Computational Issues in Model Elaboration, Diagnostics and Estimation

现代统计模型的复杂程度和复杂程度有不同的后果。这个项目涉及两个重要的、相关的方面。首先，人们如何评估模型的特定特征是否提供了正在研究的现象的准确表示？此外，如果某些特征被识别为有问题，那么应该朝哪个方向修改它们以提高模型的适合性？其次，随着模型变得越来越复杂，模型的拟合也变得更加困难。如果认为只有原始的计算能力就能跟上日益增长的复杂性，那就大错特错了。需要新的算法方法来应对现代建模实践带来的挑战。在功能更强大的计算机上使用的旧技术可能只会运行更长时间，而不会产生所需的输出。该项目在贝叶斯层次模型的理论性质和其他统计学领域(如时间序列分析和聚类分析)之间建立了一些重要和新颖的联系，导致了模型诊断和细化领域的进步，并开发了一类有效的贝叶斯混合模型拟合算法。最近计算资源的进步为建模人员提供了前所未有的机会，以非常现实的方式描述现实生活和自然现象。由于现实本质上是复杂的，现实模型往往非常复杂。对准确和可靠的建模的需要怎么强调都不为过。公共政策决策通常是根据预测经济和社会指标、预测环境因素、评估疾病爆发可能性等的概率模型作出的。模型中的微小缺陷和很小的估计误差可能会对广大人民的福祉产生影响。拟议的研究将开发跨学科的转换方法，并可用于在各种环境中改进建模和预测。建议的应用领域包括PI由于正在进行的合作而最熟悉的领域(量化心理学、市场营销和以患者为导向的医学调查)，但这项研究显然也有可能对其他领域产生影响。例如，有限混合分布模型是具体的研究主题之一，被用于各种应用环境，如人类遗传学和监测世界范围内的核试验，以区分爆炸和地震。该项目也有一个明确的教育重点，无论是在培训将在研究活动中协助PI的研究生方面，还是在提醒更广泛的研究界注意健全和现代建模战略的必要性方面。

The degree of complexity and sophistication in modern statistical models has various consequences. This project addresses two important, related aspects. First, how can one assess if specific features of a model provide an accurate representation of the phenomenon under study? Further, if some features are identified as problematic, in what direction should they be modified to improve the fit of the model? Second, as models become more complicated, fitting the models also becomes harder. It would be a mistake to think that raw computing power is all that is needed to keep pace with the increasing complexity. Novel algorithmic approaches are needed to tackle the challenges posed by modern modeling practices. Old techniques used on more powerful computers might only run longer, without producing the desired output. This project establishes some important and novel connections between the theoretical properties of Bayesian hierarchical models and some other areas of statistics, such as time series analysis and cluster analysis, leading to advances in the area of model diagnostics and elaboration and to the development of an effective class of algorithms for fitting Bayesian mixture models.Recent advances in computational resources have afforded modelers unprecedented opportunities to describe real life and natural phenomena in very realistic terms. As reality is inherently complex, realistic models tend to be highly sophisticated. The need for accurate and reliable modeling cannot be overemphasized. Publicpolicy decisions are routinely made on the basis of probabilistic models that forecast economic and social indicators, predict environmental factors, assess the potential for disease outbreak, etc. Small deficiencies in the models and little estimation inaccuracies can have consequences that might impact on the welfare of largenumbers of people. The proposed research will develop translational methodology that cuts across disciplines and can be used to improve modeling and forecasting in a variety of settings. Suggested areas of application include those with which the PI is most familiar because of his ongoing collaborations (quantitative psychology, marketing, and patient oriented medical investigation) but there is clear potential for the research to have an impact on other areas as well. For example, finite mixture distributions models, one of the specific research themes, are used in applied settings as diverse as human genetics and the monitoring of worldwide nuclear testing to tell explosions apart from earthquakes. The project also has a clear educational focus, both in terms of training of the graduate students who will assist the PI in the research activities and in terms of alerting the broader research community to the need for sound and modern modeling strategies.