Probability Density Functions from the Fisher Information Metric
Abstract
We show a general relation between the spatially disjoint product of probability density functions and the sum of their Fisher information metric tensors. We then utilise this result to give a method for constructing the probability density functions for an arbitrary Riemannian Fisher information metric tensor. We note further that this construction is extremely unconstrained, depending only on certain continuity properties of the probability density functions and a select symmetry of their domains.
 Publication:

arXiv eprints
 Pub Date:
 April 2015
 arXiv:
 arXiv:1504.03184
 Bibcode:
 2015arXiv150403184C
 Keywords:

 Computer Science  Information Theory;
 Mathematics  Differential Geometry;
 Mathematics  Statistics Theory;
 Physics  Data Analysis;
 Statistics and Probability
 EPrint:
 16 pages, no figures