Experience Accumulation for Decision Making in Multivariate Time Series
V. Peterka · IIASA PURE (International Institute of Applied Systems Analysis) · 1976
A dynamic stochastic system with multivariate input and multivariate output, possibly controlled in a closed loop, is considered. It is assumed that the input-output relation is describable by a model of a given structure but with a finite set of unknown parameters. The uncertainty of the parameters is characterized by the subjective probability density function. Functional recursion relations are derived describing the evolution of this subjective p.d.f. when it is successively conditioned by the observed data. A self-reproducing form of the conditional p.d.f. is found for the case, when the process is describable by a multivariate regression model and no parameter -- except the order -- is a priori known. This makes it possible to reduce the functional recursion into an algebraic recursion which is easy to perform.