Exploring the transient sky: From surveys to simulations

In this thesis I investigated transient sources, their detectability, and their rate.
I validated and integrated the source finder software used within the LOFAR Transients Pipeline. This is a key component of the pipeline as it extracts sources from images and measures their fluxes and locations.
I also performed a survey using LOFAR aimed at detecting transient sources. As no transients were detected, I focused on constraining the transient rate. I developed two new statistical methods that allow me to constrain it as a function of the flux of transients on a much larger interval than it was possible before, and, separately, for the first time, as a function of their durations.
I then developed simulations in order to constrain the transient rate for every combination of flux and duration of the transients for a given survey strategy. This method is valid for any transient source type as long as its light curve can be modeled and for every survey strategy at any wavelength. These simulations can help set up the best strategy to detect specific transient sources, and to analyse existing surveys to extract information on the transient rate for every combination of flux and duration of the transients.
Finally, I have used the simulations I developed in order to constrain the duty cycle of Low Mass X-ray Binaries. I have shown that when measuring this quantity with a survey, the extracted value can be substantially different from the real one depending on the survey setup.