Posted: Dec 17, 2011 12:53 pm
by Thommo
jlowder wrote:
Thommo wrote:If you regularly buy lunch at McDonalds 6 days a week (for example), then Pr(E|H) can easily be > 0.5 regardless of any predictions of H.

Not necessarily. I'm using the epistemic interpretation of probability, not the frequency interpretation. If I regularly buy lunch at McDonald's 6 days a week, that could only be relevant IF:

1. We expand the expression Pr(E|H) to Pr(E|H&B), where B represents our background knowledge.
2. We include in B the fact that I regularly buy lunch at McDonald's 6 days a week.

If we do that, then Pr(E|H&B) > 0.5. Of course, H will be explanatorily irrelevant, since it will B, not H, that will make it possible for this value to be > 0.5. In fact, H will be irrelevant precisely because Pr(E|H&B) = Pr(E|B).

Yes indeed, and it's also true if we replace the 0.5 with any 0 < x < 1, which is rather why I was wondering where the 0.5 comes into it!

Of course, if you don't like the frequentist example, feel free to consider any other method for estimating the probability of your eating lunch at McDonald's.

To put it another way, it seems rather odd to suggest it is a prediction of the theory of heliocentrism (say) that if I toss a coin twice in a row I won't get two heads, though it surely has P > 0.5 on the assumption that heliocentrism is true (again the theory is irrelevant as the probability is independent).