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.

翻译：负概率主要出现在量子理论和计算中。Bartlett基于特征函数和奇异随机变量给出了一个定义。正如Bartlett所指出的，负概率必须始终与正概率结合，先得到有效的概率分布，才能进行物理解释。在贝叶斯建模中，负概率作为未观测潜变量的混合分布出现。我们的目标是建立对偶密度与正态分布尺度混合类之间的关联。我们分析了经典的半硬币分布和费曼的负概率示例，并提供了多个带有负混合测度的对偶密度实例，包括林尼克分布、维格纳分布和稳定分布。最后，我们总结了未来研究方向。