# Theory of Inference 3

## Unit aims

The basic premise of inference is our judgement that the things we would like to know are related to other things that we can measure. This premise holds over the whole of the sciences. The distinguishing features of statistical science are

1. A probabilistic approach to quantifying uncertainty, and, within that
2. A concern to assess the principles under which we make good inferences
3. The development of tools to facilitate the making of such inferences.

This course illustrates these features at a high level of generality, while also covering the special cases that often occur in practice. See the Syllabus below for more details.

## Relation to other units

This unit addresses some issues that are taken for granted in Statistics 1 (and Statistics 2, which, however, is not a prerequisite). The technical material has all been covered in the 1st year mathematics courses, although the applications are more advanced.

## Learning objectives

To gain an understanding of some key principles of statistical inference, and how these impact upon current practice across a range of fields.

## Transferable skills

This unit exemplifies the general skills of other mathematical units, of logical thinking and the concept of proof, problem solving, abstraction, a facility with notation, self-study and self-appraisal. Some examples and homeworks will use the statistical computing environment R.

There is no set book for the unit. The following textbooks will cover all of the basic material, with a careful treatment of the more subtle issues that often confound non-statisticians. These are listed in increasing order of sophistication:

1. David Freedman et al, Statistics, Norton, 4th edn (earlier editions also good), 2007
2. John Rice, Mathematical Statistics and Data Analysis, Duxbury Press, 2nd edn, 1995.
3. Morris DeGroot and Mark Schervish, Probability and Statistics, Addison Wesley, 3rd edn, 2002.

The authors of these books are top-flight statisticians: you should pay close attention to the words as well as the symbols!

In addition, the following books are highly recommended as being readable and occasionally shocking.

1. Stephen Senn, Dicing with death: Chance, risk, and health, CUP, 2003.
2. Gerd Gigerenzer, Reckoning with risk: Learning to live with uncertainty, Penguin, 2003.
3. Imogen Evans et al, Testing treatments: Better research for better healthcare, Pinter & Martin Ltd., 2nd edition, 2011.

If you would like to read more widely, then you might enjoy Ben Goldacre's bad science blog, or the Radio 4 programme More Or Less, hosted by Tim Harford.

Unit code: MATH35600
Level of study: H/6
Credit points: 20
Teaching block (weeks): 2 (13-24)
Lecturer: Professor Simon Wood

## Pre-requisites

MATH11300 Probability 1 and MATH11400 Statistics 1.

None

## Methods of teaching

Lectures, problems classes, homeworks to be done by students, Office Hours.

## Methods of Assessment

The pass mark for this unit is 40.

The final mark is calculated as follows:

• 80% Exam
• 20% Coursework

NOTE: Calculators are NOT allowed in the examinition.

For information resit arrangements, please see the re-sit page on the intranet.

Please use these links for further information on relative weighting and marking criteria.

Further exam information can be found on the Maths Intranet.