Non-Parametric Statistical Diagnosis
Non-Parametric Statistical Diagnosis
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非参数统计诊断
DOI：
10.1007/978-94-015-9530-8
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发表时间：
2000
期刊：
影响因子：
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通讯作者：
B. Darkhovsky
中科院分区：
文献类型：
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作者：
B. Brodsky;B. Darkhovsky
这本书有一个独特的哲学，它是适当的，使它明确在一开始。在我们看来，几乎所有经典的统计推断都是基于这样一个假设（显式或隐式），即存在一个固定的数据生成概率机制。不同于经典的统计推断，这本书致力于对复杂对象的数据进行统计分析，这些对象具有一个以上的数据生成概率机制。我们认为复杂系统最重要的特征是存在多个数据生成过程（DGP）。当统计同质性假设成立时，只有一种数据生成机制，所有的统计推断都是基于大数定律。然而，当数据生成的概率定律可以改变时（在时间或相空间中），情况完全不同。在这种情况下，获得的所有数据必须在由不同概率机制生成的子样本中进行“排序”。只有这样的分类后，我们才能对所有的DGP做出正确的推断。复杂系统还存在另一类问题。在这里，重要的是检测可能的（但不可预测的）变化的DGP在线数据收集。由于复杂的系统可以改变数据生成的概率机制，因此对此类数据的正确统计分析必须从关于DGP可能变化的决策开始开始。
This book has a distinct philosophy and it is appropriate to make it explicit at the outset. In our view almost all classic statistical inference is based upon the assumption (explicit or implicit) that there exists a fixed probabilistic mechanism of data generation. Unlike classic statistical inference, this book is devoted to the statistical analysis of data about complex objects with more than one probabilistic mechanism of data generation. We think that the exis tence of more than one data generation process (DGP) is the most important characteristic of com plex systems. When the hypothesis of statistical homogeneity holds true, Le., there exists only one mechanism of data generation, all statistical inference is based upon the fundamentallaws of large numbers. However, the situation is completely different when the probabilistic law of data generation can change (in time or in the phase space). In this case all data obtained must be'sorted'in subsamples generated by different probabilistic mechanisms. Only after such classification we can make correct inferences about all DGPs. There exists yet another type of problem for complex systems. Here it is important to detect possible (but unpredictable) changes of DGPs on-line with data collection. Since the complex system can change the probabilistic mechanism of data generation, the correct statistical analysis of such data must begin with decisions about possible changes in DGPs.