Ranges of posterior probability over a distribution band. (English) Zbl 0813.62024
Summary: The sensitivity of the posterior probability of a fixed set \(C\) to the choice of the prior \(F\) is considered. A general method is described for finding the ranges of posterior probabilities when the prior c.d.f. \(F\) lies in the distribution band \(\Gamma^ D= \{F\): \(F_ L\leq F\leq F_ U\}\). This method is further extended to the unimodality restricted band \(\Gamma^ D_ U= \{F\in \Gamma^ D\): \(F\) is unimodal at \(M\}\). Several examples illustrate applications of this method.
MSC:
| 62F15 | Bayesian inference |
| 62F30 | Parametric inference under constraints |
| 62G35 | Nonparametric robustness |
Keywords:
Bayesian robustness; distribution band; Kolmogorov metric; Levy metric; choice of prior; sensitivity; ranges of posterior probabilities; unimodalityReferences:
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