speaker-0: Have you now that you've been working on that for a few years now, have you seen any any interesting applications of these kind of methods, especially using base flow, of course?

speaker-1: Yeah, we do have a lot of special. the likelihood density is available or easily available and we just, but we can efficiently

speaker-2: From these models. So we then in simulation base Bayesian inference approximate

speaker-1: which we did have like.

speaker-2: Bayesian computation for decades, but it didn't really scale beyond.

speaker-1: beyond a few parameters. And neural networks really humiliated when they came in. Made

speaker-2: And

speaker-1: SBI really feasible and scalable. And as a side project, we got this amortization property that gives us real-time Bayesian inference.

speaker-2: Mm and so all the kind of models models are sometimes

speaker-1: like physical models from psychology or biology or chemistry where we don't have these analytic likelihood densities, which you don't see at Stencon, of course. For these, the simulation-based methods are really like the state of the art, if you will. But of course, they would still not reach the reliability specifically for out of distribution data for like data for the modified.

speaker-2: Yeah,

speaker-1: then MCMC would have in comparison if we could apply MCMC. So a lot of the core applications where this has been really successful is in places where we cannot efficiently do MCMC in the first place. Because if we did, probably MCMC would still win at least in the accuracy and the trustworthiness that we get out of it. It's kind of my goal to improve that trustworthiness of the neural methods. that would be

speaker-2: We get faster inference, but

speaker-1: but similarly accurate.

speaker-0: Yeah. Can you

speaker-2: Is there is there methods yet or measures you can use to say, well this didn't quite work as we wanted it to? So

speaker-1: seeds

speaker-2: in in a way, yes. But it only works and you know that giving

speaker-1: I mean, they're just.

speaker-2: for context, it only works of course if we are simulating from the exact same model that then we are essentially fitting, right? but of course

speaker-1: If that works.

speaker-2: Let's say with MCMC implemented in STEN or wherever, then we have reasonable data, which may look a little different than the simulated data, you get an accurate

speaker-1: trust that also for real world data, still we

speaker-2: posterior approximation. So now in for for for kind of neural simulation based on amortized inference, of course we can run run L C. It's

speaker-1: be deeper.

speaker-2: more of a convergence diagnosis because we have been training the neural with actually this kind

speaker-1: exactly the

speaker-2: of simulated data. And we also know that on the neural networks are only good. to predict something that is kind of close enough to the data that is seen during training. We don't

speaker-1: So of SBC we may easily.

speaker-2: know if it will work for real world data. data

speaker-1: If the real world.

speaker-2: is somehow like out of distribution of the simulated data. Because our model

speaker-1: are usually misspecified.

speaker-2: in some way or form. So so that there's and this is actually what we're working with to trying to diagnose not when when the data when the model is misspecified for a given data, but when it is misspecified in way.

speaker-1: is that will affect our accuracy of the analytic posterior.

speaker-2: Which of course we don't know. So it's a it's a black box and the way we're doing it we are not we are we are we are having two neural networks, one is actually the posterior estimation and the other one does summarizing the in

speaker-1: data into ideally.

speaker-2: like informative ideally sufficient statistics. Check out

speaker-1: so we can check whether we are.

speaker-2: of distribution in the space of sufficient statistics. And if we are chances our posterior approximation will also be bad. Which gives us diagnostics and we have a paper soon coming out of of this that extends previous methods of ours and sometimes it works and sometimes it doesn't.