# 46 Further Reading

As mentioned, Bayes’ Theorem is usually presented as a formula. The basic question is, “What is the probability of {some event} given this evidence?” The idea is to make the probability *proportional to* both the probability of the event on its own and the probability that the evidence would exist if the event happened and to make the probability *inversely proportional* to the probability of the evidence existing, even if the event didn’t happen. So, we have this:

Or, letting A = the event, B = the evidence, and “P(A|B)” meaning “the probability of A given B”, we have:

There are *many *excellent videos about Bayes’ Theorem on YouTube. One that is exceptionally clear is from 3blue1brown, “The medical test paradox: Can redesigning Bayes rule help?”, https://youtu.be/lG4VkPoG3ko.

A fascinating book about the powerful effects of Bayes’ Theorem is Sharon Bertsch McGrayne’s *The Theory That Would Not Die: How Bayes’ Rule Cracked the Enigma Code, Hunted Down Russian Submarines & Emerged Triumphant from Two Centuries of Controversy* (Yale UP, 2011)

Hume, David. *An Enquiry Concerning Human Understanding*. Indianapolis: Hackett, 1993. Hume’s argument against believing reports of miracles is chapter 10 of his *Enquiry Concerning Human Understanding*. It is a classic!

### Media Attributions

- Bayes Formula © Charlie Huenemann is licensed under a CC BY-SA (Attribution ShareAlike) license
- Figure 10.2 © Charlie Huenemann is licensed under a CC BY-SA (Attribution ShareAlike) license