I wonder if there are any other posters here who are wondering what the hell Bayesian reasoning really IS? Or worse perhaps, who are thinking to themselves 'Each time I look it up I understand, then I forget. Do I have to go through the math again, or just admit I am too dumb?'.
Well, there is hope! But first, why should you care about Bayesian reasoning? After all, it is not necessary to your salvation, is it? Well it might be. Here is an example (sorry, but this is not a very mormonized example)
After you die, you arrive in front of St Peter, who has to make the choice as to where you go. However, he has a new game that enables you to play a role in the choice! There are three gates, numbered 1, 2 and 3. One gate leads to heaven, the other two to hell.
The rules, he explains, are as follows:
1. You choose a gate and tell him which you have chosen, but he does not open it.
2. He then opens one of the other gates you did not choose, always selecting one that leads to hell (you get to see the flames and stuff ...).
3. You then have to choose which of the two unopened gates you want to go through ... how do you do it?
Common sense reasoning says you should just toss a coin, because one of the two unopened gates must lead to heaven, and it seems equally likely that either one of the two unopened gates could be the one you want.
BUT COMMON SENSE IS WRONG!
In fact it is TWICE as likely that the the unopened gate that you did NOT choose is the one that goes to heaven. So you should ALWAYS change the gate you choose to the previously unchosen gate that St Peter did not open. Of course it may still lead to hell ... but you can't win 'em all.
So all of us need to understand Bayesian reasoning, don't we, if only to see how wrong our intuitive sense of 'likelihood' can be in the real world.
If you go to Wikipedia, you will be dropped right into the math, and may drown.
But here is an excellent site that gives you a really clear and intuitive explanation of how it works out. Have a look ...