# Bayes Theorem

### From Wiki

“Historians need solid and reliable methods. Their arguments must be logically valid and factually sound. Otherwise, they’re just composing fiction or pseudo-history. . . . [A]ll valid historical reasoning is described by Bayes Theorem (BT). . . .

“In simple terms, Bayes Theorem is a logical formula that deals with cases of empirical ambiguity, calculating how confident we can be in particular conclusion, given what we know at the time. . . .

“Though we don’t think in mathematics this way, we are nevertheless doing mathematics intuitively whenever we make any argument for any theory of evidence or events. Every time we say something is implausible or unlikely”, for example, we are covertly making a mathematical statement of probability.”

- Dr. Richard Carrier,
*Proving History*(2012), pp. 45-50.

## Simple Introduction

If you didn’t learn Bayes Theorem in math class, this simple and entertaining video will help you understand it. It is Dr. Richard Carrier’s presentation Bayes’ Theorem: Key to the Universe at Skepticon IV in 2011.

## Refresher Course

If you remember Bayes Theorem from math class this section might help refresh your memory.

Bayes Theorem is represented by this formula:

File:Http://photos.geni.com/p13/88/28/30/51/534448432012b0db/bayes formula original.jpg

In simpler terms, the probability an explanation is true is equal to:

File:Http://photos.geni.com/p13/95/00/0e/1a/534448432012b0dc/bayes natural original.jpg

Notice the structure of the equation.

- The numerator is the probability of this explanation (how typical it is multiplied by the probability the evidence supports it)

- The denominator is the sum of the probabilities of all known explanations, so it will always sum to 100 percent.

- The numerator divided by the denominator gives you the probability of this particular explanation out of the whole field of explanations.