185 research outputs found
Astrophysical data analysis with information field theory
Non-parametric imaging and data analysis in astrophysics and cosmology can be
addressed by information field theory (IFT), a means of Bayesian, data based
inference on spatially distributed signal fields. IFT is a statistical field
theory, which permits the construction of optimal signal recovery algorithms.
It exploits spatial correlations of the signal fields even for nonlinear and
non-Gaussian signal inference problems. The alleviation of a perception
threshold for recovering signals of unknown correlation structure by using IFT
will be discussed in particular as well as a novel improvement on instrumental
self-calibration schemes. IFT can be applied to many areas. Here, applications
in in cosmology (cosmic microwave background, large-scale structure) and
astrophysics (galactic magnetism, radio interferometry) are presented.Comment: 4 pages, 2 figures, accepted chapter to the conference proceedings
for MaxEnt 2013, to be published by AI
Information field theory
Non-linear image reconstruction and signal analysis deal with complex inverse
problems. To tackle such problems in a systematic way, I present information
field theory (IFT) as a means of Bayesian, data based inference on spatially
distributed signal fields. IFT is a statistical field theory, which permits the
construction of optimal signal recovery algorithms even for non-linear and
non-Gaussian signal inference problems. IFT algorithms exploit spatial
correlations of the signal fields and benefit from techniques developed to
investigate quantum and statistical field theories, such as Feynman diagrams,
re-normalisation calculations, and thermodynamic potentials. The theory can be
used in many areas, and applications in cosmology and numerics are presented.Comment: 8 pages, in-a-nutshell introduction to information field theory (see
http://www.mpa-garching.mpg.de/ift), accepted for the proceedings of MaxEnt
2012, the 32nd International Workshop on Bayesian Inference and Maximum
Entropy Methods in Science and Engineerin
The rationality of irrationality in the Monty Hall problem
The rational solution of the Monty Hall problem unsettles many people. Most
people, including the authors, think it feels wrong to switch the initial
choice of one of the three doors, despite having fully accepted the
mathematical proof for its superiority. Many people, if given the choice to
switch, think the chances are fifty-fifty between their options, but still
strongly prefer to stay with their initial choice. Is there some sense behind
these irrational feelings?
We entertain the possibility that intuition solves the problem of how to
behave in a real game show, not in the abstract textbook version of the Monty
Hall problem. A real showmaster sometimes plays evil, either to make the show
more interesting, to save money, or because he is in a bad mood. A moody
showmaster erases any information advantage the guest could extract by him
opening other doors which drives the chance of the car being behind the chosen
door towards fifty percent. Furthermore, the showmaster could try to read or
manipulate the guest's strategy to the guest's disadvantage. Given this, the
preference to stay with the initial choice turns out to be a very rational
defense strategy of the show's guest against the threat of being manipulated by
its host. Thus, the intuitive feelings most people have about the Monty Hall
problem coincide with what would be a rational strategy for a real-world game
show. Although these investigations are mainly intended to be an entertaining
mathematical commentary on an information-theoretic puzzle, they touch on
interesting psychological questions.Comment: 4 pages, no figures, revised articl
DPO - Denoising, Deconvolving, and Decomposing Photon Observations
The analysis of astronomical images is a non-trivial task. The D3PO algorithm
addresses the inference problem of denoising, deconvolving, and decomposing
photon observations. Its primary goal is the simultaneous but individual
reconstruction of the diffuse and point-like photon flux given a single photon
count image, where the fluxes are superimposed. In order to discriminate
between these morphologically different signal components, a probabilistic
algorithm is derived in the language of information field theory based on a
hierarchical Bayesian parameter model. The signal inference exploits prior
information on the spatial correlation structure of the diffuse component and
the brightness distribution of the spatially uncorrelated point-like sources. A
maximum a posteriori solution and a solution minimizing the Gibbs free energy
of the inference problem using variational Bayesian methods are discussed.
Since the derivation of the solution is not dependent on the underlying
position space, the implementation of the D3PO algorithm uses the NIFTY package
to ensure applicability to various spatial grids and at any resolution. The
fidelity of the algorithm is validated by the analysis of simulated data,
including a realistic high energy photon count image showing a 32 x 32 arcmin^2
observation with a spatial resolution of 0.1 arcmin. In all tests the D3PO
algorithm successfully denoised, deconvolved, and decomposed the data into a
diffuse and a point-like signal estimate for the respective photon flux
components.Comment: 22 pages, 8 figures, 2 tables, accepted by Astronomy & Astrophysics;
refereed version, 1 figure added, results unchanged, software available at
http://www.mpa-garching.mpg.de/ift/d3po
Noisy independent component analysis of auto-correlated components
We present a new method for the separation of superimposed, independent,
auto-correlated components from noisy multi-channel measurement. The presented
method simultaneously reconstructs and separates the components, taking all
channels into account and thereby increases the effective signal-to-noise ratio
considerably, allowing separations even in the high noise regime.
Characteristics of the measurement instruments can be included, allowing for
application in complex measurement situations. Independent posterior samples
can be provided, permitting error estimates on all desired quantities. Using
the concept of information field theory, the algorithm is not restricted to any
dimensionality of the underlying space or discretization scheme thereof
Stochastic determination of matrix determinants
Matrix determinants play an important role in data analysis, in particular
when Gaussian processes are involved. Due to currently exploding data volumes,
linear operations - matrices - acting on the data are often not accessible
directly but are only represented indirectly in form of a computer routine.
Such a routine implements the transformation a data vector undergoes under
matrix multiplication. While efficient probing routines to estimate a matrix's
diagonal or trace, based solely on such computationally affordable
matrix-vector multiplications, are well known and frequently used in signal
inference, there is no stochastic estimate for its determinant. We introduce a
probing method for the logarithm of a determinant of a linear operator. Our
method rests upon a reformulation of the log-determinant by an integral
representation and the transformation of the involved terms into stochastic
expressions. This stochastic determinant determination enables large-size
applications in Bayesian inference, in particular evidence calculations, model
comparison, and posterior determination.Comment: 8 pages, 5 figure
The Galactic Faraday depth sky revisited
The Galactic Faraday depth sky is a tracer for both the Galactic magnetic
field and the thermal electron distribution. It has been previously
reconstructed from polarimetric measurements of extra-galactic point sources.
Here, we improve on these works by using an updated inference algorithm as well
as by taking into account the free-free emission measure map from the Planck
survey. In the future, the data situation will improve drastically with the
next generation Faraday rotation measurements from SKA and its pathfinders.
Anticipating this, the aim of this paper is to update the map reconstruction
method with the latest development in imaging based on information field
theory. We demonstrate the validity of the new algorithm by applying it to the
Oppermann et al. (2012) data compilation and compare our results to the
previous map.\\ Despite using exactly the previous data set, a number of novel
findings are made: A non-parametric reconstruction of an overall amplitude
field resembles the free-free emission measure map of the Galaxy. Folding this
free-free map into the analysis allows for more detailed predictions. The joint
inference enables us to identify regions with deviations from the assumed
correlations between the free-free and Faraday data, thereby pointing us to
Galactic structures with distinguishably different physics. We e.g. find
evidence for an alignment of the magnetic field within the line of sights along
both directions of the Orion arm.Comment: 16 pages, 15 figure
Reply to "Comment on `Inference with minimal Gibbs free energy in information field theory'" by Iatsenko, Stefanovska and McClintock
We endorse the comment on our recent paper [En{\ss}lin and Weig, Phys. Rev. E
82, 051112 (2010)] by Iatsenko, Stefanovska and McClintock [Phys. Rev. E 85
033101 (2012)] and we try to clarify the origin of the apparent controversy on
two issues. The aim of the minimal Gibbs free energy approach to provide a
signal estimate is not affected by their Comment. However, if one wants to
extend the method to also infer the a posteriori signal uncertainty any
tempering of the posterior has to be undone at the end of the calculations, as
they correctly point out. Furthermore, a distinction is made here between
maximum entropy, the maximum entropy principle, and the so-called maximum
entropy method in imaging, hopefully clarifying further the second issue of
their Comment paper.Comment: 1 page, no figures, Reply to Comment pape
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