A variational approach to robust Bayesian interpolation

We detail a Bayesian interpolation procedure for linear-in-the-parameter models, which combines both effective complexity control and robustness to outliers. Robustness is obtained by adopting a student-t noise distribution, defined hierarchically in terms of an inverse-gamma prior distribution over individual Gaussian observation variances. Importantly, this hierarchical definition enables practical Bayesian variational techniques to concurrently determine both the primary model parameters and the form of the noise process. We show that the model is capable of flexibly inferring, from limited data, both Gaussian and more heavily-tailed student-t noise processes as appropriate.