New Directions in Quantile-based Modeling and Analysis

分位数作为一种数据描述和分析工具，在统计学中已经有一百多年的历史。近年来，分位数建模的研究，包括协变量的影响，并处理多元数据加速响应的需求，从广泛的应用领域。 调查解决了一个重要的，但往往被忽视的问题，后验推理的有效性分位数回归的伪贝叶斯方法，已成为流行的文献。调查人员进行了仔细的调查如何选择一个工作的可能性和选择一个事先发挥各自的作用，无论是在有限样本问题，并在渐近理论。研究人员研究了一类新的收缩先验作为渐近框架，以了解贝叶斯方法在数据稀疏区域和高维协变量问题中估计和预测分位数的效率增益。该研究将加深我们对伪后验推理有效性的理解，并为分位数回归在单或多个分位数水平上提出渐近有效和高效的推理方法。这项研究还将促进一个新的伪贝叶斯框架，用于分位数回归之外的模型选择。此外，研究者还研究了多元数据分位数的新概念，所提出的活动将激发分位数建模和贝叶斯推理领域的新颖想法和批判性思维。新的见解和新的工具将有助于估计，预测和假设检验有关罕见事件的气候研究，公共卫生和其他科学工作。 多变量分位数的概念将导致一个有效的统计降尺度方法，更好地预测局部尺度的气候。拟议的活动将使研究生直接参与，作为其学术培训的一部分。调查员将与其他研究人员和科学家合作，确保研究结果适当地传播给广大科学界。

Quantile as a data descriptive and analytic tool has earned its place in statistics for over a hundred years. In recent years, research on quantile modeling to incorporate the effect of covariates and to handle multivariate data has accelerated in response to the needs arising from a broad area of applications. The investigator addresses an important but often neglected question on the validity of posterior inference on quantile regression for the pseudo-Bayesian methods that have become popular in the literature. The investigator conducts a careful investigation into how the choice of a working likelihood and the choice of a prior play their respective roles, both in finite-sample problems, and in the asymptotic theory. The investigator studies a new class of shrinking priors as an asymptotic framework to understand the efficiency gains of the Bayesian methods for estimation and prediction of quantiles in data sparse areas and in problems involving high dimensional covariates. The proposed research will deepen our understanding of the validity of pseudo-posterior inference and suggest asymptotically valid and efficient inferential methods for quantile regression at single or multiple quantile levels. The research will also facilitate a new pseudo-Bayesian framework for model selection beyond quantile regression. Furthermore, the investigator studies a new notion of quantile for multivariate data.The proposed activities will stimulate novel ideas and critical thinking in the areas of quantile modeling and Bayesian inference. The new insights and the new tools to be developed will be useful for estimation, prediction, and hypothesis testing regarding rare events in climate research, public health, and other scientific endeavors. The notion of multivariate quantiles will lead to an efficient statistical downscaling method for better climate projections at localized scales. The proposed activities will engage graduate students directly as part of their academic training. The investigator will work with other researchers and scientists to ensure that the research results are disseminated appropriately to the broad scientific community.