Probability Density Functions from the Fisher Information Metric
Information Theory
2015-04-14 v1 Differential Geometry
math.IT
Statistics Theory
Data Analysis, Statistics and Probability
Statistics Theory
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.
Keywords
Cite
@article{arxiv.1504.03184,
title = {Probability Density Functions from the Fisher Information Metric},
author = {T. Clingman and Jeff Murugan and Jonathan P. Shock},
journal= {arXiv preprint arXiv:1504.03184},
year = {2015}
}
Comments
16 pages, no figures