Deterministic and random variables in Stan

Hello everybody!
First of all, I apologize if I am asking something obvious, I have very little experience working with Stan and in general with Bayesian statistics.
I want to create a model of peer assessment. Given a set of grades by a peer X to a group of students, and given a set of grades by a different peer Y to that same group of students, I am computing in the transformed data block the mean and variance of the resulting differences. In other words: if X has assessed v,w and z with grades G^{x}_{v}, G^{x}_{w}, G^{x}_{z}; and Y has assessed these same students with grades G^{y}_{v}, G^{y}_{w}, G^{y}_{z}, I am computing the mean \mu_{xy} = \frac{\sum_{i}G^{x}_{i} - G^{y}_{i}}{|\{G^{x}\}\cap\{G^{y}\}|}, where the denominator denotes the number of peers assessed both by X and Y. Similarly, the variance is computed as \sigma_{xy} = \frac{\sum_{i}(G^{x}_{i} - G^{y}_{i} - \mu_{xy})^{2}}{|\{G^{x}\}\cap\{G^{y}\}|}.

I intend now to use \sigma_{xy} and \mu_{xy} as the parameters of a normal distribution such that b \sim \mathcal{N}(\mu_{xy}, \sigma_{xy}), where b is a new variable.
Seeing this as a PGM, we would have the set of grades G^{x}_{v}, G^{x}_{w}, G^{x}_{z}, G^{y}_{v}, G^{y}_{w}, G^{y}_{z} as observed nodes, all of them parents of data-derived \mu_{xy} and \sigma_{xy}, which are likewise parents of an unobserved child b. As you may notice, given the deterministic definitions of \mu_{xy} and \sigma_{xy}, their existence depends on |\{G^{x}\}\cap\{G^{y}\}| \neq 0. Does Stan support such a model? Could I define b as a parameter?

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No worries - so if I’m understanding you correctly you’d like to create a PGM that looks a little like this:
(the set of grades) → data-derived mean and variance → your distribution b
I’m unsure if Stan support graphical models so hopefully someone can step in here, but yes you can define b as a distribution and since you have a fixed mean and variance (based on the context you’ve told us!) it should be fairly straightforward to sample from. :)
The one consideration I might have about your latter question, is if you have any reason to believe your set of grades follow a particular distribution - that might affect how you go about sampling from your distribution b.

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Bit out of my depth but is this related to multi membership models? If so the brms package has multimember model support so may be helpful


First of all, thank you both very much! I finally was able to make the model work! Regarding @n97 's question about the distribution followed by the grades, yes, the data that I gathered shows what seems to be something similar to a gaussian centred around 7 on a scale from 0 to 10.
I was not thinking from the perspective of multi-membership terms, @stevebronder , but that link did turn out to be useful for another project I’m in, so thank you very much for the hint!

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