THOMAS BAYES: BIOGRAPHY AND CONTRIBUTIONS - CULTURE VOCABULARY - 2025

Thomas Bayes (1702-1761) was an English theologian and mathematician, considered the first person to use inductive probability. In addition, he developed a theorem that bears his name: Bayes' Theorem.

He was the first to establish a mathematical basis for probability inference: a method of calculating the frequency with which an event has occurred previously and the probability that it will occur in future tests.

Little is known about the beginning and development of his life; however, it is known that he was a member of the Royal Society of London, a prestigious scientific society in the United Kingdom.

On the other hand, the English mathematician did not get to publish all his works in life; in fact, he only published two small works of which only one was related to the field of science and anonymously.

After his death, his works and notes were edited and published by the English philosopher Richard Price. Thanks to this, nowadays the works product of their efforts are used.

Biography

Early years and jobs

Thomas Bayes was born in 1701 or 1702; the exact date of his birth is not known. It is said that he was born in London or in the county of Hertfordshire, England. He was the eldest son of the seven children of Joshua Bayes, a Presbyterian minister from London. His mother was Anne Carpenter.

Bayes came from a prominent Protestant family that did not conform to the rules of the Church of England, known as the Mavericks. They were established in the English city of Sheffield.

For that reason, he studied with private tutors and is said to have been taught by Abraham de Moivre, a French mathematician known for his contributions to probability theory, which was highly influential on his projects.

Due to his radical religious beliefs, he was unable to enroll in universities such as Oxford or Cambridge, so he studied at Scottish schools such as the University of Edinburgh. There he studied logic and theology.

In 1722, he returned home and helped his father in the chapel before moving to Tunbridge Wells around 1734. He remained there, where he was minister of the Mount Sion chapel, until 1752.

Divine Benevolence

Divine Benevolence, or an intense proving that the main purpose of Divine Providence and Government is the happiness of their Christures, was one of the first published works of Thomas Bayes, in the year 1731.

Bayes is known to have only published two short-scale works; one related to theology and metaphysics and the second work, related to the scientific field more directed towards what their contributions were.

The metaphysical theological work is said to have been written in response to a memoir by the Anglican philosopher and minister, John Balguy.

In previous years, Balguy published an essay on Creation and Providence in which he explained that the moral principle that should guide human life can be the ways of God; that is to say, goodness in a Deity is not a mere disposition to benevolence, but an order and harmony.

From that work, Bayes responded with his publication and the controversy of "if God was not obliged to create the universe, why did He do it?"

First scientific publication

In 1736, one of his first scientific publications was published (anonymously), entitled An introduction to the doctrine of Fluxions, and a defense of mathematicians against the objections of the author of The Analyst.

The work consisted of a defense of Isaac Newton's differential calculus in response to Bishop Berleley's attack on Newton's theory of fluxions and infinite series in his work The Analyst, of 1730.

Bayes's work was basically a defense to Newton's algebraic methods, in which he allows determining the maximums and minimums of relations, tangents, curvatures, area and length.

This publication was the one that opened the doors for Thomas Bayes to become a member of the Royal Society of London in 1742, despite not having published works related to mathematics. Even so, his work, which had initially been anonymous, was discovered. This caused him to be invited to the Royal Society.

Motivations for mathematics

In his later years, he became interested in theories of probability. Chicago statistical historian Stephen Stigler thinks Bayes became interested in the subject after reviewing one of the works of English mathematician Thomas Simpson.

However, British statistician George Alfred Barnard believes that he learned and was motivated by mathematics after reading a book by his teacher Abraham Moivre.

Several historians speculate that Bayes was motivated to refute Scottish empiricist David Hume's argument, set out in his Investigation of Human Understanding, in which he was against miraculous beliefs.

In addition to the two published treatises, he wrote several articles on mathematics. One of these was included in a letter addressed to John Canton, the secretary of the Royal Society of London. The article was published in 1763 and dealt with divergent series and, specifically, with Moivre Stirling's theorems.

In spite of this, the article was not commented on in the correspondence of any mathematician of the time, so it apparently did not have great importance.

Death and legacy

Plaque located in what was once the home of Thomas Bayes, By Simon Harriyott, via Wikimedia Commons

Although there was no evidence to confirm Bayes' activities in his later years, it is known that he never abandoned his studies in mathematics; otherwise, he went much deeper into probability. On the other hand, Bayes never married, so he died alone at Tunbridge Wells in the year 1761.

In 1763, Richard Price was asked to be the "literary executor" of the works of Thomas Bayes; then he edited the work entitled An essay to solve a problem in the doctrine of possibilities. In such work is contained Bayes' theorem, one of the successful results of probability theories.

Later, Bayes' works remained ignored within the Royal Society of London and he had practically little influence on mathematicians of the time.

However, the Marquis de Condorcet, Jean Antoine Nicolás Caritat, rediscovered the writings of Thomas Bayes. Later, the French mathematician Pierre Simon Laplace took them into consideration in his work Analytical Theory of Probability, in 1812. Today their legacy continues in various fields of mathematics.

Contributions

Bayes theorem

Bayes's solution to the problem of inverse probability (an obsolete term for the probability of an unobserved variable) was presented in his work An Essay for Solving a Problem in the Doctrine of Possibilities, through his theorem. The work was read by the Royal Society of London, in 1763, after his death.

The theorem expresses the probability that an event "A" occurs, knowing that there is an event "B"; that is, it links the probability of "A" given "B" and of "B" given "A".

For example, the probability that you have muscle aches given that you have the flu, you could know the probability of having the flu if you have muscle aches.

Currently, Bayes' theorem is applied in probability theory; however, today's statistics allow only empirically grounded probabilities, and this theorem only offers subjective probabilities.

Despite this, the theorem allows us to explain how all those subjective probabilities can be modified. On the other hand, it can be applied to other cases, such as: prior or posterior probabilities, in the diagnosis of cancer, etc.

Bayesianism

The term "Bayesian" has been used since 1950 thanks to advances in computer technology that have allowed scientists to combine traditional Bayesian statistics with "random" techniques; the use of the theorem has spread in science and other fields.

Bayesian probability is an interpretation of the concept of probability, which allows reasoning with certain hypotheses; that is, the propositions can be true or false and the result will be completely uncertain.

Bayes' philosophical views on probability are difficult to assess, since his essay does not go into questions of interpretation. However, Bayes defines "probability" in a subjective way. According to Stephen Stigler, Bayes intended his results in a more limited way than modern Bayesians.

Still, Bayes theories were relevant to develop, from there, other current theories and rules.

Bayesian inference

Thomas Bayes gave rise to his renowned theorem to explain other events. At present, Bayesian inference is applied to decision theory, computer vision (a method of understanding real images in order to produce numerical information), etc.

Bayesian inference is a way to predict more accurately about the data that you have at the moment; In other words, it is a favorable method when you do not have enough references and you want to reach truthful results.

For example, there is a fairly high probability that the sun will rise again the next day; however, there is a low probability that the sun will not rise.

Bayesian interference uses a numerical stimulator to confirm the degree of belief in the hypothesis before observing the evidence and, at the same time, calculates the number of the degree of belief in the hypothesis after the observation. Bayesian interference is based on degrees of subjective beliefs or probabilities.

References

1. Thomas Bayes, publishers of Encyclopedia Britannica, (nd). Taken from britannica.com
2. Thomas Bayes. A reverend, a theorem and multiple applications, Fernando Cuartero, (nd). Taken from habladeciencia.com
3. Divine Belevolence, Thomas Bayes, (2015). Taken from books.google.com
4. Thomas Bayes, Wikipedia in English, (nd). Taken from Wikipedia.org
5. Philosophy of science: Bayisian Confirmation, Phillip Kitcher, (nd). Taken from britannica.com