You are welcome to attend the following Statistics and Stochastic colloquium (part of the Colloquium Series of the Department of Mathematics and Statistics) at La Trobe University.
In many instances, the application of approximate Bayesian methods is hampered by two practical features: 1) the requirement to project the data down to low-dimensional summary, including the choice of this projection, and which ultimately yields inefficient inference; 2) a possible lack of robustness of these methods to deviations from the underlying model structure. Motivated by these efficiency and robustness concerns, we construct a new Bayesian method that can deliver efficient estimators when the underlying model is well-specified, and which is simultaneously robust to certain forms of model misspecification. This new approach bypasses the calculation of summaries by considering a norm between empirical and simulated probability measures. For specific choices of the norm, we demonstrate that this approach can be as efficient as exact Bayesian inference, and is robust to deviations from the underlying model assumptions. We illustrate this approach using several examples that have featured in the literature.