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首页> 外文期刊>Kybernetika >φ-DIVERGENCES, SUFFICIENCY, BAYES SUFFICIENCY, AND DEFICIENCY
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φ-DIVERGENCES, SUFFICIENCY, BAYES SUFFICIENCY, AND DEFICIENCY

机译：φ-分流，充裕度，贝叶斯充裕度和不足

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摘要

The paper studies the relations between φ-divergences and fundamental concepts of decision theory such as sufficiency, Bayes sufficiency, and LeCam's deficiency. A new and considerably simplified approach is given to the spectral representation of φ-divergences already established in OEsterreicher and Feldman [28] under restrictive conditions and in Liese and Vajda [22], [23] in the general form. The simplification is achieved by a new integral representation of convex functions in terms of elementary convex functions which are strictly convex at one point only. Bayes sufficiency is characterized with the help of a binary model that consists of the joint distribution and the product of the marginal distributions of the observation and the parameter, respectively. LeCam's deficiency is expressed in terms of φ-divergences where φ belongs to a class of convex functions whose curvature measures are finite and satisfy a normalization condition.
机译：本文研究了φ散度与决策理论的基本概念（如充分性，贝叶斯充分性和LeCam缺陷）之间的关系。一种新的且相当简化的方法是对在限制性条件下在OEsterreicher和Feldman [28]中以及在一般形式的Liese和Vajda [22]，[23]中已经建立的φ-散度的频谱表示进行了描述。通过仅在一个点上严格凸出的基本凸函数方面的新的凸函数积分表示，可以实现简化。贝叶斯充足性的特征在于一个二元模型，该模型分别由联合分布以及观测值和参数的边际分布的乘积组成。 LeCam的不足用φ散度表示，其中φ属于一类凸函数，其曲率度量是有限的并且满足归一化条件。

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