Appendices

To further characterize the tail behavior, let be an isotropic multivariate normal distribution, and let us express the log-ratio as a function of instead of the posterior probability. LetA = QΛQ be the eigenvalue decomposition forA and denote = Qξ and b = Qβ. Therefore, according to Definition 2.2 in [31], v is sub-exponential with parameters( 2 A For a fixed model, minimizing the exponentiated CUBO is a valid approachforminimizingtheχ2 divergence. Finally, in many cases theχ2 divergence may be infinite. This is true even for two Gaussian distributions provided that the variance ofqφ does not cover the posterior sufficiently.