Understanding Regression Heterogeneity Through Joint Estimation of Conditional Quantiles

在许多数据驱动的科学调查中，主要目标是了解响应变量和一组预测因素之间的关系。标准统计技术试图通过平均反应的变化来检测和量化这种关系的性质。然而，在现实世界中，预测-反应关系往往更加复杂和微妙。在气候科学、生态学、经济学、公共卫生和社会学等学科中，研究人员往往对了解极端反应百分位数的变化感兴趣。通过量化一个人从平均到极端的变化速度如何变化，可以获得更多的洞察力。该项目旨在开发先进的、理论上可靠的统计工具，能够从大型和复杂的数据集中回答这些问题。统计工具是在最近流行的线性分位数回归建模框架内寻找的。所提出的框架将线性分位数回归的范围扩展到响应变量表现出额外相关性的场景。这种依赖性表现在许多常见情况中，例如，当一个人同时测量每个观察单位的多个响应变量时，当随着时间的推移重复测量响应时，或者当从个体网络中提取数据时。分位数回归的前景与其更广泛的适用性之间的障碍是缺乏一个适当的基于模型的估计框架。PI最近引入了一个建模框架，该框架导致在任意预测器空间上基于贝叶斯或惩罚似然的线性分位数平面的联合估计。拟议的模型扩展用自回归和Copula公式增强了这一框架，以解决观测单位之间的各种结构依赖。该项目将使用基于随机计算的先进贝叶斯技术和R包形式的公开开源软件开发高效的推理算法。软件开发将可能利用分布式计算体系结构来为大数据提供可伸缩性。对于所有的模型扩展，PI还将通过建立贝叶斯参数估计的大样本分布理论，对模型性能的理论保证进行尖锐的分析。

In many data-driven scientific investigations, the primary goal is to understand the relationship between a response variable and a set of predictors. Standard statistical techniques attempt to detect and quantify the nature of such relationships through changes in the average response. However, in the real world, predictor-response relationships are often more complex and nuanced. In disciplines like climate science, ecology, economics, public health and sociology, investigators are often interested in understanding changes to the extreme response percentiles. Additional insights are gained by quantifying how the rate of change varies as one moves from the average to the extremes. This project aims to develop sophisticated and theoretically sound statistical tools that can answer these questions from large and complex data sets. Statistical tools are sought within the recently popularized modeling framework of linear quantile regression. The proposed framework expands the scope of linear quantile regression to scenarios where the response variables exhibit additional dependency. Such dependency manifests in many common situations, e.g., when one simultaneously measures multiple response variables per observation unit, when a response is measured repeatedly over time, or, when data is drawn from a network of individuals. Standing between the promise of quantile regression and its wider applicability is the lack of a proper model-based estimation framework. The PI has recently introduced a modeling framework that leads to Bayesian or penalized likelihood based joint estimation of linear quantile planes over arbitrary predictor spaces. Proposed model extensions augment this framework with autoregressive and copula formulations to address various kinds of structural dependency between the observation units. The project will develop efficient inference algorithms using advanced Bayesian techniques based on stochastic computation, and public, open source software in the form of R packages. Software development will incorporate possible leveraging of distributed computing architectures to render scalability to big data. For all model extensions, the PI will also carry out sharp analyses of theoretical guarantees on model performance by working out the large sample distribution theory of Bayesian parameter estimates.