4.3. Velocity versus Density
The peculiar velocity data is compared with the distribution of galaxies in redshift space to obtain . The comparison can be performed either at the density level (e.g., velocity-inferred mass density a la POTENT versus real-space density of galaxies as extracted from redshift surveys ), or at the velocity level , , or simultaneously  (reviews: , ).
New developments: The methods are being improved to better take into account the random and systematic errors. The comparison is done in several different ways.
Pro: Some of the comparison methods allow a direct mapping of the biasing field. Certain versions of the method are straightforward to implement.
Con: It is hard to impose the same effective smoothing on the two data sets. This may cause a bias in the estimate of , and a complication due to possible scale dependence in the biasing scheme. The estimation is contaminated by the possible complexity of the biasing scheme. Each method may actually refer to a somewhat different . It is hard to distinguish nonlinear biasing from nonlinear gravitational effects.
Current Results: For IRAS galaxies, the current best estimates vary in the range 0.5 I 1.2, depending on the method, the volume used, the weighting of the different data, the smoothing scale, etc. The comparisons at the density level  tend to yield higher estimates than the comparisons at the velocity level . One of the velocity comparisons indicates a possible inconsistency in the data at large distances . The value of I seems to grow with smoothing scale, from I ~ 0.5 - 0.6 at Gaussian smoothing scales of 3 - 6 h-1Mpc ,  to I ~ 1 on scales of ~ 12 h-1Mpc , . The estimates for optical galaxies indicate a biasing parameter that is typically larger by ~ 30%.