  We propose a new method for 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
loss-based, or Gibbs, 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.
