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His findings on probability were written in Essay Towards Solving a Problem in the Doctrine of Chances (1763), published posthumously in the Philosophical Transactions of the Royal Society of London.
He is known to have published two works in his lifetime: Divine Benevolence, or an Attempt to Prove That the Principal End of the Divine Providence and Government is the Happiness of His Creatures (1731), and An Introduction to the Doctrine of Fluxions, and a Defence of the Mathematicians Against the Objections of the Author of the Analyst, in which he defended Isaac Newton's foundations of calculus (1736).
Born in London, England, he died in Tunbridge Wells, Kent. He is interred in Bunhill Fields Cemetery in London.
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Bayesian probability is the name given to several related interpretations of probability,
which have in common the application of probability to any kind of statement,
not just those involving random variables.
"Bayesian" has been used in this sense since about 1950.
It is not at all clear that Bayes himself would have embraced the very broad interpretation now called Bayesian.
It is difficult to assess Bayes' philosophical views on probability,
as the only direct evidence is his essay,
which does not go into questions of interpretation.
In the essay,
Bayes defines probability as follows (Definition 5).
Thus it can be argued, as Stigler does,
that Bayes intended his results in a rather more limited way than modern Bayesians;
given Bayes' definition of probability,
his result concerning the parameter of a binomial distribution makes sense only to the extent that one can bet on its observable consequences.
Was Bayes a Bayesian?
In modern utility theory we would say that expected utility is the probability of an event times the payoff received in case of that event.
Rearranging that to solve for the probability,
we obtain Bayes' definition.
As Stigler (citation below) points out,
this is a subjective definition, and does not require repeated events;
however, it does require that the event in question be observable,
for otherwise it could never be said to have "happened".References
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