Say I want to use Metropolis Hastings algorithm to get posterior draws of multivariate parameters.
In the one variable case, you could manipulate delta until you found something that worked (gave 40% acceptance).
However how would that work in the 2 variable case? Am I manipulating a vector of deltas that are the variance of a multivariate normal proposal distribution? How do I know if I am moving enough in both parameter spaces? Each parameter might require a different delta to move enough in their own probability space a a vector delta may not be adequate.