The role of skewed distributions in Bayesian inference: conjugacy, scalable approximations and asymptotics
Daniele Durante, Assistant Professor of Statistics at the Department of Decision Sciences, Bocconi University, Italy
Tuesday, November 08, 2022, 15:00
Building 1, Level 4, Room 4102
In this talk, I will review, unify and extend recent advances in Bayesian inference and computation for such a class of models, proving that unified skew-normal (SUN) distributions (which include Gaussians as a special case) are conjugate to the general form of the likelihood induced by these formulations. This result opens new avenues for improved posterior inference, under a broad class of widely-implemented models, via novel closed-form expressions, tractable Monte Carlo methods based on independent and identically distributed samples from the exact SUN posterior, and more accurate and scalable approximations from variational Bayes and expectation-propagation. These results will be further extended, in asymptotic regimes, to the whole class of Bayesian generalized linear models via novel limiting approximations relying on skew-symmetric distributions.