Skew-Normal Posterior Approximations

Jackson Zhou; Clara Grazian; John Ormerod

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arXiv · 2302.08614

Skew-Normal Posterior Approximations

Jackson Zhou·Clara Grazian·John Ormerod

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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.

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Jackson Zhou, Clara Grazian, John Ormerod. 2023-02-16. Skew-Normal Posterior Approximations. https://arxiv.org/abs/2302.08614

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