\sum_i p(H|i) need not add up to p(H) (or indeed to 1).
No, it doesn’t.
Edit—I’m agreeing with you. Sorry if that wasn’t clear.
\sum_i p(H|i) need not add up to p(H) (or indeed to 1).
No, it doesn’t.
Edit—I’m agreeing with you. Sorry if that wasn’t clear.