I have a quick question regarding implementation of Metropolis-Hastings for a particular problem I'm dealing with.
Suppose that I have a probability density function $P(X)$ for a continuous random variable $X$. In Metropolis-Hastings, I am required to compute acceptance probability \frac{ Pr(x') Q(x_{t}|x') } {Pr(x_{t} Q(x' | x)}. However, the probability of any single event in a continuous space is zero. Do I just replace $Pr$ with $P$ and go on my merry way?
My primary concern is that the $P(x)$ is not necessarily less than or equal to 1.