I am trying to understand the difference between posterior probability versus likelihood. Here is the source material I'm working off of:
To say that $H$ has a high likelihood, given observation $O$, is to comment on the value of $Pr(H \mid O)$, not on the value of $Pr(O \mid H)$; the latter is $H$’s posterior probability. It is perfectly possible for a hypothesis to have a high likelihood and a low posterior probability. When you hear noises in your attic, this confers a high likelihood on the hypothesis that there are gremlins up there bowling, but few of us would conclude that this hypothesis is probably true.
My question is, can we understand the likelihood of the gremlins bowling as $Pr(H \mid O)$ where $O$ is the probability of hearing noises given that $H$ occurs (that gremlins are bowling) but that $Pr(O \mid H)$ is extremely unlikely since gremlins don't exist?