PR and GA are widely known for being knowledgeable and fair reviewers. You may not like them but they are the best when it comes to understanding the material.
If you are actually interested in getting the right VB fit then this is a good paper to read. https://arxiv.org/abs/1802.02538
Good luck getting it through marketing though. I had a reviewer, likely a senior Bayesian reviewer, tell me that LOO is only an information criterion. Absolutely maddening!
The fact that PSIS is an approximation of LOO probabilities, and that LOO is cross validation, and that an information criterion is only one possible metric from the LOO probabilities was impossible for this reviewer to fathom. It was like telling someone who thinks the moon landing was staged that it was not.
It was aggravating because the PSIS approximation to LOO is the only hope we have in any modern model of actually working out more than an IC or likelihood, and looking at actual prediction performance. Else, who has the computational resources to do cross-validation with a Bayesian model and the old estimate and holdout paradigm is perfectly fine if you have a lot of data but with small ish datasets, the holdout sample is rarely well-matched to the estimation sample. The loss of efficiency in both estimating and testing is a major concern.
All of the new methods for checking VB fit or dealing with multimodal posteriors are all based on the PSIS approximation so if you do get the same person I got then well I hope your karma wallet is richer than mine. Or maybe who knows, maybe just maybe that person is gonna read this and actually read up on PSIS and update their beliefs.1. If your research is like your analogy, you deserve rejection.
2. Some senior bayesian reviewers (PR, GA) are absolute trash. This is widely known.