Statistical inference in radio astronomy
This thesis unifies several studies, which all are dedicated to the subject of statistical data\nanalysis in radio astronomy and radio astrophysics. \n\nRadio 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. \n\nMany of these have the potential to significantly advance the science of radio astrophysics and cosmology on all scales, from solar and stellar\nphysics, Galactic astrophysics and cosmic magnetic fields, to Galaxy cluster astrophysics\nand signals from the epoch of reionization.\n\nSince 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. \n\nThis thesis contributes to these greater developments in two specific subjects, radio interferometric imaging and cosmic magnetic field statistics. \n\nThroughout this study, different data analysis techniques are presented and employed\nin various settings, but all can be summarized under the broad term of statistical infer-\nence. This subject encompasses a huge variety of statistical techniques, developed to solve\nproblems 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.\n\nThe thesis contains two different sets of application for such techniques. First, situations\nwhere a complicated, and generally ill-posed measurement problem can be approached by\nassuming a statistical signal model prior to infer the desired measured variable. Such\na problem very often is met should the measurement device take less data then needed\nto constrain all degrees of freedom of the problem. The principal case investigated in\nthis thesis is the measurement problem of a radio interferometer, which takes incomplete\nsamples of the Fourier transformed intensity of the radio emission in the sky, such that it is\nimpossible to exactly recover the signal. The new imaging algorithm RESOLVE is presented,\noptimal for extended radio sources. A first showcase demonstrates the performance of the\nnew technique on real data. Further, a new Bayesian approach to multi-frequency radio\ninterferometric imaging is presented and integrated into RESOLVE.\n\nThe second field of application are astrophysical problems, in which the inherent stochas-\ntic nature of a physical process demands a description, where properties of physical quanti-\nties 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.