1. A multi-stage event detector for monitoring a system to detect the occurrence of multi-stage events in the monitored system, the multi-stage event detector including: a data store storing a plurality of models of multi-stage events, each model specifying a sequence of stages and a set of transitions from one stage to another; and processing resources including at least one processor and a memory comprising instructions that, when executed, control the multi-stage event detector to at least: (a) detect observable events occurring on the monitored system; (b) generate parameter values that vary over time dependent on behavior of the monitored system; (c) determine a likely sequence of hidden states of interest of the monitored system based on the detected observable events occurring on the monitored system, wherein the hidden states of interest of the monitored system correspond to stages in the stored models of the multi-stage events; (d) determine a likely transition occurrence, corresponding to a transition from one stage to another in the stored models of the multi-stage events, based on a comparison of a set of values of a parameter or set of parameters generated in (b) with a plurality of pre-specified functions or sets of values of a corresponding parameter or set of parameters associated with different transitions from one stage to another in the stored models of the multi-stage events; and (e) determine an estimated identity of a multi-stage event and an estimated current stage of the multi-stage event in dependence upon a comparison of both the determination in (c) of a likely sequence of hidden states of interest of the monitored system and the determination in (d) of a likely transition occurrence with the stored models of multi-stage events specifying both sequences of stages and transitions between stages, wherein (c) is performed in connection with a model of the plurality of the models of multi-stage events, the model further specifying a plurality of distinct hidden states that the monitored system can occupy, and a plurality of visible states that can be determined in (a).