Bayesian Methods for Variable Selection in Generalized/Nonlinear Models

目前的提案是建立在P.I.的基础上的她在变量选择方面的经验，并总结了她在贝叶斯方法发展方面的当前和未来方向。特别地，P.I.计划考虑扩展到广义模型和允许一组变量与响应的任意非线性关联的模型。所提出的模型的推理策略比先前工作中P.I.解决的典型线性设置更具挑战性。此外，将研究非参数先验，目的是锐化模型的选择和放松分布假设，例如随机效应和误差项，这些在实际数据应用中经常受到质疑。通过这个项目开发的方法可能对统计学和高维/小样本量数据产生的应用领域产生重大影响。对跨学科合作产生的数据的应用将证明所提出方法的实际用途。特别是，P.I.计划建立在她最近对脑成像数据的兴趣上，通过研究贝叶斯方法在变量选择中的应用和扩展，目前用于分析这些数据的广义线性和混合模型。这项建议的更广泛影响在于其教育和培训目标、传播成果的努力以及拟议研究的协作性质。私家侦探维护一个更新的网页，她的研究活动，论文和配套软件张贴在及时的方式。

The current proposal builds upon the P.I.'s experitize in variable selection and summarizes her current and future directions in the development of Bayesian methodologies. In particular, the P.I. plans to consider extensions to generalized models and to models that allow arbitrary nonlinear associations of a set of variables to a response. Inferential strategies for the proposed models are more challenging than the typical linear settings addressed by the P.I. in previous work. In addition, nonparametric priors will be investigated with the purpose of sharpening the selection and relaxing distributional assumptions of the models, such as those on random effects and on the error terms, often questionable in real-data applications.Methodologies developed through this project carry potential for significant impact in statistics and in applied fields in which high-dimension/low-sample-size data arise. Applications to data arising from interdisciplinary collaborations will demonstrate the practical usefulness of the proposed methods. In particular, the P.I. plans to build upon her recent interest in brain imaging data by investigating applications and extensions of Bayesian methods for variable selection to generalized linear and mixed models currently used for the analysis of such data. The broader impacts of this proposal are in its educational and training objectives, in its efforts to disseminate results and in the collaborative nature of the proposed research. The P.I. maintains an updated webpage on her research activities where papers and accompanying software are posted in a timely manner.