负概率

Nick Polson, Vadim Sokolov
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引用次数: 0

摘要

巴特利特根据特征函数和超常随机变量给出了一个定义。正如巴特利特所观察到的,负概率必须总是与正概率相结合,才能产生有效的概率分布,然后才能进行任何物理解释。负概率作为贝叶斯建模中未观察到的潜在变量的混合分布而出现。我们的目标是提供一种与对偶性和正态分布规模混合物类的联系。我们分析了经典的半硬币分布和费曼的负概率例子。我们还提供了一些具有负混合度量的对偶密度实例,包括林尼克分布、维格纳分布和稳定分布。最后,我们总结了未来的研究方向。
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Negative Probability
Negative probabilities arise primarily in quantum theory and computing. Bartlett provides a definition based on characteristic functions and extraordinary random variables. As Bartlett observes, negative probabilities must always be combined with positive probabilities to yield a valid probability distribution before any physical interpretation is admissible. Negative probabilities arise as mixing distributions of unobserved latent variables in Bayesian modeling. Our goal is to provide a link with dual densities and the class of scale mixtures of normal distributions. We provide an analysis of the classic half coin distribution and Feynman's negative probability examples. A number of examples of dual densities with negative mixing measures including the linnik distribution, Wigner distribution and the stable distribution are provided. Finally, we conclude with directions for future research.
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