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Description
This module aims to provide a grounding in the theoretical foundations of statistical inference and, in particular, to introduce the theory underlying statistical estimation and hypothesis testing. It is primarily intended for third and fourth year undergraduates and taught postgraduates registered on the degree programmes offered by the Department of Statistical Science (including the CSML and MASS programmes).听For these students, the academic prerequisites for this module are met either through earlier compulsory study within (UG) or successful admission to (PGT) their current programme.听It also serves as an optional module for students taking the Mathematics and Statistics stream of the Natural Sciences degree (with prerequisite: STAT0005).
Intended Learning Outcomes
- be able to describe the principal features of, and differences between, frequentist, likelihood and Bayesian inference;
- be able to define and derive a likelihood function based on a parametric model and use it to perform statistical inference using and frequentist and Bayesian approaches;
- be able to use frequentist criteria to evaluate and compare estimators;
- be able to perform hypothesis testing and interval estimation using frequentist and Bayesian approaches;
- be better able to meet the above learning outcomes when presented with a novel and challenging unseen problem (Level 7 only).
Applications - The theory of statistical inference underpins statistical design, estimation and hypothesis testing. As such, it has fundamental applications to all fields in which statistical investigations are planned or data are analysed. Important areas include engineering, physical sciences and industry, medicine and biology, economics and finance, psychology and the social sciences.
Indicative Content - Frequentist and Bayesian approaches to statistical inference. Summary statistics, sampling distributions. Sufficiency, likelihood, observed and expected Fisher information. Minimum variance unbiased estimators. Maximum likelihood estimation. Asymptotic properties of maximum likelihood estimators. Bayesian inference, including cases with a non-conjugate prior. Interval estimation. Hypothesis testing. Likelihood ratio tests.
Key Texts - Available from .
Module deliveries for 2024/25 academic year
Last updated
This module description was last updated on 8th April 2024.
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