I have a really basic question. But I am a little bit confused about that. How do I calculate the acceptance ratio within a Metropolis-Hasting step?
I have something like $min\left\{1,\frac{p(new)}{p(old)}\times \frac{h(old)}{h(new)}\right\}$.
Is $p(x)$ the DENSITY at point $x$ and $h(x)$ the PROBABILITY at point $x$? Or is it true that $h(x)$ is also the DENSITY at point $x$? That means I have to calculate the DENSITIES only and never the PROBABILITIES?
Sorry for this basic question, but some people/books mesh up this terms and no I'm really confused.