We consider a neural network model of human performance in a cognitive task (Eriksen's flanker-interference task). We develop methods for performing formal statistical inference for the model and then we consider the net as applied to a particular experiment involving subjects before and after taking amphetamines. The hypothesis that the net captures the main features of relevant cognitive behavior can be cast as a specific hypothesis about the parameterization of the net. After dealing with some difficult computational problems, we compute the Bayes factor in favor of the hypothesis of interest. One major complication is that the likelihood cannot be computed in closed form and so must be simulated. This adds a component of noise when we use a Markov chain Monte Carlo simulation. We devise a method for correcting for this noise.