Goodness-of-fit analysis of radial velocity surveys

Using eigenmode expansion of the Mark III and SFI surveys of cosmological r adial velocities, a goodness-of-fit analysis is applied on a mode-by-mode b asis. This differential analysis complements the Bayesian maximum likelihoo d analysis that finds the most probable model given the data. Analyzing the surveys with their corresponding most likely models from the CMB-like fami ly of models, as well as with the currently popular Lambda CDM model, revea ls a systematic inconsistency of the data with these "best" models. There i s a systematic trend of the cumulative chi(2) to increase with the mode num ber (where the modes are sorted by decreasing order of the eigenvalues). Th is corresponds to a decrease of the chi(2) with the variance associated wit h a mode and hence with its effective scale. It follows that the differenti al analysis finds that on small (large) scales the global analysis of all t he modes "puts" less (more) power than actually required by the data. This observed trend might indicate one of the following: (1) the theoretical mod el (i.e., power spectrum) or the error model (or both) have an excess of po wer on large scales, (2) velocity bias, or (3) the velocity data suffers fr om systematic errors that have not yet been corrected.