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Theory of Inference (MATH 35600)

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Administrative Information

  1. Unit number and title: MATH 35600 Theory of Inference
  2. Level: H/6
  3. Credit point value: 10 credit points
  4. Year: 12/13
  5. First Given in this form: 2000-01
  6. Unit Organiser: Jonty Rougier
  7. Lecturer: Jonty Rougier
  8. Teaching block: 2
  9. Prerequisites: MATH11300 Probability 1 and MATH 11400 Statistics 1.

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, and
  3. The development of tools to facilitate the making of such inferences.

In a selective approach, this course considers aspects of evidence, of experimental design, and some of the basic principles of inference.  The intention is always to illuminate current practice, eg as found in the courtroom, in medical trials, or more widely in designed (and ad hoc) experiments.

General Description of the Unit

For more details, see the course webpage at http://www.maths.bris.ac.uk/~mazjcr/ToI/home.html

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.

Teaching Methods

Lectures, exercises to be done by students.

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.

Assessment Methods

The final assessment mark is calculated from a 1½-hour written examination in May/June consisting of THREE questions. A candidate's best TWO answers will be used for assessment. Calculators are NOT permitted for this examination.

Award of Credit Points

  • Either : a final assessment mark of 40 or more, 
  • or reasonable attempts at specified written work during the course together with a final assessment mark of 30 or more.

Transferable Skills

Self-assessment by working examples sheets and using solutions provided.

Texts

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.

Syllabus

  1. Statistical approaches to evidence (including in the courtroom), likelihood ratios, p-values
  2. Multiple testing, and screening in high-dimensional experiments
  3. Conditionality, the Likelihood Principle, and its implications
  4. Designing informative experiments, applications in medical statistics