The Relationship Between Information, Sampling Rates, and Parameter Estimation Models

Abstract

To estimate parameters from experiments requires the specification of models and each model will exhibit different degrees of sensitivity to the parameters sought. Although experiments can be optimally designed without regard to the experimental data actually realized, the precision of the estimated parameters is a function of the sensitivity and the statistical characteristics of the data. The precision is affected by any correlation in the data, either auto or cross, and by the choice of the model used to estimate the parameters. An informative way of looking at an experiment is by using the concept of Information. An analysis of an actual experiment is used to show how the information, the optimal number of sensors, the optimal sampling rates, and the model are affected by the statistical nature of the signals. The paper demonstrates that one must differentiate between the data needed to specify the model and the precision in the estimated parameters provided by the data.