Expanding the Computational Statistics Toolbox for General Hierarchical Models

分层统计模型允许分析复杂数据中的模式，同时考虑时间或空间模式或共享采样单位等关系。统计研究人员已经开发了大量针对分层模型的分析算法，但社会科学家和生物学家等从业者无法使用这些算法。Nimble软件平台的开发就是为了弥合这一差距，并使科学家更容易在他们的特定数据集上使用各种算法。特别是，Nimble提供了一个编程环境，研究人员可以在其中实现算法，然后其他人可以很容易地在特定数据集的上下文中使用这些算法。该项目下的工作将扩展Nimble，以提供计算方法，用于使用非常灵活的统计方法，即贝叶斯非参数方法。这些方法允许研究人员总结变量并量化分析中不同变量之间的关系，同时比标准统计方法做出的假设更少。虽然贝叶斯非参数方法在过去的10-15年里有了很大的发展，但对于那些处理数据的人来说，这些方法中的许多都很难或很耗时。这个项目将在Nimble软件中实现许多这样的方法，从而将它们提供给从业者在他们的日常分析中使用。此外，它还将为未来不断开发和共享新的和改进的此类方法提供基础。大量研究旨在改进用于分析分层统计模型的统计和计算方法。这样的研究很重要，因为特定问题的层次模型促进了许多科学领域的快速发展。然而，统计研究人员一直缺乏一个灵活的软件平台，设计用于编程和传播许多不同的算法，如马尔可夫链蒙特卡罗、顺序蒙特卡罗和建立在它们之上的方法。Nimble系统提供了这样一个软件平台。该项目通过扩展Nimble系统来进一步填补这一空白，使其能够使用贝叶斯非参数方法，重点是非参数混合模型，其中Dirichlet过程模型和相关模型是广为人知的。这一扩展将允许将这些非参数混合模型作为任意分层模型的部分的先验分布进行常规应用。该项目将实施适合贝叶斯非参数混合的各种技术，重点是马尔可夫链蒙特卡罗算法中的折叠和阻塞采样器。这些技术方法已经得到专家们的高度发展，但由于缺乏普遍的实施，其研究和科学应用受到限制。

Hierarchical statistical models allow analysis of patterns in complex data while accounting for relationships such as temporal or spatial patterns or shared sampling units. A great variety of analysis algorithms for hierarchical models have been developed by statistical researchers but are unavailable to practitioners such as social scientists and biologists. The NIMBLE software platform was developed to bridge this gap and make it easier for scientists to use a variety of algorithms on their specific datasets. In particular NIMBLE provides a programming environment in which researchers can implement algorithms that can then be easily used by others in the context of specific datasets. The work under this project will extend NIMBLE to provide computational methods for working with very flexible statistical methods known as Bayesian nonparametric methods. These methods allow researchers to summarize variables and quantify relationships between different variables in an analysis while making fewer assumptions than standard statistical approaches. While Bayesian nonparametric methods have developed substantially in the last 10-15 years, many of these methods are hard or time-consuming for those working with data to implement on their own. This project will implement many such methods in the NIMBLE software, thereby providing them to practitioners to use in their day-to-day analyses. Moreover, it will provide a foundation for ongoing development and sharing of new and improved such methods in the future.A large amount of research aims to improve the intertwined statistical and computational methods for analysis of hierarchical statistical models. Such research is important because problem-specific hierarchical models facilitate rapid advances in many scientific fields. However, statistical researchers have lacked a flexible software platform designed for programming and disseminating the many varieties of algorithms such as Markov chain Monte Carlo, sequential Monte Carlo, and methods that build upon them. The NIMBLE system provides such a software platform. This project helps to further fill that gap by extending the NIMBLE system to enable use of Bayesian nonparametric methods, with a focus on nonparametric mixture models, of which the Dirichlet process model and related models are widely-known. This extension will allow routine application of these nonparametric mixture models as prior distributions for parts of arbitrary hierarchical models. The project will implement a variety of techniques for fitting Bayesian nonparametric mixtures, focusing on both collapsed and blocked samplers in Markov chain Monte Carlo algorithms. Such techniques methods have been highly developed by specialists but are limited in their research and scientific applications by lack of general implementation.