In real world applications how much do practitioners usually know about the target distribution $\pi$? do they know its form exactly? do they only know it up to constant multiple (I guess this is the case for Bayesian Inference)?
In the review https://arxiv.org/abs/1804.02719 the authors write
"As with most other simulation methods, there always exists ways of creating highly convergent MCMC algorithms by taking further advantage of the structure of the target distribution. Here, we mostly limit ourselves to the realistic situation where the target density is only known as the output of a computer code or to a setting similarly limited in its information content."
Can someone clarify what they mean here?