  Bayesian predictive inference analyzes a dataset to make predictions about
new observations. When a model does not match the data, predictive accuracy
suffers. We develop population empirical Bayes (POP-EB), a hierarchical
framework that explicitly models the empirical population distribution as part
of Bayesian analysis. We introduce a new concept, the latent dataset, as a
hierarchical variable and set the empirical population as its prior. This leads
to a new predictive density that mitigates model mismatch. We efficiently apply
this method to complex models by proposing a stochastic variational inference
algorithm, called bumping variational inference (BUMP-VI). We demonstrate
improved predictive accuracy over classical Bayesian inference in three models:
a linear regression model of health data, a Bayesian mixture model of natural
images, and a latent Dirichlet allocation topic model of scientific documents.
