Asymptotic global robustness in bayesian decision theory

Asymptotic Global Robustness in Bayesian Decision Theory

In Bayesian decision theory, it is known that robustness with respect to the loss and the prior can be improved by adding new observations. In this article we study the rate of robustness improvement with respect to the number of observations n. Three usual measures of posterior global robustness are considered: the (range of the) Bayes actions set derived from a class of loss functions, the ma...

Optimal alternative robustness in Bayesian Decision Theory

In Martin et al (2003), we suggested an approach to general robustness studies in Bayesian Decision Theory and Inference, based on ǫ-contamination neighborhoods. In this note, we generalise the results considering neighborhoods based on norms, specifically, the supremum norm for utilities and the total variation norm for probability distributions. We provide tools to detect changes in preferenc...

Intrinsic Robustness of Global Asymptotic Stability

Bayesian Decision Making Theory

Bayesian robustness for decision making problems: Applications in medical contexts

Practical implementation of Bayesian decision making is hindered by the fact that optimal decisions may be sensitive to the model inputs: the prior, the likelihood and/or the underlying utility function. Given the structure of a problem, the analyst has to decide which sensitivity measures are relevant and compute them efficiently. We address the issue of robustness of the optimal action in a d...