We present a PAC-Bayes-Empirical-Bernstein inequality. The inequality is based on a combination of the PAC-Bayesian bounding technique with an Empirical Bernstein bound. We show that when the empirical variance is significantly smaller than the empirical loss the PAC-Bayes-Empirical-Bernstein inequality is significantly tighter than the PAC-Bayes-kl inequality of Seeger (2002) and otherwise it ...

Bayesian predictive inference analyzes a dataset to make predictions about new observations. When a model does notmatch 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...

The wide applicability of Gibbs sampling has increased the use of more complex and multi-level hierarchical models. To use these models entails dealing with hyperparameters in the deeper levels of a hierarchy. There are three typical methods for dealing with these hyperparameters: specify them, estimate them, or use a 'flat' prior. Each of these strategies has its own associated problems. In th...

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