Understanding Uncertainity UU

Welcome to the site that tries to make sense of chance, risk, luck, uncertainty and probability. Mathematics won’t tell us what to do, but we think that understanding the numbers can help us deal with our own uncertainty and allow us to look critically at stories in the media … (full text Homepage).

Uncertainity – what do we mean?
Blog; Videos; Animations; Guests; Links; Right column: Featured Content;
Contact online.

About /What is this site? This site is produced by the Winton programme for the public understanding of risk based in the Statistical Laboratory in the University of Cambridge. The aim is to help improve the way that uncertainty and risk are discussed in society, and show how probability and statistics can be both useful and entertaining! However we also acknowledge that uncertainty is not just a matter of working out numerical chances, and aim for an appropriate balance between qualitative and quantitative insights. 

Who are we?

The current team comprises David Spiegelhalter, Mike Pearson, Owen Smith Arciris Garay-Arevalo and Ian Short, with contributions from Hauke Riesch, Owen Walker, Madeleine Cule and Hayley Jones . However we are always looking for people who would like to contribute material to this site, and you will get proper acknowledgement.

What do the ‘dots’ mean?

You will see that the ’stories’ are structured at multiple ‘levels’ corresponding to difficulty. For pages with mathematical content, these levels correspond roughly to

1. No maths, just pictures and text for general readership

2. Basic arithmetic and probability theory, at a high GCSE level (say up to aged 16). For example:

  • What are the chances shows probability calculations requiring multiplication of probabilities of independent and dependent events, as well as introducing ideas of expectation.
  • Lottery expectations and Luck or skill? compare observed and expected distributions: Binomial, normal and geometric expected distributions are provided but not derived.
  • Maternal death coincidence features quite a complex piece of probabilistic reasoning concerning the chance of two deaths occurring close in time and space.

3. Some algebra, probability distributions, basic statistical concepts at a high A level standard (ages 16 to 18). For example:

  • Maths of coincidence provides a general algebraic form for the probability of at least one event occurring, both for dependent and independent events. This uses the exponential e  and mentions the Poisson distribution.
  • Is the lottery biased? features Chi squared is a sample statistic which measures how far the sample is from expectation. The chi squared distribution is the probability distribution for the chi squared statistic.”>chi-squared tests for goodness-of-fit, the derivation of the geometric distribution, and ideas of testing hypotheses by simulating distributions of test statistics under the null hypothesis.
  • May the best team win derives the mean and variance of a test statistic under a null hypothesis and uses a normal approximation to the sampling distribution to derive confidence intervals. Uncertainty about ranks is explored using Monte Carlo methods.

4. Full mathematical exposition, at university level. No level 4 pages written yet!

  • Non-mathematical pages also have different levels according to their conceptual difficulty

What do we mean by ‘uncertainty’?

This tricky question is discussed in Uncertainty – what do we mean?. Our site name Understanding Uncertainty, is shared by an excellent recent book by Dennis Lindley

For Educators

We hope this site may be useful to people teaching about uncertainty, whether it’s the mathematics of probability and statistics, or the responses of individuals or society to risk.

For a related schools-based enrichment activity, see the Risk Roadshow offered by the Millennium Mathematics Project.

Author: David Spiegelhalter.

Comments are closed.