High-Dimensional Predictive Density Estimation

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This research concerns the development of a new methodology for predictive analysis, which extracts information from historical and current data to predict future trends and behavior patterns. The Bayesian approach is appealing for this problem because it provides a complete predictive density that assigns probabilities to every possible outcome, and it naturally incorporates the uncertainty inherent in the parameter estimation and model selection processes. The prior specification for Bayesian predictive procedures, however, becomes challenging as the number of potential predictors grows, an all too common problem as massive data sets are increasingly prevalent in many scientific areas. In this project, the PI investigates the use of Bayesian techniques for predictive density estimation and their frequentist properties, and then exploits those properties to construct new families of priors that have desirable risk properties, adapt to unknown data structures and also permit tractable computation for large and complex data sets. These priors are "minimally informative" in the sense that they allow input of subjective information through the choice of prior center, yet utilize this information in a very robust fashion. The resulting predictive estimators effectively combine information from different dimensions and therefore improve overall prediction performance. Applications in financial and social problems will be developed using the new methodology.Extracting information from massive data sets and exploiting it to make predictions of future uncertain events are fundamental problems in both statistics and the sciences. The proposed research provides not only powerful theoretical tools, but also easily-implementable computing strategies for predictive analysis. It can help researchers in various fields to better identify risks and opportunities, and thus to optimize their decision making. The methodological developments are motivated by a portfolio allocation problem in finance and a missing data imputation problem in the social sciences. The proposed procedures are applicable to many other scientific and technical areas, such as genomics, climatology, medical sciences and public health, where large data sets are collected and accurate predictive analysis is desirable. For example, in health care service studies, predicting people's future health care costs is an important topic given a high concentration of health care expenditures among a relatively small percentage of the population. Using the proposed methods, one may better exploit information in vast medical and insurance databases to identify the individuals with high health risks and to predict their future medical costs. To facilitate the use of these new methods, the PI will implement the procedures and algorithms in R or Matlab, and make this software available to the public along with the associated research reports.