Bayesian updating formula


Finally, of course, if the only viable alternative to H (the only alternative with a non-negligible prior probability) is purely random chance, then P(E|~H) will be the probability of E resulting from pure random chance.

bayesian updating formula-88

Analogously, if someone tells you their limbs grew back after having been chopped off, how frequently is "a human's arms grew back after being chopped off" actually the explanation of such evidence (that such a person, with arms and legs intact, would say something like this to you), as opposed to some other explanation being true instead (e.g.

"they're crazy," "they're lying," "they're joking," etc.)?

The second variable, P(~H), is the prior probability that H is false, which is always 1 - P(H), so the calculator already figures this for you (hence as you move one of the first two sliders, the other automatically moves to match).

The other two variables are the probability that the evidence would exist if H is true, which is P(E|H), and the probability that the evidence would exist if H is false, which is P(E|~H).

But I will leave that out in the text, as simply being understood.