Based on previous work by the authors as well as work by some others, this book summarizes a vast amount of literature concerning the modeling of uncertainty and risk assessment. A central idea is to analyze why the usage of probabilities (frequentist or Bayesian) is not enough to describe the whole of uncertainty. Part of the reasoning (as put forth in some of the works quoted by the authors) comes from establishing the fact that not all uncertainties are of a stochastic nature, and, hence, instead of trying to define non-probabilistic methods, it would be enough to find better ways of measuring (frequentist approach) or modeling (Bayesian approach).

Lingering all along are also the epistemic uncertainties, that is, those connected with lack of knowledge. The frequentist approach also assumes that in principle there are infinite “equal” or very similar repetitions, but more often than not, there is no basis for constructing probabilities upon such an assumption. Hence, several other approaches may complement probability. Among those is the usage of lower and upper probabilities, possibility theory (some sort of distribution of probability distributions), and degrees of belief (evidence theory). Examples of all of these approaches are presented and discussed succinctly, but with enough detail (including two appendices describing the operational procedures for treating uncertainty) to give the reader a good idea of how uncertainty (and hence, the numerical, approximate assessment of risk), probabilistic or not, can be treated. The details not contained in this work are more than well referenced.

The authors claim that the book is not about decision making once the risk has been assessed, but they do give key references for those interested in that subject. Indeed, this work should be treated as an important point of departure to learn, implement, or compare the different methods that exist for defining uncertainty and, as a result, performing better risk assessment. Therefore, I would recommend this book to a broad audience, from advanced undergraduates, to specialists, including probability theoreticians.