Parameter Estimation

In general, a model describes-through suitable equations-the relationship between some inputs and some (measurable) outputs. This relationship is constituted from two parts: the model structure, that is, the mathematical law that describes a family of possible behaviors and the model parameters, that is, those quantities that can vary from one situation to another and that modulate and completely define the relationship. Assuming that model structure is known, the present chapter presents the basic concepts and techniques for parameter estimation (also called model identification), that is, the capability of deriving numerical values for model parameters from a set of noisy measurements. In particular, by using suitable case studies taken from the literature, Fisherian (e.g., least squares, maximum likelihood) and Bayesian estimators (e.g., maximum a posteriori) are presented, the latter also with probability distributions handled through Markov chain Monte Carlo simulation techniques. Analysis of the residuals for model checking and computation of the parameter estimate precisions are also discussed. © 2014 Elsevier Inc. All rights reserved.