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.

翻译：许多近似贝叶斯推断方法假定后验分布具有特定的参数形式。多变量高斯分布为这类方法提供了便捷的密度形式，例如拉普拉斯近似、惩罚拟似然法、高斯变分法以及期望传播方法。然而，这些方法均忽略了后验分布可能存在的偏态性。我们提出一种考虑偏态性的修正方法，将后验分布的关键统计量与多变量偏态正态分布进行匹配。通过模拟研究与基准测试相结合，我们比较了这种偏态正态匹配方法（既作为独立近似方法，也作为事后偏态调整手段）与现有高斯及偏态近似方法的性能。实证结果表明，在低维和中维情形下，偏态正态匹配的精度远优于其他方法。作为事后偏态调整手段时，该方法仅增加极少的额外计算时间。