I just learned about likelihood from Wikipedia. It says that the likelihood of outcome $X$ given parameters $θ, L(X|θ)$ -- equals the probability of parameters θ given $X, P(θ|X)$.
I am trying to understand this paper, which on page 2 seems to talk about the likelihood of a sample (p-tilde) given the model $p$
To me, the statement above seems to translate to "the likelihood of an observed sample (p-tilde) given the model p is equivalent to the sum of all empirically observed likelihoods of each symbol $y *$ the $log$ of the probability of $y$.
But how does that have to do with the wikipedia definition of likelyhood? Does the model, p, implicitly include the parameters of the model, θ? Also, do the three bars in the equation above indicate that the thing on the left is monotonically related to the thing on the right? Wikipedia on monotonic functions does not mention this notation.