Abstract
The local sensitivity of a posterior quantity ρ(P) to the choice of the prior P is considered. When the prior Pλ is indexed by parameter λ, a natural measure is the total derivative of ρ(P λ) w.r.t. λ. Total derivative, however, is direction specific. To measure the local sensitivity of ρ(P λ) to specification of λ, one may either use the norm (maximum over all directions) of the total derivative or alternatively, the average sensitivity which evaluates the average of this total derivative over all directions. Simple expressions are given for the maximum and average sensitivity which make their evaluations very easy. Discussion and several examples illustrate implications of these ideas.
Research supported in part by ONR Grant number N00014-93-1-0174.
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© 1996 Springer Science+Business Media Dordrecht
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Basu, S., Jammalamadaka, S.R., Liu, W. (1996). Local Posterior Robustness with Parametric Priors: Maximum and Average Sensitivity. In: Heidbreder, G.R. (eds) Maximum Entropy and Bayesian Methods. Fundamental Theories of Physics, vol 62. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-8729-7_6
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DOI: https://doi.org/10.1007/978-94-015-8729-7_6
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