We present a preliminary analysis of the sensitivity of Anglo-Australian Planet Search data to the orbital parameters of extrasolar planets . To do so , we have developed new tools for the automatic analysis of large-scale simulations of Doppler velocity planet search data . One of these tools is the 2-Dimensional Keplerian Lomb-Scargle periodogram , that enables the straightforward detection of exoplanets with high eccentricities ( something the standard Lomb-Scargle periodogram routinely fails to do ) . We used this technique to re-determine the orbital parameters of HD 20782b , with one of the highest known exoplanet eccentricities ( e = 0.97 \pm 0.01 ) . We also derive a set of detection criteria that do not depend on the distribution functions of fitted Keplerian orbital parameters ( which we show are non-Gaussian with pronounced , extended wings ) . Using these tools , we examine the selection functions in orbital period , eccentricity and planet mass of Anglo-Australian Planet Search data for three planets with large-scale Monte Carlo-like simulations . We find that the detectability of exoplanets declines at high eccentricities . However , we also find that exoplanet detectability is a strong function of epoch-to-epoch data quality , number of observations , and period sampling . This strongly suggests that simple parametrisations of the detectability of exoplanets based on “ whole-of-survey ” metrics may not be accurate . We have derived empirical relationships between the uncertainty estimates for orbital parameters that are derived from least-squares Keplerian fits to our simulations , and the true 99 % limits for the errors in those parameters , which are larger than equivalent Gaussian limits by factors of 5-10 . We quantify the rate at which false positives are made by our detection criteria , and find that they do not significantly affect our final conclusions . And finally , we find that there is a bias against measuring near-zero eccentricities , which becomes more significant in small , or low signal-to-noise-ratio , data sets .