Goodness-of-Fit Analysis of Radial Velocities Surveys

Using eigenmode expansion of the Mark-3 and SFI surveys of cosmological radial velocities a goodness-of-fit analysis is applied on a mode-by-mode basis. This differential analysis complements theBayesian 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 Lambda-CDM model, reveals a systematic inconsistency of the data with these `best' models. There is a systematic trend of the cumulative chi^2 to increase with the mode number (where the modes are sorted by decreasing order of the eigenvalues). This corresponds to a decrease of the chi^2 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 followings: a. The theoretical model (i.e. power spectrum) or the error model (or both) have an excess of power on large scales; b. Velocity bias; c. The velocity data suffers from still uncorrected systematic errors.