Mendoza Manuel, Contreras-Cristán Alberto, Gutiérrez-Peña Eduardo
Departamento de Estadística, Instituto Tecnológico Autónomo de México, Río Hondo 1, Ciudad de México 01080, Mexico.
Departamento de Probabilidad y Estadística, Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas, Universidad Nacional Autónoma de México, Apartado Postal 20-126, Ciudad de México 01000, Mexico.
Entropy (Basel). 2021 Mar 8;23(3):318. doi: 10.3390/e23030318.
Statistical methods to produce inferences based on samples from finite populations have been available for at least 70 years. Topics such as and have become part of the mainstream of the statistical methodology. A wide variety of sampling schemes as well as estimators are now part of the statistical folklore. On the other hand, while the Bayesian approach is now a well-established paradigm with implications in almost every field of the statistical arena, there does not seem to exist a conventional procedure-able to deal with both continuous and discrete variables-that can be used as a kind of default for Bayesian survey sampling, even in the simple random sampling case. In this paper, the Bayesian analysis of samples from finite populations is discussed, its relationship with the notion of superpopulation is reviewed, and a nonparametric approach is proposed. Our proposal can produce inferences for population quantiles and similar quantities of interest in the same way as for population means and totals. Moreover, it can provide results relatively quickly, which may prove crucial in certain contexts such as the analysis of quick counts in electoral settings.
基于有限总体样本进行推断的统计方法至少已经存在70年了。诸如[此处原文缺失相关内容]等主题已成为统计方法主流的一部分。现在，各种各样的抽样方案以及估计量已成为统计常识的一部分。另一方面，虽然贝叶斯方法现在是一个成熟的范式，几乎在统计领域的每个领域都有影响，但似乎不存在一种常规程序——能够处理连续和离散变量——可以用作贝叶斯调查抽样的一种默认方法，即使在简单随机抽样的情况下也是如此。在本文中，讨论了来自有限总体样本的贝叶斯分析，回顾了它与超总体概念的关系，并提出了一种非参数方法。我们的提议能够以与总体均值和总量相同的方式对总体分位数和类似的感兴趣量进行推断。此外，它可以相对快速地提供结果，这在某些情况下可能至关重要，例如选举环境中的快速计票分析。
