Skew-symmetric approximations of posterior

Botond Szabó gave a BNP webinar last week on the recent paper he wrote with Bocconni colleagues Francesco Pozza and Daniele Durante, to appear in Series B. Which studies the impact of using skew-symmetric approximations of posterior distributions. Skew-symmetric distributions are easy to simulate, either by accept-reject or by exploiting the cdf x pdf structure and the symmetry in the pdf. The Bernstein-von Mises theorem can be expanded to this case, although I am not certain what this means! The main theoretical result is a gain in the magnitude of the approximation, eg in KL, which I did not expected. With questions about the choice of the cdf (which can be automatised when the original posterior is available or when a closed-form approximation replaces it) and of the symmetry point ξ for complex models (which seems to be the MAP by default.) and of the impact on marginal likelihood approximations (if it makes any sense).

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