High-Dimensional Predictive Density Estimation

这项研究涉及一种新的预测分析方法的开发，它从历史和当前数据中提取信息，以预测未来的趋势和行为模式。贝叶斯方法对这个问题很有吸引力，因为它提供了一个完整的预测密度，为每个可能的结果分配概率，而且它自然地包含了参数估计和模型选择过程中固有的不确定性。然而，随着潜在预测者的数量增加，贝叶斯预测过程的先前规范变得具有挑战性，这是一个非常常见的问题，因为海量数据集在许多科学领域日益普遍。在这个项目中，PI研究了使用贝叶斯技术进行预测密度估计及其频率特性，然后利用这些特性来构造新的先验族，这些先验族具有期望的风险特性，适应未知的数据结构，并允许对大型和复杂的数据集进行易于处理的计算。这些先验是“最小信息量”，因为它们允许通过选择先验中心来输入主观信息，但以非常健壮的方式利用这些信息。由此产生的预测估计器有效地组合了来自不同维度的信息，从而提高了整体预测性能。从海量数据集中提取信息，并利用它来预测未来的不确定事件，这是统计学和科学的基本问题。该研究不仅为预测分析提供了强大的理论工具，而且为预测分析提供了易于实现的计算策略。它可以帮助各个领域的研究人员更好地识别风险和机会，从而优化他们的决策。方法论的发展是由金融领域的投资组合分配问题和社会科学领域的数据缺失问题推动的。拟议的程序适用于许多其他科学和技术领域，如基因组学、气候学、医学和公共卫生，这些领域收集了大量数据，需要进行准确的预测分析。例如，在卫生保健服务研究中，由于卫生保健支出在相对较小的人口比例中高度集中，预测人们未来的卫生保健成本是一个重要的主题。使用所提出的方法，人们可以更好地利用庞大的医疗和保险数据库中的信息来识别具有高健康风险的个人，并预测他们未来的医疗成本。为了方便这些新方法的使用，PI将在R或MatLab中实现程序和算法，并将该软件与相关的研究报告一起向公众开放。

This research concerns the development of a new methodology for predictive analysis, which extracts information from historical and current data to predict future trends and behavior patterns. The Bayesian approach is appealing for this problem because it provides a complete predictive density that assigns probabilities to every possible outcome, and it naturally incorporates the uncertainty inherent in the parameter estimation and model selection processes. The prior specification for Bayesian predictive procedures, however, becomes challenging as the number of potential predictors grows, an all too common problem as massive data sets are increasingly prevalent in many scientific areas. In this project, the PI investigates the use of Bayesian techniques for predictive density estimation and their frequentist properties, and then exploits those properties to construct new families of priors that have desirable risk properties, adapt to unknown data structures and also permit tractable computation for large and complex data sets. These priors are "minimally informative" in the sense that they allow input of subjective information through the choice of prior center, yet utilize this information in a very robust fashion. The resulting predictive estimators effectively combine information from different dimensions and therefore improve overall prediction performance. Applications in financial and social problems will be developed using the new methodology.Extracting information from massive data sets and exploiting it to make predictions of future uncertain events are fundamental problems in both statistics and the sciences. The proposed research provides not only powerful theoretical tools, but also easily-implementable computing strategies for predictive analysis. It can help researchers in various fields to better identify risks and opportunities, and thus to optimize their decision making. The methodological developments are motivated by a portfolio allocation problem in finance and a missing data imputation problem in the social sciences. The proposed procedures are applicable to many other scientific and technical areas, such as genomics, climatology, medical sciences and public health, where large data sets are collected and accurate predictive analysis is desirable. For example, in health care service studies, predicting people's future health care costs is an important topic given a high concentration of health care expenditures among a relatively small percentage of the population. Using the proposed methods, one may better exploit information in vast medical and insurance databases to identify the individuals with high health risks and to predict their future medical costs. To facilitate the use of these new methods, the PI will implement the procedures and algorithms in R or Matlab, and make this software available to the public along with the associated research reports.