B0294
Title: A geometric perspective on Bayesian and generalized fiducial inference
Authors: Jan Hannig - University of North Carolina at Chapel Hill (United States) [presenting]
Abstract: Post-data statistical inference concerns making probability statements about model parameters conditional on observed data. When a priori knowledge about parameters is available, post-data inference can be conveniently made from Bayesian posteriors. In the absence of prior information, objective Bayes or generalized fiducial inference (GFI) may be still relied on. Inspired by approximate Bayesian computation, a novel characterization of post-data inference is proposed with the aid of differential geometry. Under suitable smoothness conditions, Bayesian posteriors and generalized fiducial distributions (GFDs) can be respectively characterized by absolutely continuous distributions supported on the same differentiable manifold: the manifold is uniquely determined by the observed data and the data generating equation of the fitted model. The geometric analysis not only sheds light on the connection and distinction between Bayesian inference and GFI but also allows for sampling from posteriors and GFDs using manifold Markov chain Monte Carlo algorithms.
