## Abstract Let __X~a,b~__ be nonnegative random variables with the property that __X~a,b~ β¦ X~a,c~ + X~c.b~__ for all 0__β¦ a < c < b β¦ T__, where __T >__ 0 is fixed. We define __M~a,b~ =__ sup {__X~a,c~: a < c β¦ h__} and establish bounds for __P__[__M~a,b~ β§ Ξ»__] in terms of given bounds for __P[X
Inequalities for estimative and predictive probabilities
β Scribed by D. R. Jensen
- Publisher
- John Wiley and Sons
- Year
- 1980
- Tongue
- English
- Weight
- 255 KB
- Volume
- 22
- Category
- Article
- ISSN
- 0323-3847
No coin nor oath required. For personal study only.
β¦ Synopsis
Abstract
Let ΞΌE be the estimative and ΞΌP the predictive measures for assessing Gaussian probabilities. It is shown for convex symmetric sets A that ~ΞΌE~(A) ~ΞΌP~(A) and that similar inequalities hold between members of a sequence of predictive measures. An application yields inequalities for generalized indices of atypicality associated with the two methods.
π SIMILAR VOLUMES
This paper concerns the evaluation and combination of subjective probability estimates for categorical events. We argue that the appropriate criterion for evaluating individual and combined estimates depends on the type of uncertainty the decision maker seeks to represent, which in turn depends on h