Wednesday, August 02, 2017

The Theory That Would Not Die: How Bayes' Rule Cracked the Enigma Code, Hunted Down Russian Submarines, and Emerged Triumphant from Two Centuries of Controversy

Bayes' rule seems very simple. However, it has produced a great deal of controversy throughout its history. Even the name itself is controversial. Bayes does appear to have been one of the first people to produce a paper on it. However, the paper we have was substantially edited by Richard Price and presented at the Royal Society after Bayes' death. Laplace later independently discovered the algorithm and ran with it. Since he was the more renowned mathematical mind, it would make sense to name it after him. However, it was later referred to as Bayes rule by those who popularized it, and that is what we have today.
The Theory That Would Not Die does not spend much time covering the details of Bayes' rule. It is assumed the reader already understands it, or will be able to understand it well enough by following the story line. Instead, the focus is on the conflicts between the "bayeseians" and the "frequentists". Bayes can help determine probabilities given scant data or unknown occurrences and was derided as "subjective". Frequency analysis deals with known observations as was considered a more theoretically accurate. Bayesian analysis would come and go in spurts during its history. In world war ii, it helped lead to cracking the German code and significantly helping the Allied war efforts. Alas, it was deemed so important that it was classified, and thus not disclosed to the general public. The ability to adjust probabilities based on past outcomes made it especially useful for insurance actuaries. Today it has applications in multitudes of fields from medical research to spam filters. It is great at helping to tease out the signal from the noise and find high probability answers given scant data.

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