# bayes theorem

Find out why the formula we use to work out conditional probabilities is true!

David Spiegelhalter, one of our favourite experts on statistics, recently joined David Attenborough, Bill Bryson and other eminent contributors on the Royal Society's People of Science series. You can watch the video here.

It would be foolish to ignore evidence. Luckily Bayes' theorem shows us how to take it in into account.

In the previous article we looked at a psychological study which claims to provide evidence that certain types of extra-sensory perception exist, using a statistical method called significance testing. But do the results of the study really justify this conclusion?

London 2012 vowed to be the cleanest Olympics ever, with more than 6,000 tests on athletes for performance enhancing drugs. But when an athlete does fail a drug test can we really conclude that they are cheating? John Haigh does the maths.

England's performance in the World Cup last summer was thankfully overshadowed by the attention given to Paul the octopus, who was reported as making an unbroken series of correct predictions of match winners. David Spiegelhalter looks at Paul's performance in an attempt to answer the question that (briefly) gripped the world: was Paul psychic?

It's Monty Hall, only better!

"It's a match!" cries the CSI. At first glance it might seem that if the police have matched a suspect's DNA to evidence from the crime scene, then the case is closed. But some statistical thinking is required to understand exactly what a match is, and importantly, how juries should assess this as part of the evidence in a trial.

Being killed in a peacekeeping mission apparently depends on your nationality, at least if you're a soldier in the Spanish army. On the 1st of February 2010 the Colombian soldier John Felipe Romero serving in the Spanish army was killed in a terrorist attack in Afghanistan. It was then made public that so far 43% of the Spanish troops killed in attacks by local forces in Afghanistan and Lebanon have been foreigners. This is in striking contrast to the fact that foreign nationals make up only 7% of the Spanish army as a whole.

What's the risk of passive smoking? Or climate change? How big is the terrorist threat? And should we trust league tables? These issues concern all of us, but it's not always easy to make sense of the barrage of media information. David Spiegelhalter, Winton Professor for the Public Understanding of Risk, gives Plus his take on uncertainty.
A new Bayesian network helps predict the severity of the disease
• Want facts and want them fast? Our Maths in a minute series explores key mathematical concepts in just a few words.