Collaborative Research: Adaptive Nonparametric Markov Chain Monte Carlo Algorithms for Social Data Models with Nonparametric Priors

协作研究：具有非参数先验的社会数据模型的自适应非参数马尔可夫链蒙特卡罗算法

• 批准号: 0631588
• 负责人: George Casella
• 金额: $ 17.25万
• 依托单位: University of Florida
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2007
• 资助国家: 美国
• 起止时间: 2007-01-01 至 2010-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0631588&HistoricalAwards=false
• 关键词: Collaborative; Research; Adaptive; Nonparametric; Markov

This project addresses the frequent under-use of prior information in social and behavioral science Bayesian models, and provides a means of applying semi-informed priors based on mixtures of Dirichlet processes that reflect both information from observations and researcher intuition where neitherdominates. The primary outcomes of interest are categorical selections representing manifestations of a latent class variable, assumed to be drawn from a mixture of Dirichlet processes. There may also be structures in the data such as unexplained clustering effects, unit heterogeneity, autocorrelation, or missingness that cast doubt on the notion of a single model. So rather than researcher specification of a single form, the investigators suggest, a nonparametric Bayesian approach that draws from a mixture of appropriate prior distributions conditional on data and parameters. Thus the determination of the discrimination processes in the models we use is done nonparametrically in the context of a parametric hierarchical model. These models typically produce irregular and multimodal posterior distributions, a problem exacerbated with higher dimension. The investigators provide develop adaptive Markov chain Monte Carlo methods that account for posterior topology and efficiently traverse the sample space. Bayesian models represent a major improvement in scientific inference because they allow the incorporation of prior information that researchers or outside experts may have. Yet there remains some controvery about how informed these prior specifications should be relative to an acquired set of data. This project develops new paradigm for semi-informed prior information in social science research that reflects both information from observations and researcher intuition, where neither dominates. This is not possible without new simulation tools, which the investigators develop. Currently, there are no other working applications of these "mixtures of Dirichlet prior process priors" in the social or behavioral sciences, despite being able to facilitate more sophisticated modeling frameworks in these areas thus helping researchers understand complex phenomena in new and difficult datasets. Furthermore, the algorithmic developments in this project can be applied in any scientific field and will contribute to the statistical literature on computer simulation for statistical inference. The development of nonparametric prior families will help resolve the historical distrust of overtly subjective prior specifications.

该项目解决了社会和行为科学贝叶斯模型中经常使用的先验信息不足的问题，并提供了一种应用基于狄利克雷过程混合的半知情先验的方法，该方法反映了来自观察和研究者直觉的信息，其中两者都不占主导地位。感兴趣的主要结果是代表潜在类别变量表现的分类选择，假设从Dirichlet过程的混合物中提取。数据中也可能存在结构，如无法解释的聚类效应、单位异质性、自相关或缺失，这些结构使人们对单一模型的概念产生怀疑。因此，研究人员建议采用一种非参数贝叶斯方法，而不是单一形式的研究人员说明，该方法从数据和参数条件下适当的先验分布的混合物中提取。因此，在我们使用的模型中判别过程的确定是在参数分层模型的背景下非参数地完成的。这些模型通常会产生不规则和多模态的后验分布，随着维度的增加，这个问题会加剧。研究人员提供了发展自适应马尔可夫链蒙特卡罗方法，该方法考虑后验拓扑并有效地遍历样本空间。贝叶斯模型代表了科学推理的重大进步，因为它们允许将研究人员或外部专家可能拥有的先验信息结合起来。然而，关于这些先前的规范应该如何与获得的一组数据相关联，仍然存在一些争议。该项目开发了社会科学研究中半知情先验信息的新范式，反映了来自观察和研究者直觉的信息，两者都不占主导地位。如果没有研究人员开发的新的模拟工具，这是不可能的。目前，这些“Dirichlet先验过程先验的混合”在社会或行为科学中还没有其他有效的应用，尽管能够在这些领域促进更复杂的建模框架，从而帮助研究人员在新的和困难的数据集中理解复杂的现象。此外，该项目的算法发展可以应用于任何科学领域，并将有助于统计推断的计算机模拟统计文献。非参数先验族的发展将有助于解决历史上对明显主观先验规范的不信任。