People of Science: Thomas Bayes and Ronald Fisher

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Thomas Bayes and inverse probabilities
Reverend Thomas Bayes (1701-1761) was elected Fellow of the Royal Society in 1742 before he elaborated the theorem now known as Bayes' law. At the time of his election, Bayes, a nonconformist preacher, had published a defense of Isaac Newton's method of fluxions.  
Bayes sent some mathematical observations to physicist John Canton FRS (1718-1772). This paper, which discusses mathematical series, was read posthumously at a meeting of the Royal Society and then published in its scientific journal, the Philosophical Transactions, in 1763. His 'Essay towards solving a problem in the doctrine of chance', which framed his theorem, however, was left within his papers. 
Bayes' theorem
Bayes' theorem was published after his death by the mathematician and radical thinker Richard Price FRS (1723-1791). The theorem allows to assess the likelihood of an event taking place, based on the conditions around the event. Price revised Bayes' paper at some length, and in 1812, French mathematician Pierre-Simon Laplace (1749-1827) published the modern mathematical formulation of the theorem. 

A simple expression of the theorem would be as follows:

P(H|E) = P(H) X P(E|H) / P(E)

Where P stands for probability, H stands for hypothesis and E for evidence.

Richard Price and Thomas Bayes rest near each other, in the Bunhill Fields Burial Grounds of Shoreditch.

The burial grounds served predominantly the nonconformist community and other figures such as Daniel Defoe or William Blake are also buried on the site.

Bayes' theorem has become fundamental for statistics. It was revived in the 20th century by mathematician Sir Harold Jeffreys FRS & physicist Bertha Swirles. They described it as occupying the same place for the theory of probability as what the Pythagorean theorem means to geometry.

You can hear in this video neuropsychologist Richard Gregory FRS (1926-2010) explain the theorem and its impact.

Sir Ronald Aylmer Fisher: towards theoretical statistics
 Sir Ronald Aylmer Fisher, FRS discussed at length the soundness of the mathematical expression of inverse probability as stated by Laplace. Fisher was himself a major contributor to statistical analysis in the 20th century, one of the founders of biostatistics. This sketch of Fisher was realised by yet another statistician: Sir Maurice Bartlett, FRS. 
R. A. Fisher led his research for over a decade at the Rothamsted Experimental Station, an agricultural research institute established in 1843. Fisher used the data on crops gathered at the institute and published 'Studies in crop variation' in 1921. From agricultural crops, Fisher then moved on to apply statistical tools to population studies. 

Fisher used statistical tools and defended the need for theoretical statistics. In a paper published in the Royal Society journal, 'Philosophical Transactions-A' he defined the aim of statistics as 'the reduction of data' to make incomprehensible amount of data understandable.

As expressed in this review of the paper, Fisher's analysis reviewed different mathematical methods to determine constants and thereby provide a solid foundation to statistical analysis.

The future of Bayes' theorem: AI?
The introduction of Bayes' law to artificial intelligence has been credited with great improvement in the field: its logic seems to strengthen machine learning by allowing decisions to be based on evidence and learn from it. This is only possible because generations of mathematicians, from Price to Fisher have improved on the original theory, which Bayes himself had not considered fit for publication. 
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