Bayes Theorem
Bayes Theorem was formulated by the Rev Thomas Bayes (c 1702-1761).
Thomas Bayes was born in London in about 1702. He became a Presbyterian
minister. As far as is known, during his lifetime he published two works:
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
(published anonymously in 1736), in which he defended the logical foundation
of Isaac Newton's calculus
against the criticism of George Berkeley, author
of The Analyst. Bayes was elected as a Fellow of the Royal Society in 1742
possibly on the strength of the Introduction to the Doctrine of Fluxions.
Bayes died in Tunbridge Wells, Kent
in 1761. He is buried in Bunhill Fields
Cemetery in London where many Nonconformists
are buried. In death, as in
life, he was separated from the Church of England.
The fame of Thomas Bayes rests on a posthumously published masterwork,
An Essay Toward Solving a Problem in the Doctrine of Chances.
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In this
he enunciated what is now known as Bayes Theorem. Bayes Theorem can be
deployed in abductive reasoning in trying to ascertain the best explanation for
something. According to one view it can be deployed in the process of fact
finding where there is a lack of direct evidence for vital facts so that they fall to
be ascertained by inference.
Operation of Theorem
To explain Bayes Theorem let us work with a simple example.
241
Assume that
in a country the probability that any person has ‘lurgi’ (a fictitious disease) is 5
percent. Thus if:
A1 refers to the event of having the disease
A2 refers to the event of not having the disease
then
P(A1) = 0.5
P(A2) = 0.95
In the context of Bayes Theorem these probabilities are called prior
probabilities because they are the existing data before additional information is
discovered about these probabilities. Thus if we select a person at random the
best estimate we now have is that the person has a 0.05 probability of having
lurgi.
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Bayes (1764)
241
This example is taken from Robert D Mason, Douglas A Lind Statistical
Techniques in Business and Economics (1993) 8th ed Sydney: Irwin, pp 185-186
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