Unit name | Statistical Methods 1 |
---|---|
Unit code | MATHM0041 |
Credit points | 20 |
Level of study | M/7 |
Teaching block(s) |
Teaching Block 1 (weeks 1 - 12) |
Unit director | Dr. Song Liu |
Open unit status | Not open |
Pre-requisites |
None |
Co-requisites |
None |
School/department | School of Mathematics |
Faculty | Faculty of Science |
This unit covers the topic of prediction, from the initial consultation with the client all the way through to delivering an effective prediction algorithm and quantifying its out-of-sample performance. Prediction is an important activity in its own right, but we also use it to illustrate many of the major topics in computational statistics. These include statistical optimality, the limitations of naive approaches such as nearest-neighbour and cross-validation, the Normal Linear Model for regression, the concepts of prior, posterior, and predictive distributions, regression modelling with basis expansions, extensions to data-dependent regressors, and the treatment of more complex parameters through optimization.
In its most sophisticated form, the extended Normal Linear Model provides a powerful and computationally tractable platform for regression and optimal prediction, but does not provide similar benefits for classification. The later part of the unit considers the challenges presented by classification, and the various approaches that are used to approximate the predictive distribution. These approaches, including numerical optimization of penalized likelihoods and approximate numerical integration, are core tools in computational statistics and machine learning.
By the end of the unit students should be able to:
Some lab based instruction
Formative: homework each week.
Summative:
T. Hastie, R. Tibshirani, and J. Friedman (2017), The Elements of Statistical Learning, 2nd edition, Springer.