Statistical inference in the big data era: using hierarchical models to estimate the socio-economic situation of Colombia's armed conflict victims wit

本研究旨在提供一种新的方法来产生非概率样本和多来源(即大数据)下的有限总体估计。尽管这种方法可能在社会科学的不同领域有许多应用，但这项研究将集中在一项将对哥伦比亚最脆弱人口产生重大影响的具体活动上。这项研究将试图对哥伦比亚武装冲突受害者的社会经济状况提供不可信的有限人口估计。有了这些信息，哥伦比亚政府将能够制定出足够详细和有影响的政策和预算，以改善近20%总人口的生活。此外，这种方法将有助于统计和人口科学以及从多个社会科学中获得的推论。自20世纪头几十年以来，随着基于设计的技术的快速发展，概率抽样一直是黄金标准。与此同时，“大数据”使研究人员、政府和公司等能够以更快、更容易和负担得起的方式访问大量数据。然而，这种不断增长的趋势对传统的统计推理方法提出了挑战。这些现代数据收集方法中有许多不符合概率抽样标准，因此产生了非概率样本。这些样本可能会导致有限总体估计中的推理问题。本研究方案侧重于应用贝叶斯推理和分层模型作为一种替代方法来提高估计的精度，并在非概率样本下确定其不确定性水平。

The present research aims to provide a novel approach to produce finite-population estimates under nonprobabilitysamples and multiple sources (i.e. big data). Although such a method might have numerousapplications in diverse areas of the social sciences, this research will concentrate on a specific exercisethat will significantly impact Colombia's most vulnerable population. The study will attempt to provideconfident finite-population estimates of the socio-economic situation of the armed conflict victims inColombia. With such information, the Colombian Government will be able to produce policies andbudgets with sufficient detail and impact to improve the lives of nearly 20% of the total population.Furthermore, such a methodology will contribute to the statistical and demographic sciences andinferences obtained in multiple social sciences.Probability sampling has been a gold standard since the early decades of the 20th century with rapiddevelopments of design-based techniques. At the same time, "big data" has allowed researchers,governments, and companies, among others, to access large amounts of data in a faster, easier andaffordable manner. However, this increasing trend has challenged traditional methods for statisticalinference. Many of these modern data-collection methods are not in line with the probability samplingstandards, therefore producing non-probability samples. These samples may induce inference problemsin finite-population estimation. This research proposal focuses on applying Bayesian inference andhierarchical models as an alternative approach to improve the precision of the estimates and determinetheir uncertainty levels under non-probability samples.