2023/02/16 by Jackson Zhou, Zhou, Jackson, Clara Grazian +3
Computer Science · Mathematics · #Bayesian Methods and Mixture Models #FOS: Computer and information sciences #Gaussian Processes and Bayesian Inference #Methodology (stat.ME) #Statistical Methods and Bayesian Inference
paper · pdf · doi:10.48550/arxiv.2302.08614
openalex publication_date 2023/02/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.