Bayes’ Theorem and the Existence of God
https://qz.com/1315731/the-most-important-formula-in-data-science-was-first-used-to-prove-the-existence-of-god/
According the article above, Bayes’ Theorem, arguably the most influential formula in all of statistics, has been used extensively in many fields of science since its development in the 18th-century. Today, the theorem is essential for statistical analysis in areas like machine learning, artificial intelligence and medicine. Ironically, however, the first ever use of Bayes’ Rule was not to bolster a scientific understanding, but quite the opposite; it was used to prove the existence of God.
One of Thomas Bayes close friend’s was a minister named Richard Price. When his friend died in 1761, Price found the famous formula in Bayes’ An Essay towards solving a Problem in the Doctrine of Chances, and published it for him posthumously in 1763. In 1767, Price employed that same theorem in an argumentative essay in support of the existence of God.
In his essay, he refutes philosopher David Hume’s position on the falsity of miracles. Hume posits that evidence for miracles comes from outside testimony of others, while evidence against miracles is experienced personally every day through the unchanging laws of nature. The only way evidence for miracles to be sufficient for their proof is if the outside testimony is more convincing and reliable than the laws of nature themselves. Hume thus reasons that miracles are impossible. Price, on the other hand, was a staunch believer in the miracles of the Bible and beyond. He argues that it is not possible to deny the chance of a miracle based on large-scale observations of normalcy, i.e. a lack of miracles. As an example of his stance, Price calculates the supposed probability of viewing the tide not coming into shore one day using Bayes’ formula. His final estimation of “somewhere between 1 in 600,000 and 1 in 3 million” indicates, that though improbable, miracles do in fact exist and are the product of a higher power. Thus, Price, the first Bayesian statistician, used the theorem to purportedly prove the reality of miracles and of God.
This article connects to our class discussion mainly through the utilization of Bayes Theorem to describe the probability of an uncertain event, based on probabilities of conditions related to said event. Though not explicitly explained in the above article, the calculation Price did is as follows and is based on the formula extensively discussed in class:
M = miracles exist, i.e.no tide
T = consistency of the tides everyday
P(M|T) = P(M) * P(T|M) / (P(M) * P(T|M) + P(~M) * P(T|~M))
Price assumed, being the God-fearing man he was, that the probability of miracles existing and not existing are equivalent, P(M) = P(~M).
P(M|T) = P(M) * P(T|M) / (P(M) * ( P(T|M) + P(T|~M))) ,
P(M|T) = P(T|M) / (P(T|M) + P(T|~M))
Price next assumed that if miracles existed, the probability of a given miracle displaying itself in the form of a lack of tide would be very very low (justifying the lack of observed miracles) around 1 in one million. Lastly, Price postulated that if there were no miracles, the tides would always be consistent.
So,
P(M|T) = P(T|M) / P(T|~M)) , since (P(T|M) << P(T|~M))
P(M|T) = 0.000001 / 1 = 1/1,000,000.
Based on his broad assumptions, Price calculated the probability of a specific miracle occurring to be around one in one million as stated above (between 1 in 600,000 and 1 in 3 million).
Price made broad assumptions in his calculation, which of course would not be acceptable in current uses of Bayes Theorem when it comes to data analysis and medicine and the examples we did in class. However, the lack of concrete related probabilities in his philosophical argument made it necessary to do so. His usage of the rule has thus stood the test of time as he was the first person ever to apply it.