  We propose a new approach to Bayesian prediction that caters for models with
a large number of parameters and is robust to model misspecification. Given a
class of high-dimensional (but parametric) predictive models, this new approach
constructs a posterior predictive using a variational approximation to a
generalized posterior that is directly focused on predictive accuracy. The
theoretical behavior of the new prediction approach is analyzed and a form of
optimality demonstrated. Applications to both simulated and empirical data
using high-dimensional Bayesian neural network and autoregressive mixture
models demonstrate that the approach provides more accurate results than
various alternatives, including misspecified likelihood-based predictions.
