Information field theory
Information field theory (IFT) is information theory, the logic of reasoning under uncertainty, applied to fields. A field can be any quantity defined over some space, e.g. the air temperature over Europe, the magnetic field strength in the Milky Way, or the matter density in the Universe. IFT describes how data and knowledge can be used to infer field properties. Mathematically it is a statistical field theory and exploits many of the tools developed for such. Practically, it is a framework for signal processing and image reconstruction.
IFT
is fully Bayesian. How else can infinitely many field degrees of
freedom be constrained by finite data?
It can be used without
the knowledge of Feynman diagrams. There is a full toolbox of
methods.
It reproduces many known well working algorithms. This
should be reassuring.
And, there were certainly previous works
in a similar spirit. See below for IFT publications and previous
works.
Anyhow, in many cases IFT provides novel rigorous ways
to extract information from data.
Please, have a look! The specific literature is listed below and more general highlight articles on the right hand side.
IFT publications:
`Information
field theory
for
cosmological perturbation reconstruction and non-linear signal
analysis'
Torsten
A. Enßlin, Mona Frommert, Francisco S. Kitaura 2009, Phys.
Rev. D 80, 105005
(Abstract)
(Source)
(Postscript) (PDF)
(eJournal)
`Inference
with minimal Gibbs free energy in information field
theory'
Torsten
A. Enßlin, Cornelius Weig 2010, Physical Review E 82, 051112
(Abstract)
(Source) (PDF)
(eJournal)
(Comment
on Paper)
(Reply
to Comment)
`Reconstruction
of signals with unknown spectra in information field theory with
parameter uncertainty'
Torsten
A. Enßlin, Mona Frommert 2011, Physical Review D 83, 105014
(Abstract)
(Source) (PDF)
(eJournal)
`Reconstructing
signals from noisy data with unknown signal and noise
covariances'
Niels
Oppermann, Georg Robbers, Torsten A. Enßlin, 2011, Physical
Review E 84, 041118
(Abstract)
(Source) (PDF)
(eJournal)
and more related papers …, as well as IFT lecture notes
IFT applications:
`Cosmic
Cartography of the Large-Scale Structure with Sloan Digital Sky
Survey Data Release 6'
Francisco
S. Kitaura, Jens Jasche, Cheng Li, Torsten A. Enßlin,
R.Benton Metcalf, Benjamin D. Wandelt, Gerard Lemson, Simon D.M.
White 2009, MNRAS 400, 183
(Abstract)
(Source)
(Postscript) (PDF)
`Bayesian
power-spectrum inference for Large Scale Structure data'
Jens
Jasche, Francisco S. Kitaura, Benjamin D. Wandelt, Torsten A.
Enßlin 2010, MNRAS 406, 60
(Abstract)
(Source) (PDF)
`Fast
Hamiltonian sampling for large-scale structure inference'
Jens
Jasche, Francisco S. Kitaura 2010, MNRAS 407, 29
(Abstract)
(Source) (PDF)
`Bayesian
non-linear large scale structure inference of the Sloan Digital
Sky Survey data release 7'
Jens
Jasche, Francisco S. Kitaura, Cheng Li, Torsten A. Enßlin
2010, MNRAS 409, 355
(Abstract)
(Source) (PDF)
(eJournal)
`Bayesian
analysis of spatially distorted cosmic signals from Poissonian
data'
Cornelius
Weig, Torsten A. Enßlin 2010, MNRAS 409, 1393
(Abstract)
(Source) (PDF)
`Probing
Magnetic Helicity with Synchrotron Radiation and Faraday
Rotation'
Niels
Oppermann, Henrik Junklewitz, Georg Robbers, Torsten A. Enßlin
2011, Astronomy and Astrophysics, 530, id.A89
(Abstract)
(Source) (PDF)
`Improving
stochastic estimates with inference methods: calculating matrix
diagonals'
Marco
Selig, Niels Oppermann, Torsten A. Enßlin, Phys. Rev. E 85,
021134 (2012)
(Abstract)
(Source)
(PDF)(eJournal)
`An
improved map of the Galactic Faraday sky'
Niels
Oppermann, et al., submitted, arXiv:1111.6186
(Abstract)
(Source) (PDF)
IFT highlight articles:
09/09:
Mathematik
digitaler Sinne / Mathematics
of digital senses
10/09: Sehhilfe
für kosmische Blindstellen
11/09: 40
000 Universen
11/01:
Datenanalyse
und Dampfmaschinen / Data
analysis and steam engines
other important openly accessible internet publications:
`Bayesian
Field Theory: Nonparametric Approaches to Density Estimation,
Regression, Classification, and Inverse Quantum Problems'
J.
C. Lemm, arXiv
e-print
(arXiv:physics/9912005)
and
more
of his works ...
`MAGIC:
Exact Bayesian Covariance Estimation and Signal Reconstruction for
Gaussian Random Fields'
B.
Wandelt, arXiv
e-print (arXiv:astro-ph/0401623)
`Lectures
on Probability, Entropy, and Statistical Physics'
A.
Caticha, arXiv
e-print (arXiv:0808.0012)
related discussion forums:
Astrostatistics and Astroinformatics Portal
Bayes Forum, a monthly seminar in Garching.
useful tools:
SAGE, a free open source software system for mathematics
contact:
Highlights
IFT
& Feynman diagrams
