Abstract

Consider two "nearby" probability distributions. One can try to determine which distribution is the true distribution by making repeated measurements on an ensemble of systems-It is natural to introduce a statistical distance between the two distributions, which is larger since it is easier to distinguish the two distributions by using the results of the measurements. The statistical distance defines a Riemannian metric on the simplex of probability distributions. For nearby distributions, the statistical distance is directly related to the inverse of the Fisher information, a quantity that comes from estimation theory; the statistical distance is also related to χ² and to the relative or Kullback information between the distributions.

© 1992 Optical Society of America