DEMPSTER-SHAFER INFERENCE WITH WEAK BELIEFS
DEMPSTER-SHAFER INFERENCE WITH WEAK BELIEFS
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弱信念的登普斯特-谢弗推论
DOI：
10.5705/ss.2011.022a
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发表时间：
2011
影响因子：
1.4
通讯作者：
Chuanhai Liu
中科院分区：
文献类型：
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作者：
Jianchun Zhang;Chuanhai Liu
A. P. Dempster 在 1960 年代的工作使用多值映射扩展了 Fisher 的参数推理的基准推理，而 G. Shafer 在 1970 年代在评估和组合证据方面的工作导致了现在被称为 Dempster-Shafer (DS) 信念函数理论。然而，DS 在参数推理中的应用可能由于其计算困难、非唯一性和缺乏频率特性而受到限制。在本文中，我们回到 Dempster 为参数推理构建置信函数的原始方法，称为基本 DS 模型（BDSM），它们是所谓焦点元素空间上的常见概率模型。我们建议通过扩大焦点元素来修改 BDSM，以获得具有所需频率特性的置信函数。我们将我们的方法称为弱信念（WB）。当将焦点元素放大到不超过必要的程度时，WB 方法称为最大置信法 (MB)。 MB方法用两个例子来说明：(i)关于二项式比例的推断，以及(ii)基于观测数据X1，...推断异常值的数量(μi 6 0)。 。 。 , Xn 与模型 Xi ind » N (μi, 1)。
The work of A. P. Dempster in 1960s extending Fisher's fiducial infer- ence for parametric inference using multivalued mapping, and that of G. Shafer in 1970s on the assessment and combination of evidence led to what is now known as the Dempster-Shafer (DS) theory of belief functions. However, application of DS for parametric inference has been limited due, perhaps, to its computational diffi- culty, non-uniqueness, and lack of frequency properties. In this paper, we return to Dempster's original approach to constructing belief functions for parametric infer- ence, called basic DS models (BDSMs), which are usual probability models on the space of the so-called focal elements. We propose to modify BDSMs by enlarging focal elements to obtain belief functions that have desired frequency properties. We call our method Weak Belief (WB). When it enlarges the focal elements no more than necessary, the method of WB is called Maximal Belief (MB). The MB method is illustrated with two examples: (i) inference about a binomial proportion, and (ii) inference about the number of outliers (µi 6 0) based on the observed data X1, . . . , Xn with the model Xi ind » N (µi, 1).