Thomas Bayes (1701-1761)

Thomas Bayes was an English minister and mathematician. He found a solution for calculating inverse probabilities, which were used for insurance and gambling. These were important mathematical problems at the time.


Thomas Bayes


Pierre-Simon Laplace (1749-1827)

Pierre-Simon Laplace discovered Bayes’ Theorema independently from Thomas Bayes. Laplace solved problems in astronomy, medical statistics, and even jurisprudence. After his death his ideas and results were rejected and classical statistics were developed.


Pierre-Simon Laplace


WW II (1939-1945)

During the Second World War, the deciphering of coded military messages was an important factor in the war tactics. In England, the German messages were cracked by, among others, Alan Turing. In the US the Japanese codes were deciphered by, among others, Solomon Kullback. Both used, without knowing each other, Bayesian methods to discover the secret keys.


Enigma decoder


The information age

With the development of ever faster computers, Bayes’ Theorema is increasingly being applied in practice. A number of names to be mentioned are Harold Jeffreys (1891 – 1989), Richard T. Cox (1898 – 1991), Claude E. Shannon (1916 – 2001), Edwin T. Jaynes (1922 – 1998). In the 1980s, the first specialized conferences were organized on this subject, in which researchers from the natural sciences in particular accelerated the use of Bayes’ Theorema.


Cambridge 1988


IRAS satellite (1983)

The standard maps of the InfraRed Astronomical Satellite (IRAS) were as on the top figure. Do Kester and Romke Bontekoe used Maximum Entropy and Bayesian statistics to calculate the bottom figure.

Andromeda – IRAS coadded image


Andromeda – IRAS high resolution image

This was the visible proof for us that Bayesian methods work better than classical statistical methods.


Some other examples where Bayesian statistics is important:

  • spam filters for unsolicited emails
  • face recognition on photos
  • recovering a crashed plane in the ocean
  • reviews of loan or mortgage applications
  • prediction of election results
  • investigation of financial fraude
  • self-driving vehicles


The theory that would not die

is a very readable book about the history of Bayes’ Theorema. It is written by Sharon Bertsch McGrayne. It deals with the history, resistances, controversies and egos of well-known names in classical statistics. It gives a good picture of why Bayesian statistics have become so important in the current computer age.