Econometrics - Gael Martin (Monash)

Title: Loss-Based Variational Bayes Prediction

Abstract: 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-dimension (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.
Whilst the current paper uses observation-driven models only as the predictive models, the presentation will contain theoretical results, and some preliminary numerical results, related to state space models. In this setting, the use of the variational approximation has to be dealt with with more care.