# Bayes’ Theorem: The Maths Tool You Use Every Day Without Realising It

The decisions we make in life often come down to Bayes’ Theorem, but most of us don’t even realise what it is. So how does it work?

Our world view and resultant actions are often driven by a simple theorem, devised in secret more than 150 years ago by a quiet English mathematician and theologian, Thomas Bayes, and only published after his death.

Bayes’ Theorem was famously used to crack the Nazi Enigma code during World War II, and now manages uncertainty across science, technology, medicine and much more.

## Bayes’ Theorem explained

Thomas Bayes’ insight was remarkably simple. The probability of a hypothesis being true depends on two criteria:

1. how sensible it is, based on current knowledge (the “prior”)
2. how well it fits new evidence.

Yet, for 100 years after his death, scientists typically evaluated their hypotheses against only the new evidence. This is the traditional hypothesis-testing (or frequentist) approach that most of us are taught in science class.

The difference between the Bayesian and frequentist approaches is starkest when an implausible explanation perfectly fits a piece of new evidence.

Let me concoct the hypothesis: “The Moon is made of cheese.”

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• eskimoau says:

I’m calling bulldust on cracking Enigma shortening WWII by two years.

Using Bayes Theorem, the hypothesis does not taken into account the existing evidence that:

a. The Russians were making significant in-roads on the eastern front.
b. Development of long range maritime patrol aircraft closed the air/sea gap making submarine operation far less effective.
c. The Manhattan Project was proceeding independently of any other aspect of the war and would have produced atomic weapons at about the same time whether of not Enigma was cracked.

• evan says:

I’m sure it contributed, and I’d think that most would agree that the two years claim is an acceptable compromise based on a variety of factors. This claim was apparently made by Sir Harry Hinsley, an official historian of WWII. Cracking Enigma had some notable successes, such as assisting with the North Africa conflict.
A more interesting note is that apparently the B-Dienst (the German Naval Intelligence) had cracked the British and allied maritime codes in 1938-39, which is why they had such success with U-boat attacks, and it seems that the British never knew.
The development of atomic weapons may have contributed and its widely claimed that the Hiromishma and Nagasaki bombings stopped the Pacific war, but there’s counter-claims that it was actually the advancement of the Russian forces toward Japan that forced them to surrender. Japan was bombed in August of 1945, while Germany surrendered in early May of 1945, so it’s unlikely that the threat of atomic weaponry contributed to that.