Decision methods in dynamic system identification

The performance of Bayesian maximum a posteriori (MAP) decision methods for dynamic system identification is investigated. By examining a finite set of a posteriori probabilities a decision is made as to which of several possible regions of the parameter space the true parameter value lies. It is shown that for the true parameter value in a prescribed region the corresponding a posteriori probability converges exponentially (mean square) to 1. The analysis is based on the asymptotic per sample formula for the Kullback information function, which is derived in this paper. We believe that the properties of Bayesian MAP decision methods discussed in this paper make them useful for application in dynamic system identification in conjunction with standard techniques such as the maximum likelihood (ML) method.