Risk assessment and decision analysis with Bayesian networks. (Q2919533)

This book provides core principles of Bayesian networks and their applications in risk assessment and decision making as well as motivation and examples of such applications. It consists of thirteen chapters and five appendices. The chapters can be conditionally classified into three parts: motivating the use of Bayesian networks (Chapters 1--3), probabilistic foundations, statistical inference and structure identification of Bayesian networks (Chapters 4--10) and applications of Bayesian networks to risk assessment and decision making (Chapters 11--13).NEWLINENEWLINEIn Chapter 1 it is argued that assessing risk is not counting of some statistics. Common fallacies and pitfalls of straightforward statistical procedures (masking effect of averaging, spurious correlations, Simpson's paradox and others) are discussed. In Chapter 2 the need of an explanatory model representing causal effects is emphasized. Chapter 3 is devoted to uncertainty and its measuring. Advantages of a subjective Bayesian view of uncertainty versus a frequentist view are indicated.NEWLINENEWLINEChapter 4 provides basics of discrete probability theory. The case of continuous probability distributions is postponed to Chapter 9. Chapter 5 is crucial for the understanding of the Bayesian approach. Here, conditional probabilities are defined and Bayes' theorem is formulated. Chapter 6 links Bayes' theorem with Bayesian networks. Modelling of multiple causes and multiple consequences via Bayesian networks are explained and illustrated by taking well-known probability paradoxes as examples. Defining the structure of Bayesian networks is addressed in Chapter 7. Specification of dependencies between nodes is based on (conditional) independence. Methods and problems of building the Bayesian networks are discussed. A separate chapter (Chapter 8) is devoted to one of them, namely the problem of calculating node probability tables for large Bayesian networks. Chapter 9 deals with continuous random variables and probability distributions. Since the standard inference algorithms of Bayesian networks only work in the case where every node has a finite set of states, continuous variables cause a problem. It is effectively solved by a dynamic discretization algorithm proposed instead of a static one. In Chapter 10 the Bayesian approach to hypothesis testing and confidence intervals is presented. It is contrasted with the classical one by demonstrating limitations and fallacies of the latter.NEWLINENEWLINEThree fields of Bayesian network applications are discussed in the book. Chapter 11 is devoted to modelling of operational risk, in particular financial risk, for any organization. The need to take a system perspective is stressed. It is also argued that Bayesian networks can replace various existing techniques, such as value-at-risk analysis, fault-tree analysis, event-tree analysis, etc. Chapter 12 deals with modelling of complex system reliability using dynamic Bayesian trees. Two different scenarios are distinguished: a case of discrete probability of failure and a case of continuous time to failure. In the last chapter it is explained how Bayesian reasoning can help lawyers to evaluate available evidence and to increase the transparency and the accuracy of their verdicts.NEWLINENEWLINEThe more mathematical and technical topics are given in five appendices: the basics of counting, the algebra of node probability tables, junction tree algorithm, dynamic discretization, statistical distributions.NEWLINENEWLINEThe focus of the book is on applications and practical Bayesian network model building. Although it is suitable for undergraduate courses on probability and risk, it is written to be understandable by other professional people generally interested in risk assessment and decision making. A free version of the commercial software tool \texttt{AgenaRisk} is available for those who have purchased the book.