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Unit information: Theory of Inference in 2015/16

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Unit name Theory of Inference
Unit code MATH35610
Credit points 10
Level of study H/6
Teaching block(s) Teaching Block 2D (weeks 19 - 24)
Unit director Professor. Jonty Rougier
Open unit status Not open
Pre-requisites

MATH11300, MATH11400, MATH20800 and MATH21100

Co-requisites

None

School/department School of Mathematics
Faculty Faculty of Science

Description

Statistical inference is the science concerned with drawing inferences on the basis of uncertain data. In contrast to numerical or graphical descriptive techniques, which have the relatively simple aim of summarising the data actually observed, in inference we intend to draw conclusions about the populations from which the data are drawn. In doing so, almost universally, a probabilistic model is built for the mechanism generating the data, and the specific objects of inference are the unknowns (parameters) appearing in such models. There are several approaches to doing this, and we shall cover the main features of the two most important of these: (a) classical (or frequentist) inference and (b) Bayesian inference.

Intended learning outcomes

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

Teaching details

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

Assessment Details

2.5 hour written examination

Reading and References

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.

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