Modified Metropolis-Hastings Algorithm for Efficient Sampling from Discrete Probability Distributions (MMH-DPD) Applied to Field Operational Tests database (SPMD)

Abstract

Metropolis-Hastings algorithm (MH) is the most popular Markov Chain Monte Carlo (MCMC) method. Essentially, the MH algorithm generates a sample, accepts or rejects the sample based on an acceptance probability that is related to the continuous target probability distribution. In this work, we propose a modified Metropolis-Hastings algorithm (MMH-DPD) that can draw samples from discrete probability distributions. For starters, the discrete probability distribution is replaced with a multimodal distribution and a new step after the rejection and acceptation step is added to the original algorithm. To reduce the error caused by the tail of the multimodal distribution, we used a mixture of Generalized Gaussians instead. Numerical results and a generalization of the proposed algorithm are provided. Our simulations show that the proposed sampler reliably creates a Markov chain that generates a sequence of values, in such a way that as the number of samples goes to infinity, we can guarantee that they reflect samples from the target discrete distribution.