Unit information: Statistics 2 in 2013/14

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. Andrieu
Open unit status	Not open
Pre-requisites	MATH 11340, MATH11002 and MATH11003
Co-requisites	None
School/department	School of Mathematics
Faculty	Faculty of Science

Description including Unit Aims

Statistical inference deals with the interpretation of sets of data that contain some random variation. It is an essential tool for anyone contemplating a career in finance, commerce or industry. However, there are often no clear-cut answers to the natural questions of interest, and two contrasting approaches have been developed - the frequentist and the Bayesian. It is important to understand what questions can be answered by each method and how the methods differ. This unit will develop the ideas introduced in the latter part of the first year unit, using practical examples to clarify the underlying theoretical results, and will provide a foundation for students taking later applied statistics units. It will cover the principles, the techniques and the optimality properties of the two approaches to Estimation, Hypothesis Testing and Confidence Intervals. The only essential prerequisite is the first year unit in Probability and Statistics.

Aims:

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

Unit homepage: http://www.maths.bris.ac.uk/~maxca/stats2/

Syllabus

• Principles of Frequentist inference
• Maximum likelihood estimation: general and asymptotic properties, Fisher information, optimality, point prediction
• Hypothesis tests and confidence sets
• New distributions: Beta, Weibull, Hypergeometric, Pareto, Multinomial
• Bayesian statistics: principles, Bayes's theorem, point prediction, conjugate analysis, asymptotic properties.
• Statistical computing in R: implementation of techniques from throughout the course.

Relation to Other Units

This unit develops the Level 1 Probability & Statistics material, and is a prerequisite for some statistics units at Levels 3 and M, namely Bayesian Modelling A, Generalised Linear Models, and Theory of Inference, and desirable for Linear Models.

Intended Learning Outcomes

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 enviroment 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

Three lectures a week, and one problems class. Weekly homework, and weekly/fortnightly office hours for statistics and for computing.

Assessment Information

The final assessment mark will be made up as follows:

• 20% from two practical assignments
• 80% from a 2½-hour examination in April (details below).

Practical Assignments

Three computer practicals are set (in roughly the fourth, seventh and tenth weeks), and the second and third count 10% each to the final assessed mark.

Deadlines: Practicals that are up to one day late will be docked 10% (ie one mark since each practical will be marked out of 10). Practicals more than one day late will score zero.

Examination

The examination in April consists of one 2 ½-hour paper consisting of FIVE questions; you should attempt FOUR. If you attempt more than four, your best four answers will be used for assessment. Candidates may bring one A4 double-sided sheet of notes into the exam. Calculators of the approved type (non-programmable, no text facility) are permitted in the examination. Statistical tables will be provided.

Reading and References

The main text is:

• Rice, J. A. 1995 Mathematical statistics and data analysis, Duxbery Press, 2nd Ed. This is now out in a 3rd edition, either one will be fine, but references will be to the second edition.

Also informative and useful:

• Morris H, DeGroot, and Mark J Schervish. 2002 Probability & Statistics, Addison Wesley, 3rd Ed.

Other reading will be given on the unit homepage (see Unit Aims).