, and their role in underpinning statistical methodology.
Learning outcomes: After taking this module students should have an appreciation of the predominant modes of inference and their inter-relationships, and should be better equipped to read the published literature on both technical and foundational aspects of inference.
Prerequisites: Students should review the following definitions and results: likelihood, sufficiency, Bayes' theorem; simple properties of normal, exponential, binomial and Poisson distributions; linear model and the method of least squares.
Topics:
- Role of formal inference, nature of probability, frequentist and Bayesian approaches.
- Role of sufficiency; role of Neyman-Pearson theory; relation between significance tests and confidence limits.
- Maximum likelihood and associated issues; properties in 'standard' situations, and in some more difficult cases.
- Exponential-family models.
- Other approaches (e.g., estimating equations, pseudo-likelihoods).
Assessment — one of:
- An essay on one of a list of topics suggested by the module leader.
- Report of a numerical investigation on one of a list of topics suggested by the module leader, e.g., comparing Bayesian and frequentist approaches to the analysis of a particular model, or assessing the accuracy of inferences based on large-sample approximation.
