Mathematical Sciences: Empirical Bayes Approaches to Multiparameter Estimation

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This research will contribute to methodology for constructing empirical Bayes confidence intervals and hypothesis tests, and will provide theory and/or simulation to validate these statistics. The investigators propose to expand current technology to include non-Gaussian distributions and vector parameters. A common feature of many empirical experiments is the desire to draw conclusions about a series of similar parameters. The statistical approach known as Empirical Bayes has proved useful in this setting. The proposal is to view each item to be estimated as part of an ensemble, thereby achieving considerable gains for the set. Current methods are applicable to very special types of data, i.e. data that is distributed in the shape of a bell (Gaussian). Developing the Empirical Bayes approach for a variety of types of data will increase the information scientists can obtain from their experiments.