Robust Bayesian Analysis with Model Uncertainty for Massive Datasets

统计学和科学中的两个基本问题是如何从大量数据集中提取信息，以及如何利用这些信息来预测未来的不确定事件。 通过建模和预测市场行为，经济学家可以更好地控制金融风险;通过建模和预测气候变化，科学家可以更好地管理环境;通过建模和预测医疗保健需求，政策制定者可以更好地分配资源以满足需求。 海量数据集带来了丰富的信息，但这些信息也伴随着一系列问题，其中最突出的是数据质量参差不齐，从“好数据”到“坏数据”不等。 拟议的研究将开发为不同质量的海量数据集提供强大，稳定的推理和预测的方法。 通用方法将适用于许多领域，包括环境科学，医学科学和企业决策分析，这些领域需要收集大量数据集并进行强大的预测分析。 贝叶斯方法在过去的二十年里取得了巨大的成功，在科学界和企业界得到了广泛的应用。 他们的成功是由他们独特的能力驱动的，这种能力将来自实验或观察性研究的联合收割机信息与通过先验分布表示的实验外信息相结合。 然而，这种成功取决于数据的质量和先验的质量。 本研究主要针对这两个问题。 首先，研究开发了贝叶斯框架中的正式预测方法，适用于中等质量的数据;其次，研究开发了贝叶斯方法，用于模型比较和模型平均，当先验信息很少时，可以提供强大而稳定的推断。 该项目的两个部分自然地联合收割机结合起来，产生完整的，有凝聚力的贝叶斯分析方法，是强大的模型错误和离群值，只需要适度的先验信息。 该项目将为几名学生提供研究和数据分析方面的培训机会，其中大部分将是跨学科性质的。

Two fundamental problems in Statistics, and in science more generally, are how to extract information from massive data sets and how to exploit this information to make predictions of future uncertain events. By modeling and predicting market behavior, economists can better control financial risk; by modeling and predicting climate change, scientists can better manage the environment; by modeling and predicting health care needs, policy makers can better allocate resources to meet the needs. Massive datasets bring a wealth of information, but this information is accompanied by a host of problems -- the most salient of which is varying data quality, ranging from "good data" to "bad data". The proposed research will develop methods which provide robust, stable inference and prediction for massive datasets of varying quality. The general methodology will be applicable to many fields, including environmental sciences, medical sciences and corporate decision analytics, where massive datasets are collected and robust predictive analysis is needed. Bayesian methods have enjoyed extraordinary success in the past two decades, and they are widely used throughout the scientific and corporate communities. Their success has been driven by their unique ability to combine information from an experiment or observational study with extra-experimental information, expressed through the prior distribution. However, this success hinges on the quality of the data and the quality of the prior. The proposed research takes aim at these two issues. For the first, the research develops formal predictive methods in the Bayesian framework which are suited to use with data of modest quality; for the second, the research develops Bayesian methods for model comparison and model averaging which provide robust and stable inference when little prior information is available. The two portions of the project naturally combine to yield complete, cohesive Bayesian analyses with methods which are robust to model misspecification and outliers, and which require only modest prior information. The project will provide several students with opportunities for training in research and data analysis, and much of this will be interdisciplinary in nature.