I found the paper Yes, but Did It Work?: Evaluating Variational Inference very insightful and was wondering whether one could apply the two proposed statistics to the following problem:

Currently people try to scale BNNs using various variational inference approaches, like for instance Weight uncertainties in neural networks, also known as “Bayes by backprop”.

Couldn’t we use, at least, the PSIS-statistics to check whether the variational approximations they use in this paper might be flawed? If I’m not mistaken, calculating the NN induced joint density function is tractable, since we can run easily forward passes in the NN. For instance one could start with the MNIST or regression example mentioned in the paper.

Just wanted to check if I oversee some complexity, here?!