Superradiance has been an outstanding problem in quantum optics since Dicke introduced the concept of enhanced directional spontaneous emission by an ensemble of identical two-level atoms. The effect is based on the correlated collective Dicke states which turn out to be highly entangled. Here we show that enhanced directional emission of spontaneous radiation can be produced also with statistically independent incoherent sources, via the measurement of higher-order correlation functions of the emitted radiation. Our analysis is applicable to a wide variety of quantum emitters, like trapped atoms, ions, quantum dots, or nitrogen-vacancy centers, and is also valid for incoherent classical emitters. This is experimentally confirmed with up to eight statistically independent thermal light sources. The arrangement to measure the higher-order correlation functions corresponds to a generalized Hanbury Brown-Twiss setup, demonstrating that the two phenomena, superradiance and the Hanbury Brown-Twiss effect, stem from the same interference phenomenon.