speaker-0: So there's some I think like Avi Feller and some other people have done some Bayesian principles graphication models in Stan. And the idea is that you would characterize people that there's an a latent variable. Well, it's observed for the people who got the mailer and not revail not observed for the others. And it's whether you would have well, I can't remember how it works, but like the people who the qu the latent variable is if you receive the stage one treatment, would you do the stage two treatment? And for the people who did receive the stage one treatment, you you know that. But the people who didn't, you don't know that. ⁓ but you can form a model and you can do inference on that. And you'd want to use pre treatment predictors. You'd want to use characteristics of the people in the study. ⁓ that the you know their their age and ⁓ where they live and whatever ⁓ spending patterns they have in the past and then you can do that you should be able to do that model. And that will then your a your es you can then from that you can estimate the effect of the you can c you can you can compare the people who would or would not ⁓ do the stage two treatment and you can estimate what would happen if someone who didn't do it were to do it. But basically you have to you'd model the whole process. I I I haven't done this myself, but I know people have done it, it seems like a a very natural Bayesian problem. And I I think that standard standard solutions such as instrumental variables would correspond to special cases of this model, assuming various things are zero or with with flat priors and various I mean, usually standard procedures usually come Correspond to some mix of some flat priors in some parameters and priors with spikes at zero on others.

speaker-1: Okay. So Richard, I'm I'm I'm sure you you wanna say something on that.

speaker-2: Yeah. And

speaker-3: But no, I mean that sounds reasonable to me. I recognize this as the like per protocol or intent to treat kind of problem. And and there's I mean that's a big literature and there's ⁓ what Andrew says sounds like it's very sensible there. You you try to do the best you can, but you you gotta be careful about what you're adding because now you have it's this downstream from treatment problem. But people have written a lot about this. But this is the yeah, the per protocol, intent to treat sort of issue. If you want to figure out mechanism how the treatment's really working, it's it's hard even if the stream is randomized, but there are ways to do it as Andrew has discussed and that's that's the way I approach it.

speaker-1: Yeah. Awesome. Yeah, I love these problems. Like I think the these kind of hard causal inference problems are among the the most interesting ones because also that's where you get to to do the the most customized models and and that's these are the fun ones where you have to these are kind of Lego bricks that you you wanna you wanna add together. So I love working on these kind of ⁓ of models. ⁓ actually

speaker-2: Actually, so we're I'm gonna start winding this down here because it's starting getting late for for Aki and Rachel.

speaker-1: ⁓ I still have so many questions for you guys, but maybe

speaker-2: Maybe so one is is there is there something you wanted to mention here that we didn't get to today?

speaker-3: No, that's a very open question. ⁓ we didn't talk about AI and workflow, and I think that's a very big and interesting topic. ⁓ maybe w you'll have to have us back and we can talk about that. But that's I think that's a big area and it's very dynamic. and it's just here, yeah. And ⁓

speaker-2: Yeah, maybe something that's not.

speaker-3: Anyway, but you've you've we don't have enough time before my food is delivered, ⁓ to discuss.

speaker-1: I know, I know. I am very frustrated and and I definitely thought on that also that ⁓ I know I've been also of course doing a lot of that myself, working on on some agent skills with ⁓ some some people like Stefan Radf, I don't know if you know but they've been on the show, and ⁓ And a lot of of great people doing that. So so yeah, I'm very interested in that also and seeing how it goes.

speaker-0: I wouldn't get ⁓ I wouldn't get Jessica, Aki and Bob on together and to watch them scream at each other. ⁓ but

speaker-1: Sounds like fun. Yeah. Let's organize that. Yeah. And Richard, I need to to have you anyways like for a solo episode on the show. Well we'll we'll dive on these on these questions.

speaker-2: Hehehe

speaker-3: I'll bring popcorn. That would be great.