Skew-Normal Posterior Approximations

TL;DR

This paper introduces a skew-normal approximation method for Bayesian posteriors, capturing skewness often ignored by Gaussian-based methods, and demonstrates improved accuracy in small to moderate dimensions.

Contribution

It proposes a novel skew-normal matching approach for Bayesian inference, enhancing posterior approximation accuracy by accounting for skewness.

Findings

Skew-normal matching outperforms Gaussian methods in accuracy for small and moderate dimensions.

Post-hoc skewness adjustment incurs minimal additional computational cost.

Empirical results show significant improvements over existing Gaussian and skewed approximations.

Abstract

Many approximate Bayesian inference methods assume a particular parametric form for approximating the posterior distribution. A multivariate Gaussian distribution provides a convenient density for such approaches; examples include the Laplace, penalized quasi-likelihood, Gaussian variational, and expectation propagation methods. Unfortunately, these all ignore the potential skewness of the posterior distribution. We propose a modification that accounts for skewness, where key statistics of the posterior distribution are matched instead to a multivariate skew-normal distribution. A combination of simulation studies and benchmarking were conducted to compare the performance of this skew-normal matching method (both as a standalone approximation and as a post-hoc skewness adjustment) with existing Gaussian and skewed approximations. We show empirically that for small and moderate dimensional cases, skew-normal matching can be much more accurate than these other approaches. For post-hoc skewness adjustments, this comes at very little cost in additional computational time.