Unit information: Statistics 2 in 2020/21

Unit name	Statistics 2
Unit code	MATH20800
Credit points	20
Level of study	I/5
Teaching block(s)	Teaching Block 1 (weeks 1 - 12)
Unit director	Professor. Anthony Lee
Open unit status	Not open
Pre-requisites	MATH10013 Probability and Statistics
Co-requisites	None
School/department	School of Mathematics
Faculty	Faculty of Science

Description including Unit Aims

Lecturers: Anthony Lee and Skevi Michael

Unit Aims

To develop the theory and practice of basic statistical inference, and statistical calculation.

Unit Description

Statistics is about inference under uncertainty, ie in situations where deductive logic cannot give a clearcut answer. In these situations our decisions must be assessed in terms of their probabilities of being correct or incorrect. Such decisions include estimating the parameters of a statistical model, making predictions, and testing hypotheses. It is often possible to identify 'optimal' or at least good decisions, and Statistics is about these decisions, and knowing where they apply. A thorough grounding in Statistics, as provided by this course, is crucial not only for anyone contemplating a career in finance or industry, but also for scientists and policymakers, as we realise that some of the biggest issues, like climate change, natural hazards, or health, are also some of the most uncertain.

Relation to Other Units

This unit develops the Level 4 Probability and Statistics material, and is a prerequisite for some statistics units at Levels 6 and 7, namely Bayesian Modelling, Linear and Generalised Linear Models, and Theory of Inference.

Intended Learning Outcomes

Learning Objectives

By the end of the course the students should be able to:

• Design powerful tests for statistical hypotheses, and understand both the power and the limitations of such tests.
• Derive estimators of statistical parameters using Maximum Likelihood (ML), including assessment of their properties and measures of uncertainty.
• Apply the Bayesian approach to estimation, prediction, and hypothesis testing, in the special case of conjugate analysis.
• Use asymptotic arguments to understand the convergence of ML and Bayesian methods for large samples.
• Choose appropriate statistical models for many common situations, and validate them.
• Use the statistical computing environment R for routine statistical calculations, and plotting.

Transferable Skills

A clearer understanding of the logical constraints on inference; facility with the R environment for statistical computing.

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, computing exercises and/or other exercises
• synchronous weekly group problem/example classes, workshops and/or tutorials
• synchronous weekly group tutorials
• synchronous weekly office hours

Assessment Information

80% Timed, open-book examination 20% Coursework

Raw scores on the examinations will be determined according to the marking scheme written on the examination paper. The marking scheme, indicating the maximum score per question, is a guide to the relative weighting of the questions. Raw scores are moderated as described in the Undergraduate Handbook.

If you fail this unit and are required to resit, reassessment is by a written examination in the August/September Resit and Supplementary exam period.

Reading and References

Recommended

• Morris DeGroot and Mark J. Schervish, Probability and Statistics, 3rd Ed,. Addison Wesley, 2002
• John A. Rice, Mathematical Statistics and Data Analysis, 2nd Ed., Duxbery Press, 2007