A chief criticism of Bayesian methods is the subjectivity of the prior. Empirical Bayes sidesteps this problem by learning the prior from the data. In nonparametric Empirical Bayes (NEB), no assumptions are made on the prior distribution whatsoever. However, most NEB methods instead make strict assumptions on the likelihood, e.g., normal distribution with variance 1, so they are not truly nonparametric. We show that fully nonparametric Empirical Bayes -- which makes no assumptions about the prior or likelihood -- is possible if we have multiple observations for each unit (i.e., replicates). Our method, called AURORA, achieves performances comparable to parametric methods that assume knowledge of the likelihood. We demonstrate an application of AURORA to an Internet-scale problem encountered at Google.

Dr. Dennis Sun is currently Associate Professor of Statistics at the California Polytechnic State University and Senior Data Scientist at Google. He will be joining Stanford University as an Associate Professor (Teaching) of Statistics in January 2023. His primary research interests are in statistical software and education, although he has also published on selective inference and audio signal processing. He has a soft spot for elegant classical statistics.