Tuesday, December 12, 2006

Thomas Bayes and his Formula

Thomas Bayes (1702-1761) was a British Presbytarian minister and mathematician. He was the first to use probability calculus for inference concerning future events based on evidence. In this context he used the formula, which as now known as Bayes formula. Using a modern notation it looks like this:

$ P(D|R) =\frac{P(R|D)P(D)}{P(R | D)P(D)+P(R|\bar D)(1-P(D))}.$

In the example with the pregnancy test $P(R |D)$ and $P(R |\bar D)$ denotes the probability of the test outcome, $R$, depending on whether the sow is pregnant or not, and $P(D)$ denotes the probability that the sow is pregnant before the test result is available. On the left side of the equation, $P(D | R)$ denotes the desired probability that the sow is pregnant after the test result is known.

A bayesian network exploits a version of the formula to calculate similar probabilities in more complex frameworks.

Thomas Bayes did not publish his Essay Towards Solving a Problem in the Doctrine of Chances himself. It was published in 1763 after his dead.

See Thomas Bayes - Wikipedia, the free encyclopedia for further information.

Translated from Bayes og hans formel

No comments: