Skew-symmetric approximations of posterior distributions
Bayesian posteriors are often skewed, whereas mainstream deterministic approximations—such as Laplace’s method and variational Bayes—rely on symmetric densities (e.g., Gaussians), leading to systematic bias and reduced accuracy. Method: We propose a generic, optimization-free skewness-aware perturbation framework that can be seamlessly integrated with any off-the-shelf symmetric approximation. Our approach constructs analytical perturbations based on skew-symmetric density families, unifying asymptotic expansion and variational analysis. Contribution/Results: We theoretically establish finite-sample accuracy improvement and prove that the asymptotic convergence rate is accelerated by at least a factor of √n. The method is model-agnostic and compatible with diverse symmetric approximation paradigms. Numerical experiments demonstrate substantial gains over standard Gaussian approximations—particularly in moderate-to-small sample regimes and under strong posterior skewness—empirically validating the predicted convergence acceleration and robustness.