Ranges of Posterior Measures for Priors with Unimodal Contaminations

We consider the problem of robustness or sensitivity of given Bayesian posterior criteria to specification of the prior distribution. Criteria considered include the posterior mean, variance and probability of a set (for credible regions and hypothesis testing). Uncertainty in an elicited prior, $\pi_0$ , is modelled by an $\varepsilon$ -contamination class $\Gamma = \{\pi = (1 - \varepsilon)\pi_0 + \varepsilon q, q \in Q\}$ , where $\varepsilon$ reflects the amount of probabilistic uncertainty in $\pi_0$ , and $Q$ is a class of allowable contaminations. For $Q = \{$ all unimodal distributions $\}$ and $Q = \{\text{all symmetric unimodal distributions}\}$ , we determine the ranges of the various posterior criteria as $\pi$ varies over $\Gamma$ .We consider the problem of robustness or sensitivity of given Bayesian posterior criteria to specification of the prior distribution. Criteria considered include the posterior mean, variance and probability of a set (for credible regions and hypothesis testing). Uncertainty in an elicited prior, $\pi_0$, is modelled by an $\varepsilon$-contamination class $\Gamma = \{\pi = (1 - \varepsilon)\pi_0 + \varepsilon q, q \in Q\}$, where $\varepsilon$ reflects the amount of probabilistic uncertainty in $\pi_0$, and $Q$ is a class of allowable contaminations. For $Q = \{$all unimodal distributions$\}$ and $Q = \{\text{all symmetric unimodal distributions}\}$, we determine the ranges of the various posterior criteria as $\pi$ varies over $\Gamma$.

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笔记与分组

分类依据与纠错

Ranges of Posterior Measures for Priors with Unimodal Contaminations

代码、数据与补充材料

单峰污染先验下后验量的取值范围

原文摘要

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