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for a past academic year. Please see the current academic year for up to date information.
| Unit name |
Statistical Methods 2 |
| Unit code |
MATHM0038 |
| Credit points |
20 |
| Level of study |
M/7
|
| Teaching block(s) |
Teaching Block 2 (weeks 13 - 24)
|
| Unit director |
Dr. Gerber |
| Open unit status |
Not open |
| Pre-requisites |
Statistical Methods 1 and Statistical Computing 1
|
| Co-requisites |
None
|
| School/department |
School of Mathematics |
| Faculty |
Faculty of Science |
Description including Unit Aims
This unit complements Statistical Modelling 1 (prerequisite) with additional material on new topics, such as generative statistical models (discriminative models were the focus of Statistical Modelling 1), and with more detailed coverage of core statistical techniques: penalization methods and sparsity, approximate and fully-Bayesian inference, and additive modelling.
Intended Learning Outcomes
By the end of the unit students should be able to:
- Distinguish between discriminative and generative statistical models, and apply generative modelling approaches to tasks including classification, clustering, dimensional reduction and data compression, and missing data imputation.
- Describe penalized likelihood approaches to model-fitting and prediction, and implement them for inference and prediction using state-of-the-art packages in R.
- Perform numerical optimizations using standard algorithms, and be able to write bespoke optimizers for functions with particular properties.
- Explain the motivation and challenges of a ‘fully Bayesian’ approach to statistical inference and prediction, and the way in which Markov Chain Monte Carlo techniques can be used to implement a Bayesian approach.
- Formulate a Bayesian hierarchical model, implement it in specialized software, and be able to perform convergence assessment and code validation.
- Describe and implement additive modelling approaches, including strategies for specifying control parameters, and approximation methods for very large datasets.
Teaching Information
The unit will be taught through a combination of
- synchronous online and, if subsequently possible, face-to-face lectures
- asynchronous online materials, including narrated presentations and worked examples
- guided asynchronous independent activities such as problem sheets and/or other exercises
- synchronous weekly group problem/example classes, workshops and/or tutorials
- synchronous weekly group tutorials
- synchronous weekly office hours
Assessment Information
Formative: a homework each week
Summative:
- A personal portfolio of notes, code snippets, and vignettes, 30%.
- Assessed coursework, 2 at 20% each.
- A group project, 30%.
Reading and References
T. Hastie, R. Tibshirani, and J. Friedman (2017), The Elements of Statistical Learning, 2nd edition, Springer
