What is Bayesian analysis?

A powerful technique named after 18th-century mathematician Thomas Bayes.

Bayesian analysis is named after an 18th-century English mathematician, Thomas Bayes, who investigated the problem of estimating the chances of a hypothesis being true, given a certain amount of observational evidence.

For example, if you suspect a coin is biased, tossing it a couple of times will not reveal any bias with much reliability. But as the number of tosses is increased, the weight of evidence either confirming or refuting your suspicions starts to accumulate.

Just how compelling the evidence is can by calculated using a mathematical recipe known as Bayes's Theorem. However, this theorem shows that evidence alone is not enough to resolve such questions: the inherent plausibility of the hypothesis under test also needs to be taken into account ... and - in line with common sense - implausible hypotheses need far more evidence to back them up before they can be regarded as compelling.

* Robert Matthews