I am reading a paper on the differences between bayesian outlook and frequentist outlook. The exact pic from the paper is:
I have read a decent amount about what likelihood is and how it is not a probability because it is defined as a function of parameters and hence does not integrate to 1. I know about conditional probabilities, or so I think. It would seem to me that in Bayes' formula $P(D|F)$ (probability that given data (assumed iid) is observed given parameter F) should be the product of probabilities independent data points being observed given the parameter $F$ which is exactly how the likelihood in frequentist approach is defined. Why is it said that $P(D|F)$ proportional to likelihood and not equal to it?
This is from a separate source.
As you can see this also claims the same point that $P(D/F)$ is proportional to Likelihood calculated by multiplying probabilities as a function of a $\theta$. I cannot square with the language used here. I am completely clear on likelihood not being a pdf in $\theta$. I just don't understand why is $P(D/F)$ not equal to probabilities of individual samples multiplied together?