The Metropolis-Hastings algorithm has been important in the recent development of Bayes methods. This algorithm generates random draws from a target distribution utilizing a sampling (or proposal) distribution. This article compares the properties of three sampling distributions - the independence chain, the random walk chain, and the Taylored chain suggested by Geweke and Tanizaki (Geweke, J., Tanizaki, H. (1999). On Markov Chain Monte-Carlo methods for nonlinear and non-Gaussian state-space models. Communications in Statistics, Simulation and Computation 28(4):867-894, Geweke, J., Tanizaki, H. (2001). Bayesian estimation of state-space model using the Metropolis-Hastings algorithm within Gibbs sampling. Computational Statistics and Data Analysis 37(2):151-170).
Geweke et al. (Sat,) studied this question.