Advances and Applications in Bayesian Density Regression

贝叶斯密度回归的进展和应用

• 批准号: 1156372
• 负责人: George Karabatsos
• 金额: $ 28万
• 依托单位: University of Illinois at Chicago
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2012
• 资助国家: 美国
• 起止时间: 2012-06-15 至 2016-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1156372&HistoricalAwards=false
• 关键词: Advances; Applications; Bayesian; Density; Regression

In many areas of empirical research, regression models often are used to make predictions in order to answer questions that aim to advance research and society. Such advancements hinge critically on accurate predictions. Commonly used regression models, however, can yield inaccurate predictions because they make questionable assumptions that often are violated by data. Questionable assumptions include that the dependent variable has linear relationships with the predictor variables, that the variance of the dependent variable does not change with the predictor variables, and that the dependent variable and random predictor effects are normally distributed. This research will investigate and develop a Bayesian nonparametric (BNP) regression model that allows the entire distribution (density) of the dependent variable to change flexibly and nonlinearly with the predictor variables. The BNP model will be defined by a predictor-dependent infinite mixture of unimodal distributions, with each unimodal distribution modeled by an infinite mixture of uniform distributions. A prior distribution on all parameters will complete the specification of the BNP model. The BNP regression model and a multi-level version of the model will be applied to analyze at least three large data sets: (1) to evaluate the effect of a new teacher education curriculum on the basic skills of its students; (2) to study the conditions under which urban school students find texts meaningful to read; and (3) to study the predictors of heritability of antisocial behavior in a meta-regression analysis. Furthermore, the performance of the BNP regression model will be evaluated through the analysis of many simulated data sets for a wide range of data-generating conditions. For all the real and simulated data sets, it is expected that the BNP model will show better predictive accuracy and will provide more scientific insights when compared with other regression models in common use.The research project will advance statistical science through the development and thorough investigation of a novel BNP regression model. This model is expected to outperform other regression models that currently are used for making predictions. Through the analysis of the three large data sets, the research will advance knowledge and scientific understanding of important societal issues, including best practices for K-12 math, science, and literacy education and the treatment of youth with emotional and behavioral disabilities. Finally, for a broad audience of researchers, this project will provide user-friendly software for performing data analysis with the BNP regression model. This will help further promote more accurate answers to research questions that are important to society.

在实证研究的许多领域，回归模型经常被用来做出预测，以回答旨在推进研究和社会的问题。这些进步关键取决于准确的预测。然而，常用的回归模型可能会产生不准确的预测，因为它们做出了有问题的假设，而这些假设经常被数据所违背。有问题的假设包括因变量与预测变量有线性关系，因变量的方差不随预测变量而变化，因变量和随机预测变量效应是正态分布的。本研究将研究和开发一个贝叶斯非参数（BNP）回归模型，该模型允许因变量的整个分布（密度）随预测变量灵活地非线性变化。BNP模型将由依赖于预测的无限混合单峰分布来定义，每个单峰分布由均匀分布的无限混合来建模。所有参数的先验分布将完成BNP模型的规范。本文将运用BNP回归模型和该模型的多级版本来分析至少三个大数据集：(1)评估新教师教育课程对学生基本技能的影响；(2)研究城市学校学生发现文本有阅读意义的条件；(3)对反社会行为遗传力的预测因素进行meta回归分析。此外，BNP回归模型的性能将通过分析许多模拟数据集来评估，用于广泛的数据生成条件。对于所有真实数据集和模拟数据集，期望BNP模型与其他常用的回归模型相比具有更好的预测精度，并提供更科学的见解。该研究项目将通过开发和深入研究一种新的BNP回归模型来推进统计科学。预计该模型将优于目前用于预测的其他回归模型。通过对三个大型数据集的分析，这项研究将促进对重要社会问题的认识和科学理解，包括K-12数学、科学和识字教育的最佳实践，以及患有情感和行为障碍的青少年的治疗。最后，对于广大研究人员，该项目将提供用户友好的软件，用于使用BNP回归模型进行数据分析。这将有助于进一步促进对社会重要的研究问题的更准确的答案。