Thomas Bayes (1701 - 1761) was an English mathematician and Presbyterian minister, known for having formulated a specific case of the theorem that bears his name: Bayes’ theorem. Bayes never published what would eventually become his most famous accomplishment; his notes were edited and published after his death by Richard Price.
   Bayes’ solution to a problem of “inverse probability” was presented in the An Essay towards solving a Problem in the Doctrine of Chances which was read to the Royal Society in 1763 after Bayes’s death. Richard Price shepherded the work through this presentation and its publication in the Philosophical Transactions of the Royal Society of London the following year. This was an argument for using a uniform prior distribution for a binomial parameter and not merely a general postulate. This essay contains a statement of a special case of Bayes’ theorem. In the first decades of the eighteenth century, many problems concerning the probability of certain events, given specified conditions, were solved. For example, given a specified number of white and black balls in an urn, what is the probability of drawing a black ball? Attention soon turned to the converse of such a problem: given that one or more balls has been drawn, what can be said about the number of white and black balls in the urn? These are sometimes called “inverse probability” problems. The Essay of Bayes contains his solution to a similar problem, posed by Abraham de Moivre, author of The Doctrine of Chances (1718).
   Bayesian probability is the name given to several related interpretations of probability, which have in common the notion of probability as something like a partial belief, rather than a frequency. This allows the application of probability to all sorts of propositions rather than just ones that come with a reference class. “Bayesian” has been used in this sense since about 1950. Since its rebirth in the 1950s, advancements in computing technology have allowed scientists from many disciplines to pair traditional Bayesian statistics with random walk techniques. The use of the Bayes theorem has been extended in science and in other fields. Bayes himself might not have embraced the broad interpretation now called Bayesian. It is difficult to assess Bayes’ philosophical views on probability, since his essay does not go into questions of interpretation.