I have been racking my brains trying to understand Bayes theorem. So, the way I have understood is that the likelihood is the probability of observing the particular outcome given a set of parameter values. The prior describes our belief probabilities over the different parameter values. The denominator acts like a normaliser ensuring that the posterior is a valid distribution.
I have a couple of things I am not clear about:
1: The likelihood is a probability and the prior is a probability as well. So, why is the numerator already not normalised between 0 and 1? Assume I have not ignored any multiplicative constants when computing the likelihood.
2: One way I think of this denominator now is that if we have a bunch of numbers and we would like to normalize them between 0 and 1, one thing we can do is divide each of these numbers by their sum. Is this what the denominator in the Bayes theorem is affectively doing?