Let's say I have some data, for example $d = 0.112$. And I have a known model $m$ which just produced uniformly distributed values over the interval $[0,.5]$. I am interested in computing the likelihood of my model given the data, in the Bayesian sense, i.e. $P(D=d | M = m)$.
What is this? is it $0$?
Given $m$ is a continuous distribution, I can't see how it could be anything other than likelihood 0? More generally, I can't see how the likelihood with any continuous model could be anything other than 0. I could imagine using the probability density function, but to be honest I am not entirely sure what this would mean, and it would give a likelihood of 2, which is greater than 1 and hence not a probability.