AbstractThe large spectral bandwidth and wide field of view of the Australian SKA Pathfinder radio telescope will open up a completely new parameter space for large extragalactic HI surveys. Here we focus on identifying and parametrising HI absorption lines which occur in the line of sight towards strong radio continuum sources. We have developed a method for simultaneously finding and fitting HI absorption lines in radio data by using multi-nested sampling, a Bayesian Monte Carlo algorithm. The method is tested on a simulated ASKAP data cube, and is shown to be reliable at detecting absorption lines in low signal-to-noise data without the need to smooth or alter the data. Estimation of the local Bayesian evidence statistic provides a quantitative criterion for assigning significance to a detection and selecting between competing analytical line-profile models.