Bayesian Approach for Inconsistent Information.
Bayesian Approach for Inconsistent Information.
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DOI：
10.1016/j.ins.2013.02.024
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发表时间：
2013-10-01
影响因子：
8.1
通讯作者：
Kreinovich, V.
中科院分区：
文献类型：
--
作者：
Stein, M.;Beer, M.;Kreinovich, V.
在工程情况下，我们通常有大量的先验知识，需要在处理数据时加以考虑。传统上，贝叶斯方法用于在存在先验知识的情况下处理数据。传统的贝叶斯方法在处理工程数据时，有时会出现数据与先验知识不一致的情况。这些不一致通常是由以下事实引起的：在传统方法中，我们假设我们知道确切的样本值，先验分布是确切已知的，等等。在现实中，由于测量误差，数据是不精确的，先验知识只是近似已知的，等等。所以，处理看似不一致的信息的自然方式是在贝叶斯方法中考虑这种不精确性-例如，通过使用模糊技术。在本文中，我们描述了几种可能的情况下模糊贝叶斯方法。特别注意估计的不精确参数之间的相互作用。在本文中，实现相应的模糊版本的贝叶斯公式，我们使用直接计算的相关表达式-这使得我们的计算相当耗时。传统（非模糊）贝叶斯方法的计算要快得多-因为它们使用贝叶斯公式的算法有效的重新表述。我们预计，类似的模糊贝叶斯公式的重新制定也将大大减少计算时间，从而提高所提出的方法的实际使用。
In engineering situations, we usually have a large amount of prior knowledge that needs to be taken into account when processing data. Traditionally, the Bayesian approach is used to process data in the presence of prior knowledge. Sometimes, when we apply the traditional Bayesian techniques to engineering data, we get inconsistencies between the data and prior knowledge. These inconsistencies are usually caused by the fact that in the traditional approach, we assume that we know the exact sample values, that the prior distribution is exactly known, etc. In reality, the data is imprecise due to measurement errors, the prior knowledge is only approximately known, etc. So, a natural way to deal with the seemingly inconsistent information is to take this imprecision into account in the Bayesian approach – e.g., by using fuzzy techniques. In this paper, we describe several possible scenarios for fuzzifying the Bayesian approach. Particular attention is paid to the interaction between the estimated imprecise parameters. In this paper, to implement the corresponding fuzzy versions of the Bayesian formulas, we use straightforward computations of the related expression – which makes our computations reasonably time-consuming. Computations in the traditional (non-fuzzy) Bayesian approach are much faster – because they use algorithmically efficient reformulations of the Bayesian formulas. We expect that similar reformulations of the fuzzy Bayesian formulas will also drastically decrease the computation time and thus, enhance the practical use of the proposed methods.
影响因子：
0.7
作者：
Viertl, R;Hareter, D
通讯作者：
Hareter, D