Thanks again to the brave souls who sacrificed their lunch break to come to the talk and for their patience during a failrly mathematicall talk and thanks also for the interesting questions
The slides are a bit "wordy" so they can be read (in theory) without having me present.
For the benefit of those who could not be there, a few notes/thoughts on the discussion:
In the original proposal, as explained (p.24) in the talk, the prior is used (only) in the loss function. In theory, the prior could encode interdependence between the sample space parameters. This would have the effect of focusing the calculation of the loss on feasible parameter constellations, but, as Andrew suspected, might confuse the evaluation of the reconstruction when the parameters are not independent (and particularly when some x that map to the same y are more right than others). In other words, the (well chosen) prior eliminates infeasible sample space parameters, but does not necessarily help when it comes to selecting the feasible ones. Or we need more experiments. But, in a multimodal experiment, the posterior of the first experiment might have cut your parameter space in an unhelpful way because the reconstruction might pick a wrong x that gives the right y, and now happily gives a zero(ish) posterior value on the true x (that also gives the right y) - and now you're stuffed because the second experiment needs a >0 prior on the true x rather than on the false x . The Classical Bayesian (if there is such a thing) might argue that the prior was not well chosen; or, obviously, we need to repeat the sequence of experiments and eventually we will hit the true x.
So this would be an example of where multimodal experiments do not commute; just like the case where the outcome of the first experiment influences the hypotheses/experiment of the second.
To see how the ML approach works in practice for reconstruction for SAXS/SANS one would now need to do (some of) the work that the original proposal proposed: to at least explore a neural network for reconstruction. Specifically, whether the proposed loss function is computationally feasible and useful (with the prior discussion above in mind.) Other suggestions for future directions/topics are in the slides. If you survived the talk, I'd welcome additional thoughts or comments.