Collaborative Research: Identifying Structure in Social Data Models using Markov Chain Monte Carlo Algorithms

对社会科学数据的分析往往是困难的，其原因往往对其他领域的影响不大。 传统统计模型特别难以处理的一个问题是故意保留与感兴趣的现象密切相关的信息。 这样的信息可以被认为是数据中未观察到的聚类。 该项目将使用广义线性混合狄利克雷模型（GLMDM）大大改善基于模型的聚类算法的现状。 研究人员的主要目标是：（1）更好地理解在社会科学数据集中普遍存在的未观察到的聚类效应，特别是在恐怖主义的实证研究中;（2）调整GLMDM算法，通过使用协变量信息的后验概率提供实质性的兴趣聚类;（3）开发一种算法方法，直接将聚类中的变量选择纳入一般聚类模型;（4）通过并行化加速同时聚类和变量选择过程;（5）将该技术作为易于使用的R软件包分发给其他人使用。本项目将建立一种新的方法，使用贝叶斯非参数方法来产生基于后验概率的聚类。 非参数聚类算法的发展有望大大改善数据聚类的现状。 算法的发展，这将被广泛传播，可以应用于任何科学领域，并将有助于马尔可夫链蒙特卡罗的统计文献。 这一新方法将被应用于恐怖主义的实证研究。 该项目还将帮助学生和博士后研究人员的智力发展，他们将从该项目的跨学科重点中受益。

The analysis of social science data is often difficult for reasons that tend to affect other fields less substantially. One problem that is particularly difficult to handle with traditional statistical models is deliberately withheld information that correlates strongly with phenomena of interest. Such information can be thought of as unobserved clustering in the data. This project will substantially improve the current state of model-based clustering algorithms using Generalized Linear Mixed Dirichlet Models (GLMDM). The investigators' key objectives are to: (1) better understand unobserved clustering effects that are pervasive in social science datasets, notably with empirical studies of terrorism; (2) adapt GLMDM algorithms to provide substantive clusters of interest through posterior probabilities using covariate information; (3) develop an algorithmic approach that directly includes variable selection within clusters into a general clustering model; (4) speed up the simultaneous clustering and variable selection process by parallelization; and (5) distribute this technology as an easy-to-use R package for general use by others.This project will establish a new approach for using Bayesian nonparametric methods to produce clustering based on posterior probabilities. The development of nonparametric clustering algorithms is expected to substantially improve the current state of data clustering. The algorithmic developments, which will be disseminated widely, can be applied in any scientific field and will contribute to the statistical literature on Markov chain Monte Carlo. This new approach will be applied to the empirical study of terrorism. The project also will aid in the intellectual development of students and a post-doctorate researcher who will benefit from the project's interdisciplinary focus.