Unit information: Statistical Methods 2 in 2021/22

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:

1. A personal portfolio of notes, code snippets, and vignettes, 30%.
2. Assessed coursework, 2 at 20% each.
3. A group project, 30%.

Resources

If this unit has a Resource List, you will normally find a link to it in the Blackboard area for the unit. Sometimes there will be a separate link for each weekly topic.

If you are unable to access a list through Blackboard, you can also find it via the Resource Lists homepage. Search for the list by the unit name or code (e.g. MATHM0038).

How much time the unit requires
Each credit equates to 10 hours of total student input. For example a 20 credit unit will take you 200 hours of study to complete. Your total learning time is made up of contact time, directed learning tasks, independent learning and assessment activity.

See the Faculty workload statement relating to this unit for more information.

Assessment
The Board of Examiners will consider all cases where students have failed or not completed the assessments required for credit. The Board considers each student's outcomes across all the units which contribute to each year's programme of study. If you have self-certificated your absence from an assessment, you will normally be required to complete it the next time it runs (this is usually in the next assessment period).
The Board of Examiners will take into account any extenuating circumstances and operates within the Regulations and Code of Practice for Taught Programmes.