The use of precautionary loss functions in risk analysis

Abstract

Risk analysis is discussed within a Bayes framework. Traditionally, Bayes parameter estimation is based on a quadratic loss-function. This paper introduces an alternative asymmetric precautionary loss-function, derives its main features, and presents a general class of precautionary loss-functions with the quadratic loss-function as a special case. These loss functions approach infinity near the origin to prevent underestimates and thus give conservative estimates, especially when, for example, low failure rates are being estimated. The conservative estimates make these loss functions useful when the consequences are major and under-estimation is serious. They are intuitively appealing and easy to calculate.