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

该项目解决了社会和行为科学贝叶斯模型中先验信息经常使用不足的问题，并提供了一种基于Dirichlet过程混合物应用半知情先验的方法，该混合物反映了来自观察和研究人员直觉的信息，其中两者都不占主导地位。 感兴趣的主要结果是分类选择，代表一个潜在的类变量的表现形式，假设是从一个混合的狄利克雷过程。 数据中也可能存在一些结构，如无法解释的聚类效应、单位异质性、自相关性或缺失性，这些结构对单一模型的概念产生了怀疑。 因此，研究人员建议采用非参数贝叶斯方法，而不是研究人员指定的单一形式，该方法从数据和参数条件下的适当先验分布的混合物中提取。 因此，我们使用的模型中的歧视过程的确定是在一个参数层次模型的上下文中非参数化地完成的。 这些模型通常会产生不规则和多峰后验分布，这是一个随着维数增加而加剧的问题。 研究人员提供开发自适应马尔可夫链蒙特卡罗方法，占后验拓扑结构和有效地遍历样本空间。 贝叶斯模型代表了科学推理的一个重大进步，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相对于所获得的数据集应该如何被告知，仍然存在一些争议。 该项目为社会科学研究中的半知情先验信息开发了新的范式，该范式反映了来自观察和研究人员直觉的信息，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“狄利克雷先验过程先验的混合物”在社会或行为科学中没有其他工作应用，尽管能够在这些领域促进更复杂的建模框架，从而帮助研究人员理解新的和困难的数据集中的复杂现象。 此外，该项目中的算法开发可以应用于任何科学领域，并将有助于统计文献的计算机模拟统计推断。 非参数先验族的发展将有助于解决历史上对公开主观先验规范的不信任。

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.