Textbook Group meeting for Parr, Pezzulo, Friston 2022 .

All right. It's cohort four, October 31st, 23, and we're at our first discussion of chapter nine. So today we can totally look at questions and look over the chapter, but is there anything that anybody wants to bring up about chapter nine? Thank you. Before we kind of look over the structure of the chapter and look over the questions. Okay. We'll just hop into the structure. A good overview seems nice on this one. Cool. Yeah. And Esmail had mentioned epistemology. So talk about leading with a epistemological assertion. The models described in this book are only useful if they can answer scientific questions. Is that the only way a model can be useful? Or is this such a broad sentiment that everything can be cast as a scientific question? So even something of purely epistemological or epistemic status could be under this scope? Anyways, in this chapter, we focus on the ways in which active inference can be applied to understanding empirical data. So that's kind of the big plot twist in chapter nine is that up till here, everything has been very much like proposed as sort of intrinsically coherent. Like the rat in the T-maze or other calculations. They're all kind of proposed as just thought experiments more than anything else. Although there's a lot of citations to the empirical work like in chapter five. Here, though, they're going to go into detail about how you interface the generative model with empirical data. And so in that way, it kind of complements chapter six, because here we're actually going to take that generative model and connect it with data. Our general goal is to recover the parameters of the generative model that a subject's brain uses to produce behavior. The subjective model. So we'll see this graphically soon. But just to be clear, to recover the parameters, a synonym there would be like to identify plausible parameters. So if we knew that the height of children in the classroom was distributed according to a normal distribution. Then we have the data, which is kind of distribution free. It's just a list of numbers. And then the task of chapter nine is basically juxtapose the structure of that model with the data and recover the parameters. Okay, section 9.2 goes into this metabasean perspective or metabasean methodology. They bring up two related reasons for fitting a computational model to observe behavior. The first is to recover parameters to give an account of a single individual from a broader population or comparing two groups or two populations or more against each other. So that is taking a fixed model structure and then multiple samples of data. It could be one person on multiple days or multiple people on multiple days or whatever the design of the experiment is. And then for a fixed model structure, identify something useful about that data, like about one group versus another. The second reason is to compare alternative hypotheses expressed as models that represent different explanations for behavioral phenomena. So here, instead of preconditioning on one model, we're actually going to use the data to interrogate a portfolio of models. So we have performance of multiple individuals on multiple days. So then we might say, okay, well, the simplest model is all individuals are the same, drawing from the same distribution, all days draw from the same distribution. Then we have a model where individuals don't differ, but days differ. Then we have individuals differing, but not days. And then we have, there's an individual by day interaction. So this is familiar to anyone who's basically done any kind of statistical modeling, which is that adding more parameters to a model, essentially, or almost by definition, always increases the accuracy of the model on the training data. That doesn't mean it increases the accuracy in and out of sample. So that's like the training and test relationship of overfitting. But adding parameters basically always gets you to fit more data or fit the data more closely.…