Goodness-of-fit analysis of radial velocity surveys

Using eigenmode expansion of the Mark III and SFI surveys of cosmological radial velocities, a goodness-of-fit analysis is applied on a mode-by-mode basis. This differential analysis complements the Bayesian maximum likelihood analysis that finds the most probable model given the data. Analyzing the surveys with their corresponding most likely models from the CMB-like family of models, as well as with the currently popular ACDM model, reveals a systematic inconsistency of the data with these "best" models. There is a systematic trend of the cumulative χ² to increase with the mode number (where the modes are sorted by decreasing order of the eigenvalues). This corresponds to a decrease of the χ₂ with the variance associated with a mode and hence with its effective scale. It follows that the differential analysis finds that on small (large) scales the global analysis of all the modes "puts" less (more) power than actually required by the data. This observed trend might indicate one of the following: (1) the theoretical model (i.e., power spectrum) or the error model (or both) have an excess of power on large scales, (2) velocity bias, or (3) the velocity data suffers from systematic errors that have not yet been corrected.