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By Allan L. Scherr

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And MARTIN, J. (2000). Bayesian sensitivity analysis: a review. To appear in Handbook on Sensitivity Analysis (A. ). New York: Wiley. , Rios INSUA, D. and RUGGERI, F. (1999). Bayesian forecasting for accident proneness evaluation. Scandinavian Actuarial Journal, 99, 134-156. RUGGERI, F. (1990). Posterior ranges of functions of parameters under priors with specified quantiles. Communications in Statistics A: Theory and Methods, 19, 127-144. RUGGERI, F. and SIVAGANESAN, S. (2000). On a global sensitivity measure for Bayesian inference.

Sensitivity of some standard Bayesian estimates to prior uncertainty - a comparison. Journal of Statistical Planning and Inference, 27, 85-103. SIVAGANESAN, S. (1993). Robust Bayesian diagnostics. Journal of Statistical Planning and Inference, 35, 171-188. SIVAGANESAN, S. (2000). Global and local robustness approaches: uses and limitations. In Robust Bayesian Analysis, (D. Rios Insua and F. ). New York: Springer-Verlag. SIVAGANESATIi, S. and BERGER, J. (1989). Ranges of posterior measures for priors with unimodal contaminations.

1. 3 23 Hierarchical approaches We have already mentioned that hierarchical modeling has certain inherent robustness properties. We further mentioned that one approach to dealing with a lack of robustness (with respect to, say, the prior) is to place a hyperprior on the class of priors, which is a type of hierarchical analysis. Indeed, if there were no possibility of obtaining additional information to deal with the lack of robustness, we would recommend this technique, with the hyperprior being chosen in some default fashion.

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