Skew-Symmetric Approximations of Posterior Distributions - Colloque des Sciences Mathématiques du Québec

Explore a comprehensive lecture on skew-symmetric approximations of posterior distributions in Bayesian statistics. Delve into the world of partially or fully discretized Gaussian linear regressions, encompassing probit, multinomial probit, and tobit models. Discover how unified skew-normal (SUN) distributions are conjugate to the general form of likelihood induced by these formulations, opening new avenues for improved sampling-based methods and more accurate deterministic approximations. Learn about a novel perturbation strategy to enhance the accuracy of symmetric approximations of posterior distributions, resulting in skew-symmetric densities with improved finite-sample accuracy. Gain theoretical insights through a refined version of the Bernstein–von Mises theorem, which relies on skew-symmetric limiting densities. This hour-long lecture, presented by Daniele Durante as part of the Colloque des sciences mathématiques du Québec, offers a deep dive into recent advances in Bayesian inference and computation for a broad class of regression models.