On random least-square analysis

Dispersion in the output data of a system can be analyzed as either noise fluctuations about a deterministic model or as the noise with added fluctuations due to randomness in the model itself. This latter interpretation finds applications in the identification of inherently random systems which provide rational models for systems such as biological and economic systems. It is shown that the computational procedure is closely related to traditional least-square analysis. Both linear and nonlinear models are considered. Results of computer simulations are presented for some simple cases.