Bayesian statistics proof question

#1
I know that if the prior distribution is chosen to be a continuous
uniform distribution, then the exact posterior distribution will simply the
normalized version of the likelihood function. I was wondering how i would write this out as a proof?
 

JesperHP

TS Contributor
#2
\(Pr(\theta \lvert y) = \frac{L(y\lvert\theta)Pr(\theta)}{Pr(y)} \propto L(y\lvert\theta)Pr(\theta) \propto L(y\lvert\theta) \)
where the last proportionality statement follows from assuming that the prior is uniform, hence having a density equal to a constant.