Write an essay on the rôle of the Metropolis-Hastings algorithm in computational Bayesian inference on a parametric model. You may for simplicity assume that the parameter space is finite. Your essay should:

(a) explain what problem in Bayesian inference the Metropolis-Hastings algorithm is used to tackle;

(b) fully justify that the algorithm does indeed deliver the required information about the model;

(c) discuss any implementational issues that need care.