Statistics and Data Science Seminar
Nick Syring
UIC
Scaling the Gibbs posterior
Abstract: In some applications, the relationship between the observable data and unknown parameters is described via a loss function rather than
likelihood. In such cases, the standard Bayesian methodology cannot be used, but a Gibbs posterior distribution can be constructed by
appropriately using the loss in place of a likelihood. Inference based on the Gibbs posterior is not straightforward, however,
because the finite-sample performance is highly sensitive to the scale of the loss function. In this talk, I will propose a Gibbs
Posterior Scaling (GPS) algorithm that adaptively selects the scaling in order to calibrate the corresponding Gibbs posterior credible
regions. Two examples, namely, classification and quantile regression, are used to demonstrate that the Gibbs posterior with scale chosen
by GPS produces valid interval estimates which are at least as efficient those obtained from other methods.
Wednesday September 9, 2015 at 4:00 PM in SEO 636