Estimating transition-probabilities in a dynamic graphic model with unobservable variables

This paper emphasizes the utility, of graphic models in describing partially observed dynamic systems, and establishes a method for estimating the parameters of the model. A dynamic graphic model with an associated graphic structure, which consists of a sequence of chain graphs with two consecutive graphs in the sequence connected by directed links, is described. The chain graphs describe relationships among the contemporaneous variables; the directed links describe the relations between noncontemporary variables. The paper assumes that some of the variables are unobservable when the model is in use, but partial observation of these variables is allowed in an estimation phase, by performing autopsies of the system: stopping the system and observing its state, including destructive observation. A recursive estimation method for the parameters is given and a simulation study evaluates its performance. In conclusion, the parameters of the model can be estimated, the rms errors of the estimates are larger for those parameters associated with longer time (because of their dependence on previous estimates), and the larger the dependence between unobservable and observable variables, the better the parameter estimates.