Geometric Sampling

This paper introduces an innovative and intuitive finite population sampling method that have been developed using a unique geometric framework. In this approach, I represent first-order inclusion probabilities as bars on a two-dimensional graph. By manipulating the positions of these bars, researchers can create a wide range of different sampling designs. This geometric visualization of sampling designs not only leads to increased creativity for researchers to provide new efficient designs but also eliminates the need for complex mathematical algorithms. This novel approach holds significant promise for tackling complex challenges in sampling, such as maximizing entropy and achieving an optimal design. By applying a version of the greedy best-first search algorithm to this geometric approach for finding an optimal design, I have demonstrated the potential for integrating intelligent algorithms into finite population sampling.