Posterior Sensitivity to the Sampling Distribution and the Prior: More than One Observation |
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Authors: | Sanjib Basu |
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Affiliation: | (1) Department of Mathematical Sciences, University of Arkansas, Fayetteville, AR, 72701, U.S.A. |
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Abstract: | Sensitivity of a posterior quantity (f, P) to the choice of the sampling distribution f and prior P is considered. Sensitivity is measured by the range of (f, P) when f and P vary in nonparametric classes f and P respectively. Direct and iterative methods are described which obtain the range of (f, P) over ff when prior P is fixed, and also the overall range over ff and PP. When multiple i.i.d. observations X1,...,Xk are observed from f, the posterior quantity (f, P) is not a ratio-linear function of f. A method of steepest descent is proposed to obtain the range of (f, P). Several examples illustrate applications of these methods. |
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Keywords: | Bayesian robustness Gâ teaux derivative model robustness model selection predictive distribution prior robustness steepest descent |
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