Computational Issues in Model Elaboration, Diagnostics and Estimation

现代统计模型的复杂程度和精密程度有各种后果。 该项目涉及两个重要的相关方面。 首先，如何评估一个模型的具体特征是否能准确地代表所研究的现象？ 此外，如果某些特征被识别为有问题，应该在什么方向上修改它们以改善模型的拟合？ 其次，随着模型变得越来越复杂，拟合模型也变得越来越困难。 如果认为原始计算能力就是跟上日益增长的复杂性所需的全部，那就错了。 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。 本计画建立贝叶斯阶层模型的理论性质与其他统计领域，如时间序列分析与丛集分析，导致了模型诊断和精细化领域的进步，并发展了一种有效的贝叶斯混合模型拟合算法。计算资源的最新进展为建模者提供了前所未有的机会，用非常现实的语言描述真实的生活和自然现象。 由于现实本身是复杂的，因此逼真的模型往往是高度复杂的。 对准确和可靠的建模的需要怎么强调都不过分。 公共政策的决策通常是基于概率模型，预测经济和社会指标，预测环境因素，评估疾病爆发的可能性等。模型中的小缺陷和小的估计不准确性可能会产生后果，可能会影响大量人的福利。 拟议的研究将开发跨学科的翻译方法，可用于改善各种环境中的建模和预测。 建议的应用领域包括PI最熟悉的领域，因为他正在进行的合作（定量心理学，市场营销和以患者为导向的医学调查），但研究也有明显的潜力对其他领域产生影响。 例如，有限混合分布模型，一个具体的研究主题，被用于不同的应用环境，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，无论是在研究生谁将协助PI在研究活动的培训方面，并在提醒更广泛的研究界需要健全和现代建模策略方面。

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.