Minimum energy representative points

The selection of a small number of representative points (RPs) that retain as much useful information as possible for representing a huge original data set or a target distribution is one of the most significant obstacles in many real-life applications. Finding a discrete distribution (i.e., RPs and their probabilities) for estimating a continuous distribution is frequently requested. There are many applications of RPs in uncertainty quantification, cluster analysis, Bayesian analysis, signal compression, statistical simulation and numerical integration. Monte Carlo RPs, Quasi-Monte Carlo RPs and Minimum mean square error RPs are the frequently used recommended classes of RPs. This paper investigates the performance of a new class of RPs, called minimum energy RPs (ME-RPs), which minimize the total electric potential energy among the RPs from physics viewpoint by assuming that these points are positively charged particles in a closed system. The performance of the ME-RPs is evaluated and compared with the existing recommended RPs from various perspectives, such as statistical inference, resampling and kernel density estimation. The main results demonstrate that the ME-RPs are superior to the existing recommended RPs for many cases. As a result, this paper urges statisticians to pay significant attention to the ME-RPs in order to provide theoretical and computational improvements for generating ME-RPs that meet practical needs.