Ranges of posterior probabilities for unimodal priors with specified quantiles. (English) Zbl 0706.62028
Bayesian statistics 3, Proc. 3rd Valencia Int. Meet., Altea/Spain 1987, 45-65 (1988).
Summary: [For the entire collection see Zbl 0702.00028.]
Suppose several quantiles of the prior distribution for \(\theta\) are specified or, equivalently, the prior probabilities of a partitioning collection of intervals \(\{I_ i\}\) are given. Suppose in addition, that the prior distribution is assumed to be unimodal. Rather than selecting a single prior distribution to perform a Bayesian analysis, the class of all prior distributions compatible with these inputs will be considered. For this class and unimodal likelihood functions, the ranges of the posterior probabilities of the \(I_ i\), and of the posterior c.d.f. at the specified prior quantiles, are determined. Small ranges ensure robustness with respect to the exact functional form of the prior.
Suppose several quantiles of the prior distribution for \(\theta\) are specified or, equivalently, the prior probabilities of a partitioning collection of intervals \(\{I_ i\}\) are given. Suppose in addition, that the prior distribution is assumed to be unimodal. Rather than selecting a single prior distribution to perform a Bayesian analysis, the class of all prior distributions compatible with these inputs will be considered. For this class and unimodal likelihood functions, the ranges of the posterior probabilities of the \(I_ i\), and of the posterior c.d.f. at the specified prior quantiles, are determined. Small ranges ensure robustness with respect to the exact functional form of the prior.
MSC:
| 62F15 | Bayesian inference |
