Foundations of Physics 29(10), pp. 1521-1541.
ISSN/ISBN: 0015-9018 DOI: 10.1023/A:1018806603833
Abstract: A new information matrix [F] with elements F_{mn}= ((y_{m} - a_{m} )(y_{n} - a_{n}) ( ∂ln p(y|a)/∂a_{m}) (∂ln p(y|a)/∂a_{n})) is analyzed. The PDF p(y|a) is the usual likelihood law. [F] differs from the Fisher information matrix by the presence of the first two factors in the given expectation. These factors make F_{mn} unitless, in contrast with the Fisher information. This lack of units allows F_{mn} values from entirely different phenomena to be compared as, for example, Shannon information values can be compared. Each element F_{mn} defines an error inequality analogous to the Cramer-Rao inequality. In the scalar case F_{mn}≡ F, for a normal p(y|a) law F = 3, while for an exponential law F = 9. A variational principle F = min (called FMIN) allows an unknown PDF p(x) to be estimated in the presence of weak information. Under certain conditions F obeys a "Boltzmann F-theorem" ∂F/∂t≤0, indicating that F is a physical entropy. Finally, the trace of [F] may be used as the scalar information quantity in an information-based principle for deriving distribution laws p of physics.
Bibtex:
@article{,
author="Frieden, B. Roy",
title="F-Information, a Unitless Variant of Fisher Information",
journal="Foundations of Physics",
year="1999",
month="Oct",
day="01",
volume="29",
number="10",
pages="1521--1541",
issn="1572-9516",
doi="10.1023/A:1018806603833",
url="https://doi.org/10.1023/A:1018806603833"
}
Reference Type: Journal Article
Subject Area(s): Physics