Why do some references say "likelihood of the data" instead of "likelihood of the parameter"?
I learned at the university that the terminology should be probability of the data and likelihood of the parameter (or model), because when the variable is the data, the probability integrates to one, and when the variable is the parameter, the likelihood may not.
But looking at several references, e.g. GES, EM, Scholar search, Wikipedia search, I've found a mixed use of the two phrases. Surprisingly, in Wikipedia, they start nicely saying that it's called likelihood function because some parameters are more likely, but then they talk repeatedly about "likelihood of the data/observation".
Is it a spread misuse, or a misunderstanding or overreaction from my side?