  Process-oriented theories of cognition must be evaluated against time-ordered
observations. Here we present a representative example for data assimilation of
the SWIFT model, a dynamical model of the control of spatial fixation position
and fixation duration during reading. First, we develop and test an approximate
likelihood function of the model, which is a combination of a pseudo-marginal
spatial likelihood and an approximate temporal likelihood function. Second, we
use a Bayesian approach to parameter inference using an adapative Markov chain
Monte Carlo procedure. Our results indicate that model parameters can be
estimated reliably for individual subjects. We conclude that approximative
Bayesian inference represents a considerable step forward for the area of
eye-movement modeling, where modelling of individual data on the basis of
process-based dynamic models has not been possible before.
