ABSTRACT
The theory of probability and statistics is an essential mathematical tool in the formulation of inverse problems, in the development of subsequent analysis and approaches to statistical hypothesis testing and model selection criteria, and in the study of uncertainty propagation in dynamic systems. Our coverage of these fundamental and important topics is brief and limited in scope. Indeed, we provide in this section a few definitions and basic concepts in the theory of probability and statistics that are essential for the understanding of estimators, confidence intervals, model selection criteria and stochastic processes. For more information on the topics in this chapter, selected references are provided at the end of these as well as subsequent chapters.
