Identifiability of a class of theories with states not directly observed over trials

The problem of identifying probabilities for sequences involving K underlying states is investigated for experiments in which there are K observed states, with the conditional distribution for these states specified for each underlying state. Conditions for finding unique estimates of the underlying probabilities are outlined for situations in which underlying transitions depend upon the last observed state as well as for situations in which no such dependency is assumed. No restrictions upon the nature of underlying transitions are assumed for a large number of trials. Applications to some known experimental situations are suggested.