Robust Bayesian Analysis with Model Uncertainty for Massive Datasets

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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.