Bayesian Generative Modelling of Student Results in Course Networks

We present an innovative modelling technique that simultaneously constrains student performance, course difficulty, and the sensitivity with which a course can differentiate between students by means of grades. Grade lists are the only necessary ingredient. Networks of courses will be constructed where the edges are populations of students that took both connected course nodes. Using idealized experiments and two real-world data sets, we show that the model, even though simple in its set-up, can constrain the properties of courses very well, as long as some basic requirements in the data set are met: (1) significant overlap in student populations, and thus information exchange through the network; (2) non-zero variance in the grades for a given course; and (3) some correlation between grades for different courses. The model can then be used to evaluate a curriculum, a course, or even subsets of students for a very wide variety of applications, ranging from program accreditation to exam fraud detection. We publicly release the code with examples that fully recreate the results presented here.