The Meeting House where Bayes was Minister

The old Meeting House on Little Mount Sion in Tunbridge Wells has two claims to fame. The first, commemorated with a blue plaque, is that John Wesley, founder of Methodism, preached there on several occasions in the 1780s. The second is that a man who was Presbyterian Minister there earlier in the 18th century was also a mathematician of national renown and a Fellow of the Royal Society.

That man was Thomas Bayes, whose name lives on among mathematicians today. He was born into a family which had grown wealthy in the Sheffield cutlery industry.

Bayes is commemorated in Tunbridge Wells by a plaque on the gatepost of his home in London Road. The date of birth is uncertain. (http://openplaques.org/)

He was well educated, including three years at Edinburgh University, where he would have studied mathematics and natural philosophy in addition to the classics and theology. He held his post as Presbyterian Minister in Tunbridge Wells from the early 1730s until 1752, during which time he wrote a number of highly regarded mathematical papers and these led to him being elected to the Royal Society. After resigning as Minister he remained in the town until his death and during this time wrote the paper on which his fame now rests. This was not published until after his death, when a friend found it and sent it to the Royal Society for publication.

Bayes’ paper concerned what he called the ‘Doctrine of chances’ and it gave birth to a branch of mathematics which is today called Bayesian statistics. Loosely speaking, Bayes’ Theorem gives a rigorous way of calculating the probability of something happening, in the light of evidence of what has happened in the past. It sounds abstract but has many practical applications in the modern world. One of these is in the design of ‘spam filters’ which weed out rubbish emails from the ones that matter. The software looks at the words in an incoming email and uses Bayesian principles to work out the probability, based on what it has ‘learnt’ from other emails in the past, that the email is or is not spam. The theory is also applied in the field of Artificial Intelligence, for example to help robots learn to do their tasks.

The paper in 'Philosophical Transactions of the Royal Society' in which Bayes' Theorem first appeared.

Thomas Bayes was an excellent mathematician, but seems not to have been as successful as a preacher – a misfortune for his congregation since sermons tended to last about an hour at that date. He died in Tunbridge Wells in 1761 and is buried in the nonconformist cemetery at Bunhill Fields in London. There is no authenticated image to show what he looked like, and even his date of birth is uncertain, but it has been estimated that there is an 80% probability he was born in the year 1701.

How was this probability worked out? Using Bayes’ Theorem of course.