Collaborative Research: Prior-free probabilistic inferential methods for "large-p-small-n" linear regression problems

研究人员用“大p，小n”回归分析研究无先验概率推理。这在研究者最近提出的推理模型（IMs）的新框架中成为可能。IMs产生的统计结果是概率性的，并且具有理想的频率特性。在这项研究中，研究人员开发了基于im的线性和某些非线性回归分析方法。在大p-小n回归背景下研究的一系列主题包括：(1)高斯回归模型中的变量选择；(2)稳健的Student-t回归；(3)二元回归模型。线性回归是统计应用中最常用的方法之一。然而，理想的无先验和频率校准的概率推断，特别是在重要的变量选择环境中，直到最近IMs的发展才可用。IM框架为研究人员目前面临的各种高维问题提供了一种新的和有前途的替代方法，以取代众所周知的贝叶斯和频率方法。在这项研究中，研究人员开发了新的统计方法和计算软件，为应用统计学家和科学家提供了有用的工具，他们在进行回归分析时受到非常高维数据的挑战。

The investigators study prior-free probabilistic inference with "large p, small n" regression analysis. This is made possible in the new framework of Inferential Models (IMs) proposed recently by the investigators. Statistical results produced by IMs are probabilistic and have desirable frequency properties. In this study, the investigators develop IM-based methods for linear and certain non-linear regression analysis. A sequence of topics in the context of large-p-small-n regression to be investigated include (1) variable selection in Gaussian regression models; (2) robust Student-t regression; and (3) binary regression models.Linear regression is one of the most commonly used methodologies in statistical applications. However, desirable prior-free and frequency-calibrated probabilistic inference, particularly in the important variable selection context, has not been available until the recent development of IMs. The IM framework provides a new and promising alternative to the well-known Bayesian and frequentist methods for various high-dimensional problems researchers currently face. In this study, the investigators develop new statistical methods and computing software, generating useful tools for applied statisticians and scientists who are challenged by very-high-dimensional data in carrying out regression analysis.