This book introduces the principles of Bayesian Decision Analysis and describes how this theory can be applied to a wide range of decision problems. It is written in two parts. The first presents what I consider to be the most important principles and good practice in mostly simple settings. The second part shows how the established methodology can be extended so that it can address the sometimes very complex and data-rich structures a decision maker might face. It will serve as a course book for a 30-lecture course on Bayesian decision modelling given to final-year undergraduates with a mathematical core to their degree programme and statistics Master's students at Warwick University. Complementary material given in two parallel courses, one on Bayesian numerical methods and the other on Bayesian Time Series given subsequently at Warwick, is largely omitted although these subjects are motivated within the text. This book contains foundational material on the subjective probability theory and multiattribute utility theory – with a detailed discussion of efficacy of various assumptions underlying these constructs – and quite an extensive treatment of frameworks such as event and decision trees, Bayesian Networks, as well as Influence Diagrams and Causal Bayesian Networks. These graphical methods help draw different aspects of a decision problem together into a coherent whole and provide frameworks where data can be used to support a Bayesian decision analysis.

This is not just a text book; it also provides additional material to help the reader develop a more profound understanding of this fascinating and highly cross-disciplinary subject.