Non-Bayesian Testing of a Stochastic Prediction
Non-Bayesian Testing of a Stochastic Prediction
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随机预测的非贝叶斯检验
DOI：
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发表时间：
2006
期刊：
影响因子：
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通讯作者：
Yossi Feinberg
中科院分区：
文献类型：
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作者：
Eddie Dekel;Yossi Feinberg
我们提出了一种检验随机过程分布预测的方法。在非贝叶斯非参数设置中，使用随机过程的实现来测试预测分布。测试为预测通过的每个预测分布关联一组实现。为了不存在类型I错误，预测会将概率1分配给它的测试集。然而，这些集合都很小，因为“大多数”分布赋予它的概率为0，因此很少有第二类错误。结果还表明，存在这样一个不能被操纵的检验，即一个假装知道真实分布的不知情预测者，无论他采用什么随机预测，都肯定会在无数次实现中失败。我们使用的小集合的概念是类别I，在论文中进行了更详细的描述。
We propose a method to test a prediction of the distribution of a stochastic process. In a non-Bayesian non-parametric setting, a predicted distribution is tested using a realization of the stochastic process. A test associates a set of realizations for each predicted distribution, on which the prediction passes. So that there are no type I errors, a prediction assigns probability 1 to its test set. Nevertheless, these sets are small, in the sense that "most" distributions assign it probability 0, and hence there are few type II errors. It is also shown that there exists such a test that cannot be manipulated, in the sense that an uninformed predictor who is pretending to know the true distribution is guaranteed to fail on an uncountable number of realizations, no matter what randomized prediction he employs. The notion of a small set we use is category I, described in more detail in the paper.