  As observations and student models become complex, educational assessments
that exploit advances in technology and cognitive psychology can outstrip
familiar testing models and analytic methods. Within the Portal conceptual
framework for assessment design, Bayesian inference networks (BINs) record
beliefs about students' knowledge and skills, in light of what they say and do.
Joining evidence model BIN fragments- which contain observable variables and
pointers to student model variables - to the student model allows one to update
belief about knowledge and skills as observations arrive. Markov Chain Monte
Carlo (MCMC) techniques can estimate the required conditional probabilities
from empirical data, supplemented by expert judgment or substantive theory.
Details for the special cases of item response theory (IRT) and multivariate
latent class modeling are given, with a numerical example of the latter.
