  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.
