Statistical inference in radio astronomy

This thesis unifies several studies, which all are dedicated to the
subject of statistical data analysis in radio astronomy and radio
astrophysics. Radio astronomy, like astronomy as a whole, has
undergone a remarkable development in the past twenty years in
introducing new instruments and technologies. New telescopes like
the upgraded VLA, LOFAR, or the SKA and its pathfinder missions
offer unprecedented sensitivities, previously uncharted frequency
domains and unmatched survey capabilities. Many of these have the
potential to significantly advance the science of radio
astrophysics and cosmology on all scales, from solar and stellar
physics, Galactic astrophysics and cosmic magnetic fields, to
Galaxy cluster astrophysics and signals from the epoch of
reionization. Since then, radio data analysis, calibration and
imaging techniques have entered a similar phase of new development
to push the boundaries and adapt the field to the new instruments
and scientific opportunities. This thesis contributes to these
greater developments in two specific subjects, radio
interferometric imaging and cosmic magnetic field statistics.
Throughout this study, different data analysis techniques are
presented and employed in various settings, but all can be
summarized under the broad term of statistical infer- ence. This
subject encompasses a huge variety of statistical techniques,
developed to solve problems in which deductions have to be made
from incomplete knowledge, data or measurements. This study focuses
especially on Bayesian inference methods that make use of a
subjective definition of probabilities, allowing for the expression
of probabilities and statistical knowledge prior to an actual
measurement. The thesis contains two different sets of application
for such techniques. First, situations where a complicated, and
generally ill-posed measurement problem can be approached by
assuming a statistical signal model prior to infer the desired
measured variable. Such a problem very often is met should the
measurement device take less data then needed to constrain all
degrees of freedom of the problem. The principal case investigated
in this thesis is the measurement problem of a radio
interferometer, which takes incomplete samples of the Fourier
transformed intensity of the radio emission in the sky, such that
it is impossible to exactly recover the signal. The new imaging
algorithm RESOLVE is presented, optimal for extended radio sources.
A first showcase demonstrates the performance of the new technique
on real data. Further, a new Bayesian approach to multi-frequency
radio interferometric imaging is presented and integrated into
RESOLVE. The second field of application are astrophysical
problems, in which the inherent stochas- tic nature of a physical
process demands a description, where properties of physical quanti-
ties can only be statistically estimated. Astrophysical plasmas for
instance are very often in a turbulent state, and thus governed by
statistical hydrodynamical laws. Two studies are presented that
show how properties of turbulent plasma magnetic fields can be
inferred from radio observations.