Detection and prediction of a stochastic process having multiple hypotheses

A system is proposed which combines hypothesis testing and prediction to estimate the future value of a stochastic process whose statistics are known only to belong to some finite set of possible hypotheses. Bayes optimization of the individual components is performed and system performance is discussed for a modified version of the usual mean-squared error predictor cost functions. An example is given illustrating various features of the system´s performance for a specific choice of input hypotheses.