I am new to Bayesian methods. I was going through a chapter on sampling. I have a few questions related to it. Please help me get these clarified.
As far as I understand, rejection sampling will not overestimate the density of the target distribution. This is inherent in it's acceptance probability. Do we always get exact density if we sample enough and if we have appropriate proposal distribution?
How many samples are usually rejected in rejection sampling? Is there a general formula to determine this?
How to determine the constant c for the proposal distribution such that c*Q(x) > P(x)? Is there any trick if we cannot visualize the distribution??(Especially in high dimensional cases?
This is related to previous question? Do people use rejection sampling alone while sampling from high dimensional distributions? Or is it used say in combination with Gibbs sampling? I would prefer the latter. But is the former better than the latter in any case?