What does Bayes’ Theorem mean? What do the different parts of the equation say in plain language?
Let’s first recall that Bayes’ theorem is stated as follows
P(A|B) = P(B|A) * P(A) / P(B)
In plain language, Bayes’ theorem is saying
If we know that B is true and would like to find when A is also true, we should
- focus our attention on the outcomes where B is true
- and then once focused there, look at all the outcomes in this area where A is true.
The first point first. Since all probabilities are between 0 and 1, if we consider the number 1 to mean all possible outcomes, then
P(B) means all outcomes where B is true. So this is where the denominator of
P(B) in the equation comes from.
For the second point, we’re asking here about the intersection of A and B which we can write as
P(B|A) * P(A), explaining the numerator of the equation.