We look at the problem in belief revision of trying to make inferences about what an agent believed--or will believe--at a given moment, based on an observation of how the agent has responded to some sequence of previous belief revision inputs over time. We adopt a `reverse engineering' approach to this problem. Assuming a framework for iterated belief revision which is based on sequences, we construct a model of the agent that `best explains' the observation. Further considerations on this best-explaining model then allow inferences about the agent's epistemic behaviour to be made. We also provide an algorithm which computes this best explanation.