A Markov chain Monte Carlo construction of space-filling Latin Hypercube Samples

This paper aims to construct Latin Hypercube Samples (LHSs) with enhanced repulsion between their points. Our main contribution is a novel Markov chain Monte Carlo algorithm designed to generate an LHS with a large Euclidean distance between each pair of points, thus promoting better spread. The proposed algorithm is a Metropolis–Hastings algorithm that defines a Markov chain whose stationary distribution favors samples with greater separation between points. The convergence of the algorithm is rigorously Moreover, numerical experiments are presented to demonstrate that the LHSs produced by our algorithm exhibit improved point distribution, leading to better uniform coverage of the sampling space compared to standard Latin Hypercube designs. In addition, the method yields a diverse collection of designs with better spread of points (reflected in small values of a scattering criterion), highlighting the value of variety among well-performing designs.