On a Directionally Adjusted Metropolis-Hastings Algorithm

We propose a new Metropolis-Hastings algorithm for sampling from smooth, unimodal distributions; a restriction to the method is that the target be optimizable. The method can be viewed as a mixture of two types of MCMC algorithm; specifically, we seek to combine the versatility of the random walk Metropolis and the efficiency of the independence sampler as found with various types of target distribution. This is achieved through a directional argument that allows us to adjust the thickness of the tails of the proposal density from one iteration to another. We discuss the relationship between the acceptance rate of the algorithm and its efficiency. We finally apply the method to a regression example concerning the cost of construction of nuclear power plants, and compare its performance to the random walk Metropolis algorithm with Gaussian proposal.