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

This paper emphasizes the utility, of graphic models in describing partiall y observed dynamic systems, and establishes a method for estimating the par ameters of the model. A dynamic graphic model with an associated graphic st ructure, 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 dir ected links describe the relations between noncontemporary variables. The p aper assumes that some of the variables are unobservable when the model is in use, but partial observation of these variables is allowed in an estimat ion phase, by performing autopsies of the system: stopping the system and o bserving its state, including destructive observation. A recursive estimati on method for the parameters is given and a simulation study evaluates its performance. In conclusion, the parameters of the model can be estimated, t he rms errors of the estimates are larger for those parameters associated w ith longer time (because of their dependence on previous estimates), and th e larger the dependence between unobservable and observable variables, the better the parameter estimates.