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Description
This module aims to provide students with the tools to implement computational approaches to statistical modelling, inference and testing, including an understanding of what can and cannot be achieved with computational approaches, and an introduction to the mathematical ideas underpinning some of the key computational approaches of the previous century. 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 MASS programmes). The academic prerequisites for these students (in addition to their compulsory modules) are STAT0007, STAT0008 and STAT0023 (UG), or STAT0008 and STAT0030 (PGT).
Intended Learning Outcomes
- be able to implement computationally-intensive methods that are used in modern statistical modelling and inference, primarily using either R or python;
- understand various procedures for modelling, inference, model selection/comparison and testing, that are at the interface of modern statistics and machine learning;
- be familiar with proofs of correctness for simulation algorithms, asymptotics related to various re-sampling procedures, and some elements of Markov chains on general state spaces and their convergence to equilibrium;
- be able to describe at a deeper level the theoretical underpinnings of various simulation algorithms that are introduced throughout the course (Level 7 only);
- be able to critique different types of computational statistical methodology, both in terms of mathematical validity and computational suitability for a given task (Level 7 only).
Applications - A good grasp of computationally-intensive methods is an essential part of the toolkit of the modern statistician and machine learner, and this module will equip students with this toolkit in such a way that they are ready to use and build on these methods in their future work. In addition, the second half of the course covers algorithms that are also used extensively in statistical physics and computational chemistry.
Indicative Content - General learning principles: overview of computational approaches and computational complexity, simulation of random variables, resampling methods: permutation and Monte Carlo testing, the bootstrap, simulation-based uncertainty quantification and selected other computationally-intensive approaches. Introduction to Bayesian computation, Markov chain Monte Carlo, the Metropolis鈥擧astings algorithm, selected alternative approaches.
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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