Local robustness measures for posterior summaries

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Local robustness measures for posterior summaries

Author Info

Passarin Katia () (Università della Svizzera Italiana, Istituto di Finanza, Facoltà di Economia)

Abstract

This paper deals with measures of local robustness for particular Bayesian quantities, i.e. posterior summaries. We build a framework where any Bayesian quantity can be seen as a posterior functional and its sensitivity to all inputs is checked. First, we use the Gateaux derivatives to measure the impact on posterior summaries of perturbations of prior or sampling models, giving some general expressions. Such quantities capture both a ’data effect’ and a ’model effect’ on the functional. Secondly, we check the sensitivity to one observation in the sample, once a particular combination of prior/sampling models has been chosen. Moreover, we propose a new estimator of the Bayes factor for practical implementation. Finally, illustrative examples on sensitivity analysis are provided and discussed.

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Paper provided by Department of Economics, University of Insubria in its series Economics and Quantitative Methods with number qf0405.

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Length: 35 pages
Date of creation: May 2004
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Handle: RePEc:ins:quaeco:qf0405

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Sivaganesan, Siva, 1999. "A likelihood based robust Bayesian summary," Statistics & Probability Letters, Elsevier, vol. 43(1), pages 5-12, May. [Downloadable!] (restricted)
Peña, Daniel & Zamar, Ruben, 1997. "A simple diagnostic tool for local prior sensitivity," Statistics & Probability Letters, Elsevier, vol. 36(2), pages 205-212, December. [Downloadable!] (restricted)
Sanjib Basu, 1999. "Posterior Sensitivity to the Sampling Distribution and the Prior: More than One Observation," Annals of the Institute of Statistical Mathematics, Springer, vol. 51(3), pages 499-513, September. [Downloadable!] (restricted)
Chib S. & Jeliazkov I., 2001. "Marginal Likelihood From the Metropolis-Hastings Output," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 270-281, March. [Downloadable!] (restricted)
Mira Antonietta & Nicholls Geoff, 2001. "Bridge estimation of the probability density at a point," Economics and Quantitative Methods qf0105, Department of Economics, University of Insubria. [Downloadable!]

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