The Parameters of Bayes' Theorem, Part 1
First off, Thomas Bayes (1701–1761) had a stroke of brilliance in creating his theorem! This is how we wish everyone should think when evaluating claims, events and promises. In a way, one cannot help but be in awe of it. Nothing I say is to indicate otherwise. My only beef is how it's been misused in cases where it shouldn't be used. The formula is below. Notice that the prior probability of event "B" cannot be zero. That sets the major limitation for how Bayes is used. Anything that is given a zero prior probability is not the subject for Bayes' Theorem. Got it? To use it in cases where there is a zero probability is to use it incorrectly. That's the point, not that every claim has a nonzero prior probability to it.
In the following simplified video explaining Bayes' Theorem, take a close look at the 45 second mark.
The narrator says something like this:
"Let's say you know one student in a class of twenty has the flu. Then the prior probability that a student in that class named Sally has the flu, is 1/20. That is your prior probability." Notice you have some factual information, that is, one student in a class of twenty has the flu. This is significant. First comes data, then comes prior probabilities. Bayes is dealing with factual data from the beginning. Without it there is nothing to compute. Compute?
In the following simplified video explaining Bayes' Theorem, take a close look at the 45 second mark.
The narrator says something like this:
"Let's say you know one student in a class of twenty has the flu. Then the prior probability that a student in that class named Sally has the flu, is 1/20. That is your prior probability." Notice you have some factual information, that is, one student in a class of twenty has the flu. This is significant. First comes data, then comes prior probabilities. Bayes is dealing with factual data from the beginning. Without it there is nothing to compute. Compute?