Title: Posterior concentration rates using new empirical priors
Authors: Ryan Martin - North Carolina State University (United States) [presenting]
Abstract: In high- and infinite-dimensional problems, Bayesian prior specification can be a challenge. For example, in a high-dimensional regression case, while sparsity considerations drive the choice of prior on the model, there is no genuine prior information available about the coefficients in a given model. Moreover, the choice of prior for the model parameters impacts both the computational and theoretical performance of the posterior. As an alternative, one might be tempted to choose an ``informative'' empirical prior on the model-specific parameters, depending on data in a suitable way. We will present a new approach for empirical prior specification in high-dimensional problems, based on the idea of centering the prior on a suitable estimator. We will give general conditions that guarantee the corresponding ``empirical Bayes'' posterior distribution achieves a target rate, even adaptively, and specialize to some examples.