Efficient and rigorous source finding techniques are needed for the upcoming large data sets from telescopes like MeerKAT, LSST and the SKA. Most of the current source-finding algorithms lack full statistical rigor. Typically these algorithms use some form of thresholding to find sources, which leads to contamination and missed sources. Ideally we would like to use all the available information when performing source detection, including any prior knowledge we may have. Bayesian statistics is the obvious approach as it allows precise statistical interrogations of the data and the inclusion of all available information. In this thesis, we implement nested sampling and Monte Carlo Markov Chain (MCMC) techniques to develop a new Bayesian source finding technique called FireFly. FireFly employs a technique of switching ‘on’ and ‘off’ sources during sampling to deal with the fact that we don’t know how many true sources are present. It therefore tackles one of the critical questions in source finding, which is estimating the number of real sources in the image. We compare FireFly against a Bayesian evidence-based search method and show on simulated astronomical images that FireFly outperforms the evidence-based approach. We further investigate two implementations of FireFly: the first with nested sampling and the second with MCMC. Our results show that MCMC FireFly has better computational scaling than the nested sampling version FireFly but the nested sampling version of FireFly appears to perform somewhat better than MCMC FireFly. Future work should examine how best to quantify FireFly performance and extend the formalism developed here to deal with multiwavelength data.

Beyond gravitational evidence for dark matter, a set of search techniques are employed in the present thesis within the particle dark matter paradigm. Under the possibility of dark matter annihilating into particles of the Standard Model of Particle Physics, we study the products of annihilation with cosmic-ray detectors, such as AMS, Fermi-LAT and PAMELA, and radio telescopes, such as the SKA. In this work, we focus on the positron fraction measured in the Solar System due to dark matter annihilating in the dark matter galactic halo, but also on radio signals from the Milky Way and dwarf spheroidal galaxies. Our main purpose is to constrain the dark matter parameter space under the light of the latest experimental data for cosmic-rays and the new sensitivities reached in radio astronomy. Furthermore, we discuss some of the most promising locations and synchrotron frequencies to search for dark matter with masses around the TeV scale. The analysis presented in this thesis lies in setting constraints on modelindependent dark matter. However, some specific dark matter candidates in the context of extra-dimensional theories are considered as well. Indeed, brane fluctuations, dubbed branons, are new degrees of freedom appearing in flexible brane-world models. These new fields behave as standard weakly interacting massive particles with a significant associated thermal relic density and would explain dark matter observational features.