Introduction to Imprecise Probabilities

A brief outline of this book

This book consists of 16 closely interrelated chapters. It starts by introducing the basic concepts of the theory (Chapters 1 to 6), then turns to general fields of application (Chapters 7 to 11), provides an insight into the use of imprecise probabilities in engineering, financial risk measurement and reliability analysis (Chapters 12 to 14) and concludes with aspects of elicitation and computation (Chapters 15 and 16).

The notion of desirability, as described in Chapter 1, lies at the core of the behavioural approach to imprecise probabilities, and the discussion there provides a foundation and justification for the account of lower previsions presented in later chapters. It deals with coherence, and with the associated notion of inference using natural extension, marginalization and conditioning.

Chapter 2 discusses (conditional) lower previsions and the notions of coherence associated with them. It also shows how the notion of natural extension provides the theory with a powerful method of conservative (or least committal) probabilistic inference.

Chapter 3 explains how to deal with structural assessments of independence and symmetry in the theory of coherent lower previsions. In particular, the different concepts of independence used in later chapters are explained in detail.

Chapter 4 investigates simplified representations by less general model classes, which are often useful as they are easier for computation and elicitation, and because ...