A1065
Title: Skewed Bernstein-von Mises theorem and skew-modal approximations
Authors: Francesco Pozza - Università Bocconi (Italy) [presenting]
Abstract: Gaussian deterministic approximations are routinely employed in Bayesian statistics to ease inference when the posterior distribution is intractable. Although these approximations are justified, in asymptotic regimes, by Bernstein-von Mises type results, in practice, the predicated Gaussian behavior may poorly represent the actual shape of the exact posterior, thereby affecting approximation accuracy. Motivated by these considerations, an improved class of closed-form and valid deterministic approximations of posterior distributions is derived, which arise from a novel treatment of a third-order version of the Laplace method yielding approximations within a tractable family of skew-symmetric distributions. Under general assumptions which allow to account for misspecified models, non-i.i.d. settings and various asymptotic regimes, this novel family of approximations is shown to have a total variation distance from the exact posterior whose rate of convergence improves by at least one order of magnitude the one achieved by the Gaussian from the classical Bernstein-von Mises theorem. The same improvement is also proved for polynomially bounded posterior functionals, and for a scalable strategy, approximate posterior marginals are derived. Through two real data applications, it is shown that the proposed approximations can be remarkably more accurate than their Gaussian counterparts.
