The HI luminosity function from 'blind' surveys

Recent neutral hydrogen (HI) surveys have detected enough sources to make initial predictions of the extragalactic HI luminosity function. These surveys provide useful pointers for the Parkes Multibeam Survey, highlighting various advantages and disadvantages of different observing and analysis procedures. The newest surveys are also large enough to permit some statistical tests of their completeness. The detection rates clearly fall short of what would be expected based on a simple propagation of errors, suggesting the need for further development of detection software. I suggest several procedures for determining the effective sensitivity of HI surveys. Applied to two recent Arecibo surveys, these suggest that the HI luminosity function may be much steeper than its optical counterpart, and that the Parkes surveys may detect a large number of low-mass sources.