ABSTRACT
This chapter is intended to provide a summary of the main definitions and features of the concepts of probability theory and statistics that underlie sensitivity and uncertainty analysis of data and models. The main interpretations of probability commonly encountered in data and model analysis are that of relative frequency (which is used, in particular, for assigning statistical errors to measurements) and that of subjective probability (which is used, in particular, to quantify systematic uncertainties). From a mathematical point of view, however, the concepts of probability theory are optimally introduced by using Kolmogorov's axiomatic approach, in which probability is postulated in terms of abstract functions operating on well-defined event spaces. This axiomatic approach avoids both the mathematical ambiguities inherent to the concept of relative frequencies and the pitfalls of inadvertently misusing the concept of inductive reasoning. Nevertheless, all three interpretations of probability will be employed for the purposes of sensitivity and uncertainty analysis of models and data, in order to take advantage of their respective strengths.
