i.e. Tossing a fair coin
$p_H =$ probability of heads $= 0.5$
$L(p_H | HH) = P(X = HH | p_H) $
Okay, right-hand of equation I understand,
$P(X = HH | p_H) = 0.25 =$ probability of "$X = HH$" given $p_H$
but what does the value resulting from the left side mean if it's not probability.
$L(p_H | HH) = 0.25 =$ Likelihood of $p_H$ given we observed $HH$ is $0.25$ ??
What does that even mean? Certainly it's not the same as $P(p_H | HH)$