Differential pressure

• p(pearl) = 40%
• p(blue|pearl) = 30%
• p(blue|~pearl) = 10%
• p(pearl|blue) = ?

Differential pressure between the two conditional probabilities,  p(blue|pearl) and p(blue|~pearl) 의 개념

it's easier to see why the final answer depends on all three probabilities; it's the differential pressure between the two conditional probabilities,  p(blue|pearl) and p(blue|~pearl), that slides the prior probability p(pearl) to the posterior probability p(pearl|blue).

...

you can see that when the conditional probabilities are equal, there's no differential pressure - the arrows are the same size - so the prior probability doesn't slide between the top bar and the bottom bar.

In the frequency visualization, ... The bottom bar is shorter than the top bar, just as the number of eggs painted blue is less than the total number of eggs.

The gif file created from the applet at http://yudkowsky.net/rational/bayes