This book gives an overview of rigorous risk analysis, linking it to Bayesian decision theory and demonstrating practical implementations. Risk analysis is the final step before decision-making. But what is risk, and how do we quantify the key components of risk? This book aims to provide clear definitions, formulas and algorithms.Risk is the expectation of loss due to a hazard. It is high when both hazard probability and system vulnerability are high. We show how these terms should be defined to allow a formal decomposition of risk as the mathematical product of hazard probability and system vulnerability. From these definitions we derive a comprehensive theory of risk analysis and its links with Bayesian decision theory (BDT). We present formulas for risk and its components, and for quantifying the uncertainties associated with these estimates. We also show how the formulas for PRA and BDT can be implemented in R. All the computer code used in this book, including that for producing tables and figures, can be downloaded from the book's public GitHub repository.This book is intended for researchers and decision-makers with an interest in rigorous risk analysis. Some familiarity with probability theory will make the book easier to digest, but it includes simple introductions to both probabilistic risk analysis and Bayesian decision theory. Jargon is avoided as much as possible, and all terms are defined within the book itself. Many examples of applications are included, mostly using simple data sets. The examples are from the environmental sciences, but the analytical methods are completely generic. The theory is applicable to both discrete event hazards (e.g. earthquakes) and continuous hazards (e.g. pollution or water availability).This second edition adds new sections on uncertainty quantification, continuous risk analysis, interacting hazards, dataset quality, and the Value of Information concept in decision theory. Literature references have been updated throughout, and exercises have been added to each chapter, all with solutions.
