QMC sampling from empirical datasets

This paper presents a simple idea for the use of quasi-Monte Carlo sampling with empirical datasets, such as those generated by MCMC methods. It also presents and analyses a related idea of taking advantage of the Hilbert space-filling curve. Theoretical and numerical analyses are provided for both. We find that when applying the proposed QMC sampling methods to datasets coming from a known distribution, they give similar performance as the standard QMC method directly sampling from this known distribution