A CALCULUS OF STOCHASTIC-SYSTEMS FOR THE SPECIFICATION, SIMULATION, AND HIDDEN STATE ESTIMATION OF MIXED STOCHASTIC NONSTOCHASTIC SYSTEMS

In this paper, we consider mixed systems containing both stochastic an d nonstochastic(1) components. To compose such systems, we introduce a general combinator which allows the specification of an arbitrary mix ed system in terms of elementary components of only two types. Thus, s ystems are obtained hierarchically, by composing subsystems, where eac h subsystem can be viewed as an ''increment'' in the decomposition of the full system. The resulting mixed stochastic system specifications are generally not ''executable'', since they do not necessarily permit the incremental simulation of the system variables, Such a simulation requires compiling the dependency relations existing between the syst em variables. Another issue involves finding the most likely internal states of a stochastic system from a set of observations. We provide a small set of primitives for transforming mixed systems, which allows the solution of the two problems of incremental simulation and estimat ion of stochastic systems within a common framework. The complete mode l is called CSS (a Calculus of Stochastic Systems), and is implemented by the SIG language, derived from the SIGNAL synchronous language. Ou r results are applicable to pattern recognition problems formulated in terms of Markov random fields or hidden Markov models (HMMs), and to the automatic generation of diagnostic systems for industrial plants s tarting from their risk analysis.