  An important problem for HCI researchers is to estimate the parameter values
of a cognitive model from behavioral data. This is a difficult problem, because
of the substantial complexity and variety in human behavioral strategies. We
report an investigation into a new approach using approximate Bayesian
computation (ABC) to condition model parameters to data and prior knowledge. As
the case study we examine menu interaction, where we have click time data only
to infer a cognitive model that implements a search behaviour with parameters
such as fixation duration and recall probability. Our results demonstrate that
ABC (i) improves estimates of model parameter values, (ii) enables meaningful
comparisons between model variants, and (iii) supports fitting models to
individual users. ABC provides ample opportunities for theoretical HCI research
by allowing principled inference of model parameter values and their
uncertainty.
