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The area of quantitative operational risk has undergone explosive development for the last five years and is of critical importance for the banking industry. It is driven mainly by recent Basel II regulatory requirements that introduced definitions and capital charges for operational risk. The area of quantitative operational risk is very new and the different approaches to it are heatedly debated. This book is devoted to quantitative issues in the loss distribution approach for operational risk being adopted in many banks. In particular, the use of the Bayesian inference method is the main focus of this book. Though it is very new in this area, the Bayesian approach is well suited for modelling operational risk, as it provides a consistent and convenient statistical framework to quantify the uncertainties involved. It also allows the combination of expert opinions with historical internal and external data in estimation procedures. These are critical, especially for operational risks with small datasets.